Bibliographic Cross-References
|
|
Metamath Proof Explorer Bibliographic Cross-References |
|
| Mirrors > Home > MPE Home > Bibliographic Cross-References | ||
| Color key: |
Metamath Proof Explorer |
Hilbert Space Explorer |
 User Mathboxes |
| Bibliographic Reference | Description | Metamath Proof Explorer Page(s) |
|---|---|---|
| [Adamek] p. 21 | Definition 3.1 | df-cat 17871 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17871 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18280 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17892 0funcg 50405 df-termc 50813 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 50893 prsthinc 50804 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 50921 df-mndtc 50921 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 50917 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17915 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 50909 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 50934 oppgoppchom 50933 oppgoppcid 50935 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17985 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17973 invisoinvl 17994 |
| [Adamek] p. 28 | Example 3.13 | idinv 17993 idiso 17992 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17978 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17952 df-iso 17953 dfiso2 17976 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17959 |
| [Adamek] p. 29 | Remark 3.16 | cicer 18010 cicerALT 50365 |
| [Adamek] p. 29 | Definition 3.15 | cic 18003 df-cic 18000 |
| [Adamek] p. 29 | Definition 3.17 | df-func 18062 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17974 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17975 isoco 17981 |
| [Adamek] p. 30 | Remark 3.19 | df-func 18062 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 18085 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 50631 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 18078 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 50917 discthing 50801 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 50758 prsthinc 50804 thincciso 50793 thincciso2 50795 thincciso3 50796 thinccisod 50794 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 50921 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 18092 cofucla 50416 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 50483 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18315 catcisoi 50740 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18370 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 18111 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 18110 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18370 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 18135 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 18141 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 18140 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18355 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18355 |
| [Adamek] p. 39 | Remark 3.42 | 2oppf 50453 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 50444 funcoppc 18079 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18303 elcatchom 50737 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 18129 fthoppf 50485 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 18128 fulloppf 50484 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18312 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 50405 df-catc 18303 |
| [Adamek] p. 45 | Exercise 3G | incat 50944 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 50947 nelsubc3 50390 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 50472 imasubc2 50473 imasubc3 50477 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 18042 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 18043 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 50390 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 18054 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 18016 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 50481 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 50480 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 50482 ressffth 18144 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 50945 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 18150 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 18171 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 18175 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 18151 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 18177 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 50405 df-inito 18188 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 50405 df-termc 50813 initc 50411 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21815 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 18189 oppctermo 50563 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 18216 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 18220 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 50564 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 18190 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21816 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 18223 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17951 |
| [Adamek] p. 107 | Example 7.20(7) | thincinv 50809 |
| [Adamek] p. 108 | Example 7.25(4) | thincsect2 50808 |
| [Adamek] p. 110 | Example 7.33(9) | thincmon 50773 |
| [Adamek] p. 110 | Proposition 7.35 | sectmon 17986 |
| [Adamek] p. 112 | Proposition 7.42 | sectepi 17988 |
| [Adamek] p. 185 | Section 10.67 | updjud 10042 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 51033 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 51033 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 51033 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 51034 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 51034 |
| [Adamek] p. 478 | Item Rng | df-ringc 20928 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 49865 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 49887 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14743 df-pfx 14849 df-substr 14817 df-word 14686 lencl 14705 wrd0 14711 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 25057 df-nmoo 31377 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32785 hmopidmchi 32783 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32833 pjcmul2i 32834 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 32550 unoplin 32552 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 32551 unopadj2 32570 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 32645 lnopunii 32644 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32718 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 28343 |
| [Alling] p. 184 | Axiom B | bdayfo 28064 |
| [Alling] p. 184 | Axiom O | ltsso 28063 |
| [Alling] p. 184 | Axiom SD | nodense 28079 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 28171 |
| [Alling] p. 185 | Theorem | conway 28195 |
| [Alling] p. 185 | Axiom FE | noeta 28130 |
| [Alling] p. 186 | Theorem 4 | lesrec 28215 lesrecd 28216 |
| [Alling], p. 2 | Definition | rp-brsslt 44616 |
| [Alling], p. 3 | Note | nla0001 44619 nla0002 44617 nla0003 44618 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11521 addcan2d 11541 addcan2i 11531 addcand 11540 addcani 11530 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11574 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11633 negsubd 11702 negsubi 11663 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11635 negnegd 11687 negnegi 11655 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11776 subdid 11799 subdii 11792 subdir 11777 subdird 11800 subdiri 11793 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11516 mul01d 11536 mul01i 11527 mul02 11515 mul02d 11535 mul02i 11526 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11980 mulcan2d 11977 mulcand 11976 mulcani 11982 |
| [Apostol] p. 18 | Theorem I.8 | receu 11988 xreceu 33558 |
| [Apostol] p. 18 | Theorem I.9 | divrec 12017 divrecd 12123 divreci 12089 divreczi 12082 |
| [Apostol] p. 18 | Theorem I.10 | recrec 12041 recreci 12076 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11983 mul0ord 11991 mul0ori 11990 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11782 mul2negd 11798 mul2negi 11791 mulneg1 11779 mulneg1d 11796 mulneg1i 11789 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 12059 divadddivd 12164 divadddivi 12106 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 12044 divmuldivd 12161 divmuldivi 12104 rdivmuldivd 20673 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 12045 divdivdivd 12167 divdivdivi 12107 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 13171 rpaddcld 13206 rpmulcl 13172 rpmulcld 13207 |
| [Apostol] p. 20 | Axiom 8 | rpneg 13181 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 13184 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11463 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11936 ltadd1dd 11954 ltadd1i 11897 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12194 ltmul1a 12193 ltmul1i 12262 ltmul1ii 12272 ltmul2 12195 ltmul2d 13233 ltmul2dd 13247 ltmul2i 12265 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11863 msqgt0d 11910 msqgt0i 11880 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11865 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11849 lt0neg1d 11912 ltneg 11843 ltnegd 11921 ltnegi 11887 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11828 lt2addd 11966 lt2addi 11905 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 13148 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12190 recgt0d 12278 recgt0i 12249 recgt0ii 12250 |
| [Apostol] p. 22 | Definition of integers | df-z 12721 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12376 |
| [Apostol] p. 22 | Definition of rationals | df-q 13103 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9473 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12629 |
| [Apostol] p. 26 | Theorem I.29 | arch 12630 archd 46382 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12829 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12631 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 13101 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 13100 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13356 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16538 zneo 12809 zneoALTV 48972 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 27088 msqsqrtd 15639 resqrtth 15451 sqrtth 15561 sqrtthi 15567 sqsqrtd 15638 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12365 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 13067 |
| [Apostol] p. 361 | Remark | crreczi 14399 |
| [Apostol] p. 363 | Remark | absgt0i 15596 |
| [Apostol] p. 363 | Example | abssubd 15652 abssubi 15600 |
| [ApostolNT] p. 7 | Remark | fmtno0 48830 fmtno1 48831 fmtno2 48840 fmtno3 48841 fmtno4 48842 fmtno5fac 48872 fmtnofz04prm 48867 |
| [ApostolNT] p. 7 | Definition | df-fmtno 48818 |
| [ApostolNT] p. 8 | Definition | df-ppi 27457 |
| [ApostolNT] p. 14 | Definition | df-dvds 16452 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16468 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16493 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16488 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16481 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16483 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16469 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16470 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16475 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16510 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16512 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16514 |
| [ApostolNT] p. 15 | Definition | df-gcd 16694 dfgcd2 16748 |
| [ApostolNT] p. 16 | Definition | isprm2 16886 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16857 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 17122 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16714 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16749 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16751 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16730 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16721 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16916 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16918 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 17135 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 17129 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16602 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16791 |
| [ApostolNT] p. 24 | Definition | df-mu 27458 |
| [ApostolNT] p. 25 | Definition | df-phi 16972 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27548 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16997 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16982 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16986 |
| [ApostolNT] p. 32 | Definition | df-vma 27455 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27550 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27573 |
| [ApostolNT] p. 38 | Remark | df-sgm 27459 |
| [ApostolNT] p. 38 | Definition | df-sgm 27459 |
| [ApostolNT] p. 75 | Definition | df-chp 27456 df-cht 27454 |
| [ApostolNT] p. 104 | Definition | congr 16868 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16455 |
| [ApostolNT] p. 106 | Definition | moddvds 16462 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16545 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16546 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 14055 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 14095 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14409 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16487 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16871 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17281 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16873 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16989 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 17008 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16990 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27429 |
| [ApostolNT] p. 179 | Definition | df-lgs 27652 lgsprme0 27696 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27697 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27673 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27688 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27745 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27764 2lgsoddprm 27773 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27731 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27740 |
| [ApostolNT] p. 188 | Definition | df-lgs 27652 lgs1 27698 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27689 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27691 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27699 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27700 |
| [Baer] p. 40 | Property (b) | mapdord 42887 |
| [Baer] p. 40 | Property (c) | mapd11 42888 |
| [Baer] p. 40 | Property (e) | mapdin 42911 mapdlsm 42913 |
| [Baer] p. 40 | Property (f) | mapd0 42914 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 42874 mapd1o 42897 |
| [Baer] p. 41 | Property (g) | mapdat 42916 |
| [Baer] p. 44 | Part (1) | mapdpg 42955 |
| [Baer] p. 45 | Part (2) | hdmap1eq 43050 mapdheq 42977 mapdheq2 42978 mapdheq2biN 42979 |
| [Baer] p. 45 | Part (3) | baerlem3 42962 |
| [Baer] p. 46 | Part (4) | mapdheq4 42981 mapdheq4lem 42980 |
| [Baer] p. 46 | Part (5) | baerlem5a 42963 baerlem5abmN 42967 baerlem5amN 42965 baerlem5b 42964 baerlem5bmN 42966 |
| [Baer] p. 47 | Part (6) | hdmap1l6 43070 hdmap1l6a 43058 hdmap1l6e 43063 hdmap1l6f 43064 hdmap1l6g 43065 hdmap1l6lem1 43056 hdmap1l6lem2 43057 mapdh6N 42996 mapdh6aN 42984 mapdh6eN 42989 mapdh6fN 42990 mapdh6gN 42991 mapdh6lem1N 42982 mapdh6lem2N 42983 |
| [Baer] p. 48 | Part 9 | hdmapval 43077 |
| [Baer] p. 48 | Part 10 | hdmap10 43089 |
| [Baer] p. 48 | Part 11 | hdmapadd 43092 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 43066 mapdh6hN 42992 |
| [Baer] p. 48 | Part (7) | mapdh75cN 43002 mapdh75d 43003 mapdh75e 43001 mapdh75fN 43004 mapdh7cN 42998 mapdh7dN 42999 mapdh7eN 42997 mapdh7fN 43000 |
| [Baer] p. 48 | Part (8) | mapdh8 43037 mapdh8a 43024 mapdh8aa 43025 mapdh8ab 43026 mapdh8ac 43027 mapdh8ad 43028 mapdh8b 43029 mapdh8c 43030 mapdh8d 43032 mapdh8d0N 43031 mapdh8e 43033 mapdh8g 43034 mapdh8i 43035 mapdh8j 43036 |
| [Baer] p. 48 | Part (9) | mapdh9a 43038 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 43018 |
| [Baer] p. 49 | Part 12 | hdmap11 43097 hdmapeq0 43093 hdmapf1oN 43114 hdmapneg 43095 hdmaprnN 43113 hdmaprnlem1N 43098 hdmaprnlem3N 43099 hdmaprnlem3uN 43100 hdmaprnlem4N 43102 hdmaprnlem6N 43103 hdmaprnlem7N 43104 hdmaprnlem8N 43105 hdmaprnlem9N 43106 hdmapsub 43096 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 43117 hdmap14lem10 43126 hdmap14lem1a 43115 hdmap14lem2N 43118 hdmap14lem2a 43116 hdmap14lem3 43119 hdmap14lem8 43124 hdmap14lem9 43125 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 43127 hdmap14lem12 43128 hdmap14lem13 43129 hdmap14lem14 43130 hdmap14lem15 43131 hgmapval 43136 |
| [Baer] p. 50 | Part 15 | hgmapadd 43143 hgmapmul 43144 hgmaprnlem2N 43146 hgmapvs 43140 |
| [Baer] p. 50 | Part 16 | hgmaprnN 43150 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 43166 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 43167 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 43168 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 43169 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 43171 hgmapvv 43175 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 43170 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 43172 |
| [Baer] p. 111 | Line 15 | hdmapg 43179 hdmapglem7 43178 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 27089 2irrexpqALT 27158 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 24 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2597 |
| [BellMachover] p. 460 | Notation | df-mo 2567 |
| [BellMachover] p. 460 | Definition | mo3 2592 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2735 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2739 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5242 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5252 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 38170 sepex 5258 |
| [BellMachover] p. 466 | Problem | axpow2 5333 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5334 |
| [BellMachover] p. 466 | Axiom Union | axun2 7777 |
| [BellMachover] p. 468 | Definition | df-ord 6383 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6398 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6405 onelond 37126 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6400 |
| [BellMachover] p. 471 | Definition of N | df-om 7902 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7839 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6385 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9670 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7917 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9795 |
| [BellMachover] p. 478 | Definition | rankval2 9854 rankval2b 9862 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9816 r1ord3g 9813 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9617 |
| [BellMachover] p. 488 | Axiom AC | ac5 10582 dfac4 10228 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10216 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 40568 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32985 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 33027 chirredi 33026 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 33015 |
| [Beran] p. 3 | Definition of join | sshjval3 31986 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 32248 cmcm2i 32225 cmcm2ii 32230 cmt2N 40499 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 32249 lecmi 32234 lecmii 32235 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 32223 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 32252 cm2ji 32257 cm2mi 32258 |
| [Beran] p. 95 | Definition | df-sh 31839 issh2 31841 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31718 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31731 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31722 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 32460 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 32462 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 32461 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 32463 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31714 his1i 31732 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31715 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31716 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31717 |
| [Beran] p. 96 | Definition of norm | df-hnorm 31600 dfhnorm2 31754 normval 31756 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31816 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 31605 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31873 |
| [Beran] p. 96 | Definition of converge | df-hlim 31604 hlimi 31820 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31765 norm-i 31761 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31769 norm-ii 31770 normlem0 31741 normlem1 31742 normlem2 31743 normlem3 31744 normlem4 31745 normlem5 31746 normlem6 31747 normlem7 31748 normlem7tALT 31751 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31771 norm-iii 31772 |
| [Beran] p. 98 | Remark 3.4 | bcs 31813 bcsiALT 31811 bcsiHIL 31812 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31753 normpar 31787 normpari 31786 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31778 normpyth 31777 normpythi 31774 |
| [Beran] p. 99 | Remark | lnfn0 32679 lnfn0i 32674 lnop0 32598 lnop0i 32602 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32658 nmcfnex 32685 nmcfnexi 32683 nmcopex 32661 nmcopexi 32659 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32686 nmcfnlbi 32684 nmcoplb 32662 nmcoplbi 32660 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32688 lnfnconi 32687 lnopcon 32667 lnopconi 32666 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31788 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31785 norm3adifii 31780 norm3dif 31782 norm3difi 31779 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31933 pjhth 32025 pjhtheu 32026 pjpjhth 32057 pjpjhthi 32058 pjth 25790 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 32038 ococi 32037 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32693 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32694 riesz4 32696 riesz4i 32695 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32711 cnlnadjeu 32710 cnlnadjeui 32709 cnlnadji 32708 cnlnadjlem1 32699 nmopadjlei 32720 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32723 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32722 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32724 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 32568 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32734 nmopcoadji 32733 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32725 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32735 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32732 pjadj2coi 32836 pjadjcoi 32793 |
| [Beran] p. 107 | Definition | df-ch 31853 isch2 31855 |
| [Beran] p. 107 | Remark 3.12 | choccl 31938 isch3 31873 occl 31936 ocsh 31915 shoccl 31937 shocsh 31916 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 32040 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31964 |
| [Beran] p. 109 | Property (i) | pjadj2 32819 pjadj3 32820 pjadji 32317 pjadjii 32306 |
| [Beran] p. 109 | Property (ii) | pjidmco 32813 pjidmcoi 32809 pjidmi 32305 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32805 |
| [Beran] p. 111 | Remark | ho0val 32382 pjch1 32302 |
| [Beran] p. 111 | Definition | df-hfmul 32366 df-hfsum 32365 df-hodif 32364 df-homul 32363 df-hosum 32362 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 32303 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 32326 pjchi 32064 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 32071 pjoc2i 32070 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 32312 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32797 pjssmii 32313 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32796 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32795 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32800 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32798 pjssge0ii 32314 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32799 pjdifnormii 32315 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1809 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1807 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1810 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1805 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34994 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 35002 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 35000 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 35004 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 35024 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 35055 df-sitm 35033 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 35055 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 35032 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29656 isuhgrop 29678 isusgrop 29773 isuspgrop 29772 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 49164 df-subgr 29879 uhgrspan1 29914 uhgrspansubgr 29902 |
| [Bollobas] p. 3 | Definition | df-gric 49184 gricuspgr 49221 isuspgrim 49199 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 30065 df-clnbgr 49122 df-cusgr 30023 df-nbgr 29944 fusgrmaxsize 30075 |
| [Bollobas] p. 4 | Definition | df-upwlks 49437 df-wlks 30210 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 30161 finsumvtxdgeven 30163 fusgr1th 30162 fusgrvtxdgonume 30165 vtxdgoddnumeven 30164 |
| [Bollobas] p. 5 | Notation | df-pths 30329 |
| [Bollobas] p. 5 | Definition | df-crcts 30403 df-cycls 30404 df-trls 30305 df-wlkson 30211 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29667 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 49502 df-cllaw 49488 df-mgm 18845 df-mgm2 49521 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 49503 df-asslaw 49490 df-sgrp 18937 df-sgrp2 49523 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 49522 df-comlaw 49489 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18953 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33657 mndlactf1o 33661 mndractf1 33659 mndractf1o 33662 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20491 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20405 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 34335 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 34339 assarrginv 34338 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 34380 fldextrspunfld 34378 fldextrspunlem1 34377 fldextrspunlem2 34379 fldextrspunlsp 34376 fldextrspunlsplem 34375 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 34139 dfufd2 34152 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7318 fcofo 7319 |
| [BourbakiTop1] p. | Remark | xnegmnf 13367 xnegpnf 13366 |
| [BourbakiTop1] p. | Remark | rexneg 13368 |
| [BourbakiTop1] p. | Remark 3 | ust0 24569 ustfilxp 24562 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24439 |
| [BourbakiTop1] p. | Criterion | ishmeo 24108 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24632 iducn 24631 snfil 24213 |
| [BourbakiTop1] p. | Example 2 | neifil 24229 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 24416 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24652 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 34659 |
| [BourbakiTop1] p. | Paragraph 3 | infil 24212 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24624 df-ust 24550 filintn0 24210 filn0 24211 istgp 24426 ucnprima 24630 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24635 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24646 df-usp 24606 df-utop 24580 trust 24578 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 34558 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23464 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23617 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24555 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24558 |
| [BourbakiTop1] p. | Property V_ii | innei 23473 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23481 neissex 23475 |
| [BourbakiTop1] p. | Proposition 1 | neips 23461 neiss 23457 ucncn 24633 ustund 24571 ustuqtop 24595 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23615 neiptopreu 23481 utop2nei 24599 utop3cls 24600 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24640 uspreg 24622 utopreg 24601 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 24040 imasncls 24041 imasnopn 24039 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 24349 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24557 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24559 |
| [BourbakiTop1] p. | Property V_iii | elnei 23459 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24651 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24556 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24560 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23735 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 24195 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 23242 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 34555 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 47277 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 47279 stoweid 47278 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 47216 stoweidlem10 47225 stoweidlem14 47229 stoweidlem15 47230 stoweidlem35 47250 stoweidlem36 47251 stoweidlem37 47252 stoweidlem38 47253 stoweidlem40 47255 stoweidlem41 47256 stoweidlem43 47258 stoweidlem44 47259 stoweidlem46 47261 stoweidlem5 47220 stoweidlem50 47265 stoweidlem52 47267 stoweidlem53 47268 stoweidlem55 47270 stoweidlem56 47271 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 47238 stoweidlem24 47239 stoweidlem27 47242 stoweidlem28 47243 stoweidlem30 47245 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 47249 stoweidlem59 47274 stoweidlem60 47275 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 47260 stoweidlem49 47264 stoweidlem7 47222 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 47246 stoweidlem39 47254 stoweidlem42 47257 stoweidlem48 47263 stoweidlem51 47266 stoweidlem54 47269 stoweidlem57 47272 stoweidlem58 47273 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 47240 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 47232 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 47226 stoweidlem13 47228 stoweidlem26 47241 stoweidlem61 47276 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 47233 |
| [Bruck] p. 1 | Section I.1 | df-clintop 49502 df-mgm 18845 df-mgm2 49521 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18937 df-sgrp2 49523 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 19278 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5190 |
| [Church] p. 129 | Section II.24 | df-ifp 1079 dfifp2 1080 |
| [Clemente] p. 10 | Definition IT | natded 31034 |
| [Clemente] p. 10 | Definition I` `m,n | natded 31034 |
| [Clemente] p. 11 | Definition E=>m,n | natded 31034 |
| [Clemente] p. 11 | Definition I=>m,n | natded 31034 |
| [Clemente] p. 11 | Definition E` `(1) | natded 31034 |
| [Clemente] p. 11 | Definition E` `(2) | natded 31034 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 31034 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 31034 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 31034 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 31034 |
| [Clemente] p. 14 | Proof 5.11 | natded 31034 |
| [Clemente] p. 14 | Definition E` `n | natded 31034 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 31036 ex-natded5.2 31035 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 31039 ex-natded5.3 31038 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 31041 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 31043 ex-natded5.7 31042 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 31045 ex-natded5.8 31044 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 31047 ex-natded5.13 31046 |
| [Clemente] p. 32 | Definition I` `n | natded 31034 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 31034 |
| [Clemente] p. 32 | Definition E` `n,t | natded 31034 |
| [Clemente] p. 32 | Definition I` `n,t | natded 31034 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 31048 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 31049 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 31051 ex-natded9.26 31050 |
| [Cohen] p. 301 | Remark | relogoprlem 26949 |
| [Cohen] p. 301 | Property 2 | relogmul 26950 relogmuld 26983 |
| [Cohen] p. 301 | Property 3 | relogdiv 26951 relogdivd 26984 |
| [Cohen] p. 301 | Property 4 | relogexp 26954 |
| [Cohen] p. 301 | Property 1a | log1 26943 |
| [Cohen] p. 301 | Property 1b | loge 26944 |
| [Cohen4] p. 348 | Observation | relogbcxpb 27145 |
| [Cohen4] p. 349 | Property | relogbf 27149 |
| [Cohen4] p. 352 | Definition | elogb 27128 |
| [Cohen4] p. 361 | Property 2 | relogbmul 27135 |
| [Cohen4] p. 361 | Property 3 | logbrec 27140 relogbdiv 27137 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 27133 |
| [Cohen4] p. 361 | Property 6 | relogbexp 27138 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 27126 |
| [Cohen4] p. 361 | Property 1(b) | logb1 27127 |
| [Cohen4] p. 367 | Property | logbchbase 27129 |
| [Cohen4] p. 377 | Property 2 | logblt 27142 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34987 sxbrsigalem4 34989 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18760 acsinfd 18759 acsinfdimd 18761 acsmap2d 18758 acsmapd 18757 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34992 |
| [Connell] p. 57 | Definition | df-scmat 22836 df-scmatalt 49716 |
| [Conway] p. 4 | Definition | lesrec 28215 lesrecd 28216 |
| [Conway] p. 5 | Definition | addsval 28378 addsval2 28379 df-adds 28376 df-muls 28523 df-negs 28437 |
| [Conway] p. 7 | Theorem | 0lt1s 28228 |
| [Conway] p. 12 | Theorem 12 | pw2cut2 28878 |
| [Conway] p. 16 | Theorem 0(i) | sltsright 28277 |
| [Conway] p. 16 | Theorem 0(ii) | sltsleft 28276 |
| [Conway] p. 16 | Theorem 0(iii) | lesid 28154 |
| [Conway] p. 17 | Theorem 3 | addsass 28421 addsassd 28422 addscom 28382 addscomd 28383 addsrid 28380 addsridd 28381 |
| [Conway] p. 17 | Definition | df-0s 28223 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 28460 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 28457 negsidd 28458 |
| [Conway] p. 18 | Theorem 5 | leadds1 28405 leadds1d 28411 |
| [Conway] p. 18 | Definition | df-1s 28224 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 28452 negscld 28453 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 28396 |
| [Conway] p. 19 | Note | mulsunif2 28586 |
| [Conway] p. 19 | Theorem 7 | addsdi 28571 addsdid 28572 addsdird 28573 mulnegs1d 28576 mulnegs2d 28577 mulsass 28582 mulsassd 28583 mulscom 28555 mulscomd 28556 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28550 mulscld 28551 |
| [Conway] p. 19 | Theorem 8(iii) | lemulsd 28554 ltmuls 28552 ltmulsd 28553 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28560 mulsgt0d 28561 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28634 |
| [Conway] p. 23 | Theorem 11 | eqcuts3 28220 |
| [Conway] p. 24 | Definition | df-reno 28906 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28915 remulscl 28918 renegscl 28914 |
| [Conway] p. 27 | Definition | df-ons 28668 elons2 28674 |
| [Conway] p. 27 | Theorem 14 | ltonsex 28678 |
| [Conway] p. 28 | Theorem 15 | oncutlt 28680 onswe 28688 |
| [Conway] p. 29 | Remark | madebday 28316 newbday 28318 oldbday 28317 |
| [Conway] p. 29 | Definition | df-made 28243 df-new 28245 df-old 28244 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 14028 |
| [Crawley] p. 1 | Definition of poset | df-poset 18516 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 40635 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 41439 dalaw 41135 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 43210 |
| [Crawley] p. 111 | Definition of set W | df-watsN 41239 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 41355 df-ldil 41353 isldil 41359 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 41354 df-trnN 41356 isltrn 41368 ltrnu 41370 |
| [Crawley] p. 112 | Lemma A | cdlema1N 41040 cdlema2N 41041 exatleN 40653 |
| [Crawley] p. 112 | Lemma B | 1cvrat 40725 cdlemb 41043 cdlemb2 41290 cdlemb3 41855 idltrn 41399 l1cvat 40304 lhpat 41292 lhpat2 41294 lshpat 40305 ltrnel 41388 ltrnmw 41400 |
| [Crawley] p. 112 | Lemma C | cdlemc1 41440 cdlemc2 41441 ltrnnidn 41423 trlat 41418 trljat1 41415 trljat2 41416 trljat3 41417 trlne 41434 trlnidat 41422 trlnle 41435 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 41240 |
| [Crawley] p. 113 | Lemma C | cdlemc 41446 cdlemc3 41442 cdlemc4 41443 |
| [Crawley] p. 113 | Lemma D | cdlemd 41456 cdlemd1 41447 cdlemd2 41448 cdlemd3 41449 cdlemd4 41450 cdlemd5 41451 cdlemd6 41452 cdlemd7 41453 cdlemd8 41454 cdlemd9 41455 cdleme31sde 41634 cdleme31se 41631 cdleme31se2 41632 cdleme31snd 41635 cdleme32a 41690 cdleme32b 41691 cdleme32c 41692 cdleme32d 41693 cdleme32e 41694 cdleme32f 41695 cdleme32fva 41686 cdleme32fva1 41687 cdleme32fvcl 41689 cdleme32le 41696 cdleme48fv 41748 cdleme4gfv 41756 cdleme50eq 41790 cdleme50f 41791 cdleme50f1 41792 cdleme50f1o 41795 cdleme50laut 41796 cdleme50ldil 41797 cdleme50lebi 41789 cdleme50rn 41794 cdleme50rnlem 41793 cdlemeg49le 41760 cdlemeg49lebilem 41788 |
| [Crawley] p. 113 | Lemma E | cdleme 41809 cdleme00a 41458 cdleme01N 41470 cdleme02N 41471 cdleme0a 41460 cdleme0aa 41459 cdleme0b 41461 cdleme0c 41462 cdleme0cp 41463 cdleme0cq 41464 cdleme0dN 41465 cdleme0e 41466 cdleme0ex1N 41472 cdleme0ex2N 41473 cdleme0fN 41467 cdleme0gN 41468 cdleme0moN 41474 cdleme1 41476 cdleme10 41503 cdleme10tN 41507 cdleme11 41519 cdleme11a 41509 cdleme11c 41510 cdleme11dN 41511 cdleme11e 41512 cdleme11fN 41513 cdleme11g 41514 cdleme11h 41515 cdleme11j 41516 cdleme11k 41517 cdleme11l 41518 cdleme12 41520 cdleme13 41521 cdleme14 41522 cdleme15 41527 cdleme15a 41523 cdleme15b 41524 cdleme15c 41525 cdleme15d 41526 cdleme16 41534 cdleme16aN 41508 cdleme16b 41528 cdleme16c 41529 cdleme16d 41530 cdleme16e 41531 cdleme16f 41532 cdleme16g 41533 cdleme19a 41552 cdleme19b 41553 cdleme19c 41554 cdleme19d 41555 cdleme19e 41556 cdleme19f 41557 cdleme1b 41475 cdleme2 41477 cdleme20aN 41558 cdleme20bN 41559 cdleme20c 41560 cdleme20d 41561 cdleme20e 41562 cdleme20f 41563 cdleme20g 41564 cdleme20h 41565 cdleme20i 41566 cdleme20j 41567 cdleme20k 41568 cdleme20l 41571 cdleme20l1 41569 cdleme20l2 41570 cdleme20m 41572 cdleme20y 41551 cdleme20zN 41550 cdleme21 41586 cdleme21d 41579 cdleme21e 41580 cdleme22a 41589 cdleme22aa 41588 cdleme22b 41590 cdleme22cN 41591 cdleme22d 41592 cdleme22e 41593 cdleme22eALTN 41594 cdleme22f 41595 cdleme22f2 41596 cdleme22g 41597 cdleme23a 41598 cdleme23b 41599 cdleme23c 41600 cdleme26e 41608 cdleme26eALTN 41610 cdleme26ee 41609 cdleme26f 41612 cdleme26f2 41614 cdleme26f2ALTN 41613 cdleme26fALTN 41611 cdleme27N 41618 cdleme27a 41616 cdleme27cl 41615 cdleme28c 41621 cdleme3 41486 cdleme30a 41627 cdleme31fv 41639 cdleme31fv1 41640 cdleme31fv1s 41641 cdleme31fv2 41642 cdleme31id 41643 cdleme31sc 41633 cdleme31sdnN 41636 cdleme31sn 41629 cdleme31sn1 41630 cdleme31sn1c 41637 cdleme31sn2 41638 cdleme31so 41628 cdleme35a 41697 cdleme35b 41699 cdleme35c 41700 cdleme35d 41701 cdleme35e 41702 cdleme35f 41703 cdleme35fnpq 41698 cdleme35g 41704 cdleme35h 41705 cdleme35h2 41706 cdleme35sn2aw 41707 cdleme35sn3a 41708 cdleme36a 41709 cdleme36m 41710 cdleme37m 41711 cdleme38m 41712 cdleme38n 41713 cdleme39a 41714 cdleme39n 41715 cdleme3b 41478 cdleme3c 41479 cdleme3d 41480 cdleme3e 41481 cdleme3fN 41482 cdleme3fa 41485 cdleme3g 41483 cdleme3h 41484 cdleme4 41487 cdleme40m 41716 cdleme40n 41717 cdleme40v 41718 cdleme40w 41719 cdleme41fva11 41726 cdleme41sn3aw 41723 cdleme41sn4aw 41724 cdleme41snaw 41725 cdleme42a 41720 cdleme42b 41727 cdleme42c 41721 cdleme42d 41722 cdleme42e 41728 cdleme42f 41729 cdleme42g 41730 cdleme42h 41731 cdleme42i 41732 cdleme42k 41733 cdleme42ke 41734 cdleme42keg 41735 cdleme42mN 41736 cdleme42mgN 41737 cdleme43aN 41738 cdleme43bN 41739 cdleme43cN 41740 cdleme43dN 41741 cdleme5 41489 cdleme50ex 41808 cdleme50ltrn 41806 cdleme51finvN 41805 cdleme51finvfvN 41804 cdleme51finvtrN 41807 cdleme6 41490 cdleme7 41498 cdleme7a 41492 cdleme7aa 41491 cdleme7b 41493 cdleme7c 41494 cdleme7d 41495 cdleme7e 41496 cdleme7ga 41497 cdleme8 41499 cdleme8tN 41504 cdleme9 41502 cdleme9a 41500 cdleme9b 41501 cdleme9tN 41506 cdleme9taN 41505 cdlemeda 41547 cdlemedb 41546 cdlemednpq 41548 cdlemednuN 41549 cdlemefr27cl 41652 cdlemefr32fva1 41659 cdlemefr32fvaN 41658 cdlemefrs32fva 41649 cdlemefrs32fva1 41650 cdlemefs27cl 41662 cdlemefs32fva1 41672 cdlemefs32fvaN 41671 cdlemesner 41545 cdlemeulpq 41469 |
| [Crawley] p. 114 | Lemma E | 4atex 41325 4atexlem7 41324 cdleme0nex 41539 cdleme17a 41535 cdleme17c 41537 cdleme17d 41747 cdleme17d1 41538 cdleme17d2 41744 cdleme18a 41540 cdleme18b 41541 cdleme18c 41542 cdleme18d 41544 cdleme4a 41488 |
| [Crawley] p. 115 | Lemma E | cdleme21a 41574 cdleme21at 41577 cdleme21b 41575 cdleme21c 41576 cdleme21ct 41578 cdleme21f 41581 cdleme21g 41582 cdleme21h 41583 cdleme21i 41584 cdleme22gb 41543 |
| [Crawley] p. 116 | Lemma F | cdlemf 41812 cdlemf1 41810 cdlemf2 41811 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 41816 cdlemg16 41906 cdlemg28 41953 cdlemg28a 41942 cdlemg28b 41952 cdlemg3a 41846 cdlemg42 41978 cdlemg43 41979 cdlemg44 41982 cdlemg44a 41980 cdlemg46 41984 cdlemg47 41985 cdlemg9 41883 ltrnco 41968 ltrncom 41987 tgrpabl 42000 trlco 41976 |
| [Crawley] p. 116 | Definition of G | df-tgrp 41992 |
| [Crawley] p. 117 | Lemma G | cdlemg17 41926 cdlemg17b 41911 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 42005 df-edring 42006 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 42009 |
| [Crawley] p. 118 | Remark | tendopltp 42029 |
| [Crawley] p. 118 | Lemma H | cdlemh 42066 cdlemh1 42064 cdlemh2 42065 |
| [Crawley] p. 118 | Lemma I | cdlemi 42069 cdlemi1 42067 cdlemi2 42068 |
| [Crawley] p. 118 | Lemma J | cdlemj1 42070 cdlemj2 42071 cdlemj3 42072 tendocan 42073 |
| [Crawley] p. 118 | Lemma K | cdlemk 42223 cdlemk1 42080 cdlemk10 42092 cdlemk11 42098 cdlemk11t 42195 cdlemk11ta 42178 cdlemk11tb 42180 cdlemk11tc 42194 cdlemk11u-2N 42138 cdlemk11u 42120 cdlemk12 42099 cdlemk12u-2N 42139 cdlemk12u 42121 cdlemk13-2N 42125 cdlemk13 42101 cdlemk14-2N 42127 cdlemk14 42103 cdlemk15-2N 42128 cdlemk15 42104 cdlemk16-2N 42129 cdlemk16 42106 cdlemk16a 42105 cdlemk17-2N 42130 cdlemk17 42107 cdlemk18-2N 42135 cdlemk18-3N 42149 cdlemk18 42117 cdlemk19-2N 42136 cdlemk19 42118 cdlemk19u 42219 cdlemk1u 42108 cdlemk2 42081 cdlemk20-2N 42141 cdlemk20 42123 cdlemk21-2N 42140 cdlemk21N 42122 cdlemk22-3 42150 cdlemk22 42142 cdlemk23-3 42151 cdlemk24-3 42152 cdlemk25-3 42153 cdlemk26-3 42155 cdlemk26b-3 42154 cdlemk27-3 42156 cdlemk28-3 42157 cdlemk29-3 42160 cdlemk3 42082 cdlemk30 42143 cdlemk31 42145 cdlemk32 42146 cdlemk33N 42158 cdlemk34 42159 cdlemk35 42161 cdlemk36 42162 cdlemk37 42163 cdlemk38 42164 cdlemk39 42165 cdlemk39u 42217 cdlemk4 42083 cdlemk41 42169 cdlemk42 42190 cdlemk42yN 42193 cdlemk43N 42212 cdlemk45 42196 cdlemk46 42197 cdlemk47 42198 cdlemk48 42199 cdlemk49 42200 cdlemk5 42085 cdlemk50 42201 cdlemk51 42202 cdlemk52 42203 cdlemk53 42206 cdlemk54 42207 cdlemk55 42210 cdlemk55u 42215 cdlemk56 42220 cdlemk5a 42084 cdlemk5auN 42109 cdlemk5u 42110 cdlemk6 42086 cdlemk6u 42111 cdlemk7 42097 cdlemk7u-2N 42137 cdlemk7u 42119 cdlemk8 42087 cdlemk9 42088 cdlemk9bN 42089 cdlemki 42090 cdlemkid 42185 cdlemkj-2N 42131 cdlemkj 42112 cdlemksat 42095 cdlemksel 42094 cdlemksv 42093 cdlemksv2 42096 cdlemkuat 42115 cdlemkuel-2N 42133 cdlemkuel-3 42147 cdlemkuel 42114 cdlemkuv-2N 42132 cdlemkuv2-2 42134 cdlemkuv2-3N 42148 cdlemkuv2 42116 cdlemkuvN 42113 cdlemkvcl 42091 cdlemky 42175 cdlemkyyN 42211 tendoex 42224 |
| [Crawley] p. 120 | Remark | dva1dim 42234 |
| [Crawley] p. 120 | Lemma L | cdleml1N 42225 cdleml2N 42226 cdleml3N 42227 cdleml4N 42228 cdleml5N 42229 cdleml6 42230 cdleml7 42231 cdleml8 42232 cdleml9 42233 dia1dim 42310 |
| [Crawley] p. 120 | Lemma M | dia11N 42297 diaf11N 42298 dialss 42295 diaord 42296 dibf11N 42410 djajN 42386 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 42281 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 42367 dia2dimlem1 42313 dia2dimlem2 42314 dia2dimlem3 42315 dia2dimlem4 42316 dia2dimlem5 42317 diaf1oN 42379 diarnN 42378 dvheveccl 42361 dvhopN 42365 |
| [Crawley] p. 121 | Lemma N | cdlemn 42461 cdlemn10 42455 cdlemn11 42460 cdlemn11a 42456 cdlemn11b 42457 cdlemn11c 42458 cdlemn11pre 42459 cdlemn2 42444 cdlemn2a 42445 cdlemn3 42446 cdlemn4 42447 cdlemn4a 42448 cdlemn5 42450 cdlemn5pre 42449 cdlemn6 42451 cdlemn7 42452 cdlemn8 42453 cdlemn9 42454 diclspsn 42443 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 42422 |
| [Crawley] p. 122 | Lemma N | dih11 42514 dihf11 42516 dihjust 42466 dihjustlem 42465 dihord 42513 dihord1 42467 dihord10 42472 dihord11b 42471 dihord11c 42473 dihord2 42476 dihord2a 42468 dihord2b 42469 dihord2cN 42470 dihord2pre 42474 dihord2pre2 42475 dihordlem6 42462 dihordlem7 42463 dihordlem7b 42464 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 42479 dihfval 42480 dihval 42481 |
| [Diestel] p. 3 | Definition | df-gric 49184 df-grim 49181 isuspgrim 49199 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 30023 df-nbgr 29944 |
| [Diestel] p. 3 | Definition by | df-grisom 49180 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 49164 df-subgr 29879 uhgrspan1 29914 uhgrspansubgr 29902 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 30165 vtxdgoddnumeven 30164 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29667 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 34566 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 34578 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 34570 zarcls1 34571 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 34581 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 34584 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 34587 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 4050 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9675 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8877 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9683 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 10088 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10666 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5262 |
| [Enderton] p. 19 | Definition | df-tp 4593 |
| [Enderton] p. 26 | Exercise 5 | unissb 4904 |
| [Enderton] p. 26 | Exercise 10 | pwel 5347 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5548 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5042 iinin2 5041 iinun2 5034 iunin1 5033 iunin1f 33224 iunin2 5032 uniin1 5036 uniin2 5037 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5040 iundif2 5035 |
| [Enderton] p. 32 | Exercise 20 | unineq 4236 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5061 |
| [Enderton] p. 33 | Exercise 25 | iununi 5062 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5069 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7809 iunpwss 5070 |
| [Enderton] p. 36 | Definition | opthwiener 5491 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5422 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4909 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5443 rnex 7946 rnexg 7938 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5903 rnuni 6152 |
| [Enderton] p. 42 | Definition of a function | dffun7 6587 dffun8 6588 |
| [Enderton] p. 43 | Definition of function value | funfv2 6996 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6631 |
| [Enderton] p. 44 | Definition (d) | dfima2 6070 dfima3 6071 |
| [Enderton] p. 47 | Theorem 3H | fvco2 7005 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10578 ac7g 10579 df-ac 10222 dfac2 10237 dfac2a 10235 dfac2b 10236 dfac3 10227 dfac7 10238 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7273 |
| [Enderton] p. 52 | Definition | df-map 8877 |
| [Enderton] p. 53 | Exercise 21 | coass 6284 |
| [Enderton] p. 53 | Exercise 27 | dmco 6269 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6638 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6067 |
| [Enderton] p. 54 | Remark | ixpf 8976 ixpssmap 8988 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8954 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10588 ac9s 10598 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 39818 erref 8766 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 39821 erthi 8802 |
| [Enderton] p. 57 | Definition | df-ec 8747 |
| [Enderton] p. 58 | Definition | df-qs 8751 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8747 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5899 |
| [Enderton] p. 68 | Definition of successor | df-suc 6386 |
| [Enderton] p. 71 | Definition | df-tr 5216 dftr4 5221 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6462 unisucg 6461 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6462 unisucg 6461 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5231 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5233 trintALT 46054 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8641 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8643 onasuc 8564 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7446 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8642 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8644 onmsuc 8565 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8659 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8646 nnacom 8654 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8660 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8661 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8663 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8647 nnmsucr 8662 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8675 |
| [Enderton] p. 129 | Definition | df-en 9002 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7397 |
| [Enderton] p. 133 | Exercise 1 | xpomen 10121 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16410 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9250 |
| [Enderton] p. 135 | Corollary 6C | php3 9252 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9249 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9281 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9283 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9212 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9216 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9188 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10285 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10286 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10281 dju1en 10277 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9360 unifi 9361 unifi2 9362 |
| [Enderton] p. 144 | Corollary 6K | undif2 4434 unfi 9214 unfi2 9330 |
| [Enderton] p. 145 | Figure 38 | ffoss 7982 |
| [Enderton] p. 145 | Definition | df-dom 9003 |
| [Enderton] p. 146 | Example 1 | domen 9016 domeng 9017 |
| [Enderton] p. 146 | Example 3 | nndomo 9261 nnsdom 9682 nnsdomg 9319 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10289 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9189 xpdom1 9123 xpdom1g 9121 xpdom2g 9120 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9195 |
| [Enderton] p. 151 | Theorem 6M | zorn 10612 zorng 10609 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10597 dfac5 10234 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10687 |
| [Enderton] p. 164 | Example | infdif 10313 |
| [Enderton] p. 168 | Definition | df-po 5563 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6496 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6428 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6495 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6436 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7874 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7819 |
| [Enderton] p. 194 | Remark | onprc 7816 |
| [Enderton] p. 194 | Exercise 16 | suc11 6490 |
| [Enderton] p. 197 | Definition | df-card 10047 |
| [Enderton] p. 197 | Theorem 7P | carden 10662 |
| [Enderton] p. 200 | Exercise 25 | tfis 7890 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9810 |
| [Enderton] p. 202 | Definition | df-r1 9795 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9820 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9911 rankval4b 9907 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9634 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9898 rankprb 9892 rankpw 9883 rankpwi 9859 rankuniss 9910 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9646 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9647 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10216 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 10182 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10196 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8377 |
| [Enderton] p. 222 | Definition | df-kard 35918 |
| [Enderton] p. 222 | Definition of kard | karden 9986 kardex 9984 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8634 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8636 |
| [Enderton] p. 240 | Exercise 25 | oarec 8598 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10354 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17845 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17787 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18756 mrieqv2d 17842 mrieqvd 17841 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17846 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17851 mreexexlem2d 17848 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18762 mreexfidimd 17853 |
| [Frege1879] p. 11 | Statement | df3or2 44960 |
| [Frege1879] p. 12 | Statement | df3an2 44961 dfxor4 44958 dfxor5 44959 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 44982 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 44983 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 44987 |
| [Frege1879] p. 31 | Proposition 4 | frege4 44991 |
| [Frege1879] p. 32 | Proposition 5 | frege5 44992 |
| [Frege1879] p. 33 | Proposition 6 | frege6 44998 |
| [Frege1879] p. 34 | Proposition 7 | frege7 45000 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 45001 axfrege8 44999 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 91 wl-luk-pm2.04 38560 |
| [Frege1879] p. 35 | Proposition 9 | frege9 45004 |
| [Frege1879] p. 36 | Proposition 10 | frege10 45012 |
| [Frege1879] p. 36 | Proposition 11 | frege11 45006 |
| [Frege1879] p. 37 | Proposition 12 | frege12 45005 |
| [Frege1879] p. 37 | Proposition 13 | frege13 45014 |
| [Frege1879] p. 37 | Proposition 14 | frege14 45015 |
| [Frege1879] p. 38 | Proposition 15 | frege15 45018 |
| [Frege1879] p. 38 | Proposition 16 | frege16 45008 |
| [Frege1879] p. 39 | Proposition 17 | frege17 45013 |
| [Frege1879] p. 39 | Proposition 18 | frege18 45010 |
| [Frege1879] p. 39 | Proposition 19 | frege19 45016 |
| [Frege1879] p. 40 | Proposition 20 | frege20 45020 |
| [Frege1879] p. 40 | Proposition 21 | frege21 45019 |
| [Frege1879] p. 41 | Proposition 22 | frege22 45011 |
| [Frege1879] p. 42 | Proposition 23 | frege23 45017 |
| [Frege1879] p. 42 | Proposition 24 | frege24 45007 |
| [Frege1879] p. 42 | Proposition 25 | frege25 45009 rp-frege25 44997 |
| [Frege1879] p. 42 | Proposition 26 | frege26 45002 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 45022 |
| [Frege1879] p. 43 | Proposition 27 | frege27 45003 |
| [Frege1879] p. 43 | Proposition 28 | con3 154 |
| [Frege1879] p. 43 | Proposition 29 | frege29 45023 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 45026 axfrege31 45025 |
| [Frege1879] p. 44 | Proposition 30 | frege30 45024 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 131 |
| [Frege1879] p. 44 | Proposition 32 | frege32 45027 |
| [Frege1879] p. 44 | Proposition 33 | frege33 45028 |
| [Frege1879] p. 45 | Proposition 34 | frege34 45029 |
| [Frege1879] p. 45 | Proposition 35 | frege35 45030 |
| [Frege1879] p. 45 | Proposition 36 | frege36 45031 |
| [Frege1879] p. 46 | Proposition 37 | frege37 45032 |
| [Frege1879] p. 46 | Proposition 38 | frege38 45033 |
| [Frege1879] p. 46 | Proposition 39 | frege39 45034 |
| [Frege1879] p. 46 | Proposition 40 | frege40 45035 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 45037 axfrege41 45036 |
| [Frege1879] p. 47 | Proposition 41 | notnot 143 |
| [Frege1879] p. 47 | Proposition 42 | frege42 45038 |
| [Frege1879] p. 47 | Proposition 43 | frege43 45039 |
| [Frege1879] p. 47 | Proposition 44 | frege44 45040 |
| [Frege1879] p. 47 | Proposition 45 | frege45 45041 |
| [Frege1879] p. 48 | Proposition 46 | frege46 45042 |
| [Frege1879] p. 48 | Proposition 47 | frege47 45043 |
| [Frege1879] p. 49 | Proposition 48 | frege48 45044 |
| [Frege1879] p. 49 | Proposition 49 | frege49 45045 |
| [Frege1879] p. 49 | Proposition 50 | frege50 45046 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 45049 ax-frege52c 45080 frege52aid 45050 frege52b 45081 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 45054 ax-frege54c 45084 frege54b 45085 |
| [Frege1879] p. 50 | Proposition 51 | frege51 45047 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3744 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 45052 frege53aid 45051 frege53b 45082 frege53c 45106 |
| [Frege1879] p. 50 | Proposition 54 | biid 264 eqid 2763 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 45060 frege55aid 45057 frege55b 45089 frege55c 45110 frege55cor1a 45061 frege55lem2a 45059 frege55lem2b 45088 frege55lem2c 45109 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 45063 frege56aid 45062 frege56b 45090 frege56c 45111 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 45067 ax-frege58b 45093 frege58bid 45094 frege58c 45113 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 45065 frege57aid 45064 frege57b 45091 frege57c 45112 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3755 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 45069 frege59b 45096 frege59c 45114 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 45070 frege60b 45097 frege60c 45115 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 45071 frege61b 45098 frege61c 45116 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 45072 frege62b 45099 frege62c 45117 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 45073 frege63b 45100 frege63c 45118 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 45074 frege64b 45101 frege64c 45119 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 45075 frege65b 45102 frege65c 45120 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 45076 frege66b 45103 frege66c 45121 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 45077 frege67b 45104 frege67c 45122 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 45078 frege68b 45105 frege68c 45123 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 45124 |
| [Frege1879] p. 58 | Proposition 70 | frege70 45125 |
| [Frege1879] p. 59 | Proposition 71 | frege71 45126 |
| [Frege1879] p. 59 | Proposition 72 | frege72 45127 |
| [Frege1879] p. 59 | Proposition 73 | frege73 45128 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 45131 |
| [Frege1879] p. 60 | Proposition 74 | frege74 45129 |
| [Frege1879] p. 60 | Proposition 75 | frege75 45130 |
| [Frege1879] p. 62 | Proposition 77 | frege77 45132 frege77d 44938 |
| [Frege1879] p. 63 | Proposition 78 | frege78 45133 |
| [Frege1879] p. 63 | Proposition 79 | frege79 45134 |
| [Frege1879] p. 63 | Proposition 80 | frege80 45135 |
| [Frege1879] p. 63 | Proposition 81 | frege81 45136 frege81d 44939 |
| [Frege1879] p. 64 | Proposition 82 | frege82 45137 |
| [Frege1879] p. 65 | Proposition 83 | frege83 45138 frege83d 44940 |
| [Frege1879] p. 65 | Proposition 84 | frege84 45139 |
| [Frege1879] p. 66 | Proposition 85 | frege85 45140 |
| [Frege1879] p. 66 | Proposition 86 | frege86 45141 |
| [Frege1879] p. 66 | Proposition 87 | frege87 45142 frege87d 44942 |
| [Frege1879] p. 67 | Proposition 88 | frege88 45143 |
| [Frege1879] p. 68 | Proposition 89 | frege89 45144 |
| [Frege1879] p. 68 | Proposition 90 | frege90 45145 |
| [Frege1879] p. 68 | Proposition 91 | frege91 45146 frege91d 44943 |
| [Frege1879] p. 69 | Proposition 92 | frege92 45147 |
| [Frege1879] p. 70 | Proposition 93 | frege93 45148 |
| [Frege1879] p. 70 | Proposition 94 | frege94 45149 |
| [Frege1879] p. 70 | Proposition 95 | frege95 45150 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 45154 |
| [Frege1879] p. 71 | Proposition 96 | frege96 45151 frege96d 44941 |
| [Frege1879] p. 71 | Proposition 97 | frege97 45152 frege97d 44944 |
| [Frege1879] p. 71 | Proposition 98 | frege98 45153 frege98d 44945 |
| [Frege1879] p. 72 | Proposition 100 | frege100 45155 |
| [Frege1879] p. 72 | Proposition 101 | frege101 45156 |
| [Frege1879] p. 72 | Proposition 102 | frege102 45157 frege102d 44946 |
| [Frege1879] p. 73 | Proposition 103 | frege103 45158 |
| [Frege1879] p. 73 | Proposition 104 | frege104 45159 |
| [Frege1879] p. 73 | Proposition 105 | frege105 45160 |
| [Frege1879] p. 73 | Proposition 106 | frege106 45161 frege106d 44947 |
| [Frege1879] p. 74 | Proposition 107 | frege107 45162 |
| [Frege1879] p. 74 | Proposition 108 | frege108 45163 frege108d 44948 |
| [Frege1879] p. 74 | Proposition 109 | frege109 45164 frege109d 44949 |
| [Frege1879] p. 75 | Proposition 110 | frege110 45165 |
| [Frege1879] p. 75 | Proposition 111 | frege111 45166 frege111d 44951 |
| [Frege1879] p. 76 | Proposition 112 | frege112 45167 |
| [Frege1879] p. 76 | Proposition 113 | frege113 45168 |
| [Frege1879] p. 76 | Proposition 114 | frege114 45169 frege114d 44950 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 45170 |
| [Frege1879] p. 77 | Proposition 116 | frege116 45171 |
| [Frege1879] p. 78 | Proposition 117 | frege117 45172 |
| [Frege1879] p. 78 | Proposition 118 | frege118 45173 |
| [Frege1879] p. 78 | Proposition 119 | frege119 45174 |
| [Frege1879] p. 78 | Proposition 120 | frege120 45175 |
| [Frege1879] p. 79 | Proposition 121 | frege121 45176 |
| [Frege1879] p. 79 | Proposition 122 | frege122 45177 frege122d 44952 |
| [Frege1879] p. 79 | Proposition 123 | frege123 45178 |
| [Frege1879] p. 80 | Proposition 124 | frege124 45179 frege124d 44953 |
| [Frege1879] p. 81 | Proposition 125 | frege125 45180 |
| [Frege1879] p. 81 | Proposition 126 | frege126 45181 frege126d 44954 |
| [Frege1879] p. 82 | Proposition 127 | frege127 45182 |
| [Frege1879] p. 83 | Proposition 128 | frege128 45183 |
| [Frege1879] p. 83 | Proposition 129 | frege129 45184 frege129d 44955 |
| [Frege1879] p. 84 | Proposition 130 | frege130 45185 |
| [Frege1879] p. 85 | Proposition 131 | frege131 45186 frege131d 44956 |
| [Frege1879] p. 86 | Proposition 132 | frege132 45187 |
| [Frege1879] p. 86 | Proposition 133 | frege133 45188 frege133d 44957 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 47528 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 47851 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 47551 |
| [Fremlin1] p. 14 | Definition 112A | ismea 47666 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 47686 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 47677 meadjunre 47691 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 47678 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 47679 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 47675 meaiunle 47684 meaiunlelem 47683 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 47696 meaiuninc2 47697 meaiuninc3 47700 meaiuninc3v 47699 meaiunincf 47698 meaiuninclem 47695 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 47702 meaiininc2 47703 meaiininclem 47701 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 47721 caragendifcl 47729 caratheodory 47743 omelesplit 47733 |
| [Fremlin1] p. 19 | Definition 113A | isome 47709 isomennd 47746 isomenndlem 47745 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 47731 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 47750 voncmpl 47836 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 47713 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 47738 carageniuncllem1 47736 carageniuncllem2 47737 caragenuncl 47728 caragenuncllem 47727 caragenunicl 47739 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 47747 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 47741 caratheodorylem2 47742 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 47750 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 47809 hoidmv1lelem1 47806 hoidmv1lelem2 47807 hoidmv1lelem3 47808 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 47853 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 47809 hoidmvle 47815 hoidmvlelem1 47810 hoidmvlelem2 47811 hoidmvlelem3 47812 hoidmvlelem4 47813 hoidmvlelem5 47814 hsphoidmvle2 47800 hsphoif 47791 hsphoival 47794 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 47763 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 47771 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 47798 hoidmvn0val 47799 hoidmvval 47792 hoidmvval0 47802 hoidmvval0b 47805 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 47803 hsphoidmvle 47801 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 47752 df-voln 47754 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 47819 ovn0 47781 ovn0lem 47780 ovnf 47778 ovnome 47788 ovnssle 47776 ovnsslelem 47775 ovnsupge0 47772 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 47818 ovnhoilem1 47816 ovnhoilem2 47817 vonhoi 47882 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 47835 hoidifhspf 47833 hoidifhspval 47823 hoidifhspval2 47830 hoidifhspval3 47834 hspmbl 47844 hspmbllem1 47841 hspmbllem2 47842 hspmbllem3 47843 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 47836 vonmea 47789 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 47787 ovnsubadd2 47861 ovnsubadd2lem 47860 ovnsubaddlem1 47785 ovnsubaddlem2 47786 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 47846 hoimbl2 47880 hoimbllem 47845 hspdifhsp 47831 opnvonmbl 47849 opnvonmbllem2 47848 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 47851 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 47894 iccvonmbllem 47893 ioovonmbl 47892 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 47900 vonicclem2 47899 vonioo 47897 vonioolem2 47896 vonn0icc 47903 vonn0icc2 47907 vonn0ioo 47902 vonn0ioo2 47905 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 47904 snvonmbl 47901 vonct 47908 vonsn 47906 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 47574 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 47573 subsaliuncllem 47572 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 47940 salpreimalegt 47924 salpreimaltle 47941 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 47943 issmff 47949 issmflem 47942 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 47960 issmflelem 47959 smfpreimale 47969 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 47971 issmfgtlem 47970 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 47911 issmf 47943 issmff 47949 issmfge 47985 issmfgelem 47984 issmfgt 47971 issmfgtlem 47970 issmfle 47960 issmflelem 47959 issmflem 47942 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 47922 salpreimagtlt 47945 salpreimalelt 47944 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 47985 issmfgelem 47984 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 47968 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 47966 cnfsmf 47955 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 47982 decsmflem 47981 incsmf 47957 incsmflem 47956 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 47916 pimconstlt1 47917 smfconst 47964 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 47980 smfaddlem1 47978 smfaddlem2 47979 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 48011 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 48010 smfmullem1 48006 smfmullem2 48007 smfmullem3 48008 smfmullem4 48009 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 48012 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 48015 smfpimbor1lem2 48014 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 48017 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 48005 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 48004 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 48013 smfresal 48003 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 47992 smflim2 48021 smflimlem1 47986 smflimlem2 47987 smflimlem3 47988 smflimlem4 47989 smflimlem5 47990 smflimlem6 47991 smflimmpt 48025 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 48029 smfsuplem1 48026 smfsuplem2 48027 smfsuplem3 48028 smfsupmpt 48030 smfsupxr 48031 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 48033 smfinflem 48032 smfinfmpt 48034 |
| [Fremlin1] p. 39 | Remark 121G | smflim 47992 smflim2 48021 smflimmpt 48025 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 48023 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 48053 smfdivdmmbl2 48056 smfinfdmmbl 48064 smfinfdmmbllem 48063 smfsupdmmbl 48060 smfsupdmmbllem 48059 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 48043 smflimsuplem2 48036 smflimsuplem6 48040 smflimsuplem7 48041 smflimsuplem8 48042 smflimsupmpt 48044 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 48046 smfliminflem 48045 smfliminfmpt 48047 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 47911 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 48057 fsupdm2 48058 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 48048 adddmmbl2 48049 finfdm 48061 finfdm2 48062 fsupdm 48057 fsupdm2 48058 muldmmbl 48050 muldmmbl2 48051 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 48061 finfdm2 48062 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25887 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25930 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25940 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 38808 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 38811 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9666 inf1 9650 inf2 9651 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 11023 enqer 11033 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 11028 df-nq 11024 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 11020 df-plq 11026 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7682 df-mpq 11021 df-mq 11027 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 11029 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 11087 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 11088 ltbtwnnq 11090 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 11083 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 11084 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 11091 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 11093 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 11105 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 11107 |
| [Gleason] p. 122 | Definition | df-1p 11094 |
| [Gleason] p. 122 | Remark (1) | prub 11106 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 11145 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 11097 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 11144 psslinpr 11143 supexpr 11166 suplem1pr 11164 suplem2pr 11165 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 11130 addclprlem1 11128 addclprlem2 11129 df-plp 11095 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 11134 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 11133 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 11146 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 11155 ltexprlem1 11148 ltexprlem2 11149 ltexprlem3 11150 ltexprlem4 11151 ltexprlem5 11152 ltexprlem6 11153 ltexprlem7 11154 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 11157 ltaprlem 11156 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 11158 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 11159 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 11096 mulclpr 11132 mulclprlem 11131 reclem2pr 11160 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 11141 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 11136 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 11135 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 11140 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 11163 reclem3pr 11161 reclem4pr 11162 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 11167 enrer 11175 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 11172 df-1r 11173 df-nr 11168 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 11170 df-plr 11169 negexsr 11214 recexsr 11219 recexsrlem 11215 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 11171 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12342 creur 12341 cru 12339 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11300 axcnre 11276 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15311 crimd 15428 crimi 15389 crre 15310 crred 15427 crrei 15388 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15313 remimd 15394 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15480 absval2d 15644 absval2i 15594 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15337 cjaddd 15416 cjaddi 15384 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15338 cjmuld 15417 cjmuli 15385 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15336 cjcjd 15395 cjcji 15367 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15335 cjreb 15319 cjrebd 15398 cjrebi 15370 cjred 15422 rere 15318 rereb 15316 rerebd 15397 rerebi 15369 rered 15420 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15344 addcjd 15408 addcji 15379 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15434 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15475 abscjd 15649 abscji 15598 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15485 abs00d 15645 abs00i 15595 absne0d 15646 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15518 releabsd 15650 releabsi 15599 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15490 absmuld 15653 absmuli 15601 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15478 sqabsaddi 15602 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15527 abstrid 15655 abstrii 15605 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14232 exp0 14235 expp1 14238 expp1d 14317 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 27037 cxpaddd 27075 expadd 14274 expaddd 14318 expaddz 14276 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 27046 cxpmuld 27095 expmul 14277 expmuld 14319 expmulz 14278 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 27043 mulcxpd 27086 mulexp 14271 mulexpd 14331 mulexpz 14272 |
| [Gleason] p. 140 | Exercise 1 | znnen 16409 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13668 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15828 rlimadd 15839 rlimdiv 15842 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15830 rlimsub 15840 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15829 rlimmul 15841 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15833 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15779 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15800 climcj 15801 climim 15803 climre 15802 rlimabs 15805 rlimcj 15806 rlimim 15808 rlimre 15807 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11375 df-xr 11374 ltxr 13271 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15667 limsupval 15670 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15866 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15875 caucvgb 15876 caucvgbf 46704 caucvgr 15872 climcau 15867 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 16012 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 16081 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15532 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13995 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21702 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24692 xmet0 24691 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24708 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24699 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24701 mstri 24818 xmettri 24700 xmstri 24817 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24731 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23997 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25661 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24889 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 25215 addcn2 15790 mulcn 25217 mulcn2 15792 subcn 25216 subcn2 15791 |
| [Gleason] p. 295 | Remark | bcval3 14477 bcval4 14478 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14492 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14475 df-bc 14474 |
| [Gleason] p. 296 | Remark | bcn0 14481 bcnn 14483 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 16028 |
| [Gleason] p. 308 | Equation 2 | ef0 16286 |
| [Gleason] p. 308 | Equation 3 | efcj 16287 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16293 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16298 |
| [Gleason] p. 310 | Equation 14 | sinadd 16361 |
| [Gleason] p. 310 | Equation 15 | cosadd 16362 |
| [Gleason] p. 311 | Equation 17 | sincossq 16373 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16378 sinbnd 16377 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14387 sqeqori 14385 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16267 |
| [Godowski] p. 730 | Equation SF | goeqi 32905 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 32300 |
| [Golan] p. 1 | Remark | srgisid 20465 |
| [Golan] p. 1 | Definition | df-srg 20443 |
| [Golan] p. 149 | Definition | df-slmd 33832 |
| [Gonshor] p. 7 | Definition | df-cuts 28176 |
| [Gonshor] p. 9 | Theorem 2.5 | lesrec 28215 lesrecd 28216 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 28336 cofcut1d 28337 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 28338 cofcut2d 28339 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 28340 cofcutr1d 28341 cofcutr2d 28342 |
| [Gonshor] p. 13 | Definition | df-adds 28376 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 28392 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 28418 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28546 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28566 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28874 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28876 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28875 |
| [Gonshor] p. 39 | Theorem 4.4(b) | elreno2 28911 |
| [Gonshor] p. 95 | Theorem 6.1 | addbday 28434 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 37102 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17785 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17787 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 49490 df-cllaw 49488 df-comlaw 49489 |
| [Hall] p. 2 | Section 1.2 | df-clintop 49502 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 49523 |
| [Halmos] p. 28 | Partition ` ` | df-parts 39992 dfmembpart2 39997 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32697 riesz2 32698 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 32573 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32805 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32817 elpjidm 32816 pjnmopi 32780 |
| [Halmos] p. 44 | Remark | pjinormi 32319 pjinormii 32308 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32821 pjrn 32339 pjrni 32334 pjvec 32328 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 32359 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32786 hmopidmpji 32784 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32823 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32812 pjocvec 32329 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32801 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32804 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32807 pjssdif2i 32806 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 32487 |
| [Hamilton] p. 28 | Definition 2.1 | ax-1 6 |
| [Hamilton] p. 31 | Example 2.7(a) | idALT 24 |
| [Hamilton] p. 73 | Rule 1 | ax-mp 5 |
| [Hamilton] p. 74 | Rule 2 | ax-gen 1828 |
| [Hatcher] p. 25 | Definition | df-phtpc 25343 df-phtpy 25322 |
| [Hatcher] p. 26 | Definition | df-pco 25356 df-pi1 25359 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 25346 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 25401 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22835 df-dmatalt 49715 |
| [Helfgott] p. 2 | Theorem | tgoldbach 49120 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 49105 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 49117 bgoldbtbnd 49112 bgoldbtbnd 49112 tgblthelfgott 49118 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 35341 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 35342 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 35356 hgt750lemb 35355 hgt750leme 35357 hgt750lemf 35352 hgt750lemg 35353 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 49114 tgoldbachgt 35362 tgoldbachgtALTV 49115 tgoldbachgtd 35361 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 35343 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 31125 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 19184 grpoideu 31141 mndideu 18963 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 19214 grpoinveu 31151 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 19245 grpo2inv 31163 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 19257 grpoinvop 31165 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 19279 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1801 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1802 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1804 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 33052 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 33065 cdj3i 33073 cdj3lem1 33066 cdjreui 33064 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 33063 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 43210 |
| [Holland95] p. 14 | Line 15 | hgmapvs 43140 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 43162 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 43163 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 43160 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 43166 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 43085 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 43180 |
| [Holland95] p. 204 | Definition of involution | df-srng 21127 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 40752 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 42777 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 42730 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 41182 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 42626 poml4N 41202 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 42717 pexmidALTN 41227 pexmidN 41218 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 42782 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 40373 ldualset 40374 |
| [Holland95] p. 222 | Item 1 | df-lines 40750 df-pointsN 40751 |
| [Holland95] p. 222 | Item 2 | df-polarityN 41152 |
| [Holland95] p. 223 | Remark | ispsubcl2N 41196 omllaw4 40495 pol1N 41159 polcon3N 41166 |
| [Holland95] p. 223 | Definition | df-psubclN 41184 |
| [Holland95] p. 223 | Equation for polarity | polval2N 41155 |
| [Holmes] p. 40 | Definition | df-xrn 39504 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31716 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32814 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 32595 eigre 32467 eigrei 32466 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 32596 eigorth 32470 eigorthi 32469 |
| [Hughes] p. 137 | Remark (ii) | eigposi 32468 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30940 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30936 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30937 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30938 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30956 frgrregorufr0 30955 frgrregorufrg 30957 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30963 frrusgrord 30972 frrusgrord0 30971 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30709 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30946 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30949 frgrwopreg2 30950 frgrwopregasn 30947 frgrwopregbsn 30948 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30952 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30966 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30969 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30707 numclwlk1 31002 numclwlk1lem1 31000 numclwlk1lem2 31001 numclwwlk1 30992 numclwwlk8 31023 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30943 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 30388 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30978 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 31004 numclwwlkovh0 31003 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 31012 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 30599 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 31016 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 31019 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 31022 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 31034 natded 31034 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 31034 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 31034 natded 31034 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 31034 |
| [Jech] p. 4 | Definition of class | cv 1569 cvjust 2757 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10691 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10689 alephmul 10690 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10688 infmap2 10322 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9849 |
| [Jech] p. 72 | Equation 9.3 | df-scott 9956 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9911 rankval4b 9907 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9981 |
| [Jech] p. 78 | Note | opthprc 5719 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 44115 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 44203 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 44204 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 44127 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 44131 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 44132 rmyp1 44133 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 44134 rmym1 44135 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 44125 rmx1 44126 rmxluc 44136 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 44129 rmy1 44130 rmyluc 44137 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 44139 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 44140 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 44160 jm2.17b 44161 jm2.17c 44162 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 44193 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 44197 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 44188 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 44163 jm2.24nn 44159 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 44202 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 44208 rmygeid 44164 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 44220 |
| [Juillerat] p. 11 | Section *5 | etransc 47498 etransclem47 47496 etransclem48 47497 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 47493 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 47495 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 47481 |
| [Juillerat] p. 13 | Proof | etransclem35 47484 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 47487 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 47473 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 47490 |
| [Juillerat] p. 14 | Proof | etransclem23 47472 |
| [KalishMontague] p. 81 | Note 1 | ax-6 2002 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2047 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2052 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2042 cbvaliw 2041 wl-cbvmotv 38637 wl-motae 38639 wl-moteq 38638 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 2021 spimw 2005 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2068 spw 2069 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 32148 chabs1i 32150 chabs2 32149 chabs2i 32151 chjass 32165 chjassi 32118 latabs1 18678 latabs2 18679 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32970 ela 32971 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32915 cvrval2 40523 |
| [Kalmbach] p. 16 | Definition | df-ol 40427 df-oml 40428 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 32216 cmbri 32222 cmtvalN 40460 df-cm 32215 df-cmtN 40426 |
| [Kalmbach] p. 22 | Remark | omllaw5N 40496 pjoml5 32245 pjoml5i 32220 |
| [Kalmbach] p. 22 | Definition | pjoml2 32243 pjoml2i 32217 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 32246 cmcmi 32224 cmcmii 32229 cmtcomN 40498 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 40494 omlsi 32036 pjoml 32068 pjomli 32067 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 40493 |
| [Kalmbach] p. 23 | Remark | cmbr2i 32228 cmcm3 32247 cmcm3i 32226 cmcm3ii 32231 cmcm4i 32227 cmt3N 40500 cmt4N 40501 cmtbr2N 40502 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 32240 cmbr3i 32232 cmtbr3N 40503 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 32250 fh1i 32253 fh2 32251 fh2i 32254 omlfh1N 40507 |
| [Kalmbach] p. 65 | Remark | chjatom 32989 chslej 32130 chsleji 32090 shslej 32012 shsleji 32002 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 32127 chocini 32086 chsupcl 31972 chsupval2 32042 h0elch 31887 helch 31875 hsupval2 32041 ocin 31928 ococss 31925 shococss 31926 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31944 |
| [Kalmbach] p. 66 | Remark | df-pjh 32027 pjssmi 32797 pjssmii 32313 |
| [Kalmbach] p. 67 | Lemma 3 | osum 32277 osumi 32274 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32832 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 33032 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32942 |
| [Kalmbach] p. 140 | Remark | hatomic 32992 hatomici 32991 hatomistici 32994 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 40568 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 33013 lsatexch 40292 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32987 cvlcvr1 40588 cvr1 40659 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 33006 cvexchi 33001 cvrexch 40669 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32996 hlrelat 40651 hlrelat5N 40650 lrelat 40263 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21449 lsmsatcv 40259 spansncv 32285 spansncvi 32284 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 40278 spansncv2 32925 |
| [Kalmbach] p. 266 | Definition | df-st 32843 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 32481 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10758 fpwwe2 10755 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10759 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10766 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10761 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10763 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10776 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10780 gchxpidm 10781 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10792 gchhar 10791 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10320 unxpwdom 9610 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10782 |
| [Kreyszig] p. 3 | Property M1 | metcl 24681 xmetcl 24680 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24688 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24921 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 12061 muleqadd 11987 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24787 |
| [Kreyszig] p. 19 | Remark | mopntopon 24788 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24847 mopnm 24793 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24845 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24850 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24891 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23606 lmmbr 25609 lmmbr2 25610 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23728 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25664 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25627 iscmet2 25645 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25667 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23810 metelcls 25656 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25657 metcld2 25658 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25450 lmodvneg1 21210 nvinv 31271 vcm 31208 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25446 lmod0vs 21200 slmd0vs 33855 vc0 31206 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 21201 slmdvs0 33856 vcz 31207 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 31323 ngpmet 24952 nrmmetd 24923 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 31318 imsdval2 31319 ncvspds 25512 ngpds 24953 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24938 nvnd 31320 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24967 nmge0 24966 nvge0 31305 nvz 31301 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24973 nvabs 31304 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 31433 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 31377 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 31439 blocni 31437 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 31438 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25555 ipeq0 21974 ipz 31351 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25567 pythi 31482 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 31486 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25589 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 16054 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25787 minveco 31516 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 31382 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25680 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 31505 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32755 leopg 32754 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32773 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 31550 |
| [Kulpa] p. 547 | Theorem | poimir 38763 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 38762 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 38761 |
| [Kulpa] p. 548 | Theorem | broucube 38764 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 38756 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 38757 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2415 axnul 5262 |
| [Kunen] p. 11 | Axiom 3 | axnul 5262 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 5245 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8886 mapvalg 8884 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10627 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7976 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9795 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9841 r1elssi 9840 |
| [Kunen] p. 107 | Exercise 4 | rankop 9899 rankopb 9893 rankuni 9906 rankxplim 9923 rankxpsuc 9926 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 46139 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 46147 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 46146 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 46148 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 46153 rexabso 46154 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 46160 n0abso 46161 ssabso 46159 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 46162 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 46172 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 46167 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 46170 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 46171 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 46166 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 46178 wfaxpr 46183 wfaxreg 46185 wfaxrep 46179 wfaxsep 46180 wfaxun 46184 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 46169 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 46182 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 46178 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 46177 omelaxinf2 46174 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 46187 wfaxinf2 46186 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 46200 permaxext 46190 permaxinf2 46198 permaxnul 46193 permaxpow 46194 permaxpr 46195 permaxrep 46191 permaxsep 46192 permaxun 46196 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 46188 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 46199 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4967 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 34367 |
| [Lang] p. | Definition | df-rn 5666 |
| [Lang] p. 3 | Statement | lidrideqd 18879 mndbn0 18969 |
| [Lang] p. 3 | Definition | df-mnd 18953 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18905 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 19066 |
| [Lang] p. 5 | Equation | gsumreidx 20161 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 49484 |
| [Lang] p. 6 | Example | nn0mnd 49481 |
| [Lang] p. 6 | Equation | gsumxp2 20224 |
| [Lang] p. 6 | Statement | cycsubm 19446 |
| [Lang] p. 6 | Definition | mulgnn0gsum 19319 |
| [Lang] p. 6 | Observation | mndlsmidm 19914 |
| [Lang] p. 7 | Definition | dfgrp2e 19203 |
| [Lang] p. 30 | Definition | df-tocyc 33738 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33783 |
| [Lang] p. 32 | Property (b) | cyc3conja 33788 cycpmconjv 33773 |
| [Lang] p. 53 | Definition | df-cat 17871 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18301 cat1lem 18300 |
| [Lang] p. 54 | Definition | df-iso 17953 |
| [Lang] p. 57 | Definition | df-inito 18188 df-termo 18189 |
| [Lang] p. 58 | Example | irinitoringc 21815 |
| [Lang] p. 58 | Statement | initoeu1 18215 termoeu1 18222 |
| [Lang] p. 62 | Definition | df-func 18062 |
| [Lang] p. 65 | Definition | df-nat 18150 |
| [Lang] p. 83 | Definition of "ring with unit" | dfring2 20547 |
| [Lang] p. 91 | Note | df-ringc 20928 |
| [Lang] p. 92 | Statement | mxidlprm 34065 |
| [Lang] p. 92 | Definition | isprmidlc 21658 |
| [Lang] p. 128 | Remark | dsmmlmod 22081 |
| [Lang] p. 129 | Proof | lincscm 49747 lincscmcl 49749 lincsum 49746 lincsumcl 49748 |
| [Lang] p. 129 | Statement | lincolss 49751 |
| [Lang] p. 129 | Observation | dsmmfi 22074 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 34329 qusdimsum 34330 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 34310 |
| [Lang] p. 147 | Definition | snlindsntor 49788 |
| [Lang] p. 504 | Statement | mat1 22792 matring 22788 |
| [Lang] p. 504 | Definition | df-mamu 22736 |
| [Lang] p. 505 | Statement | mamuass 22747 mamutpos 22803 matassa 22789 mattposvs 22800 tposmap 22802 |
| [Lang] p. 513 | Definition | mdet1 22946 mdetf 22940 |
| [Lang] p. 513 | Theorem 4.4 | cramer 23039 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22932 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22956 |
| [Lang] p. 515 | Definition | df-minmar1 22980 smadiadetr 23020 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22955 mdetralt 22953 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22968 |
| [Lang] p. 518 | Definition | df-madu 22979 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22990 madurid 22989 matinv 23022 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 23238 |
| [Lang], p. 190 | Chapter 6 | vieta 34282 |
| [Lang], p. 224 | Proposition 1.1 | extdgfialg 34396 finextalg 34400 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 34365 fedgmul 34333 |
| [Lang], p. 225 | Proposition 1.4 | algextdeg 34427 |
| [Lang], p. 561 | Remark | chpmatply1 23180 |
| [Lang], p. 561 | Definition | df-chpmat 23175 |
| [Lang2] p. 3 | Notations | df-ind 12348 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 45510 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 45505 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 45511 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5262 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2742 wl-df.clab 38622 |
| [Levy] p. 59 | Definition | df-ttrcl 9736 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9782 |
| [Levy] p. 338 | Axiom | df-clel 2839 df-cleq 2755 wl-df.cleq 38623 |
| [Levy] p. 338 | Axiom. See also comments under ~ df-clab , ~ df-cleq , and ~ eqabb . Alternate characterizations | wl-df.clel 38626 |
| [Levy] p. 357 | Definition extends to class variables a relation already valid for set variables, and is therefore conservative. This only sketches the conservativity arguement; for details see Appendix | wl-df.clel 38626 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2839 df-cleq 2755 wl-df.cleq 38623 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2742 wl-df.clab 38622 |
| [Levy] p. 358 | Axiom | df-clab 2742 wl-df.clab 38622 |
| [Levy58] p. 2 | Definition I | isfin1-3 10491 |
| [Levy58] p. 2 | Definition II | df-fin2 10391 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10390 |
| [Levy58] p. 2 | Definition III | df-fin3 10393 |
| [Levy58] p. 3 | Definition V | df-fin5 10394 |
| [Levy58] p. 3 | Definition IV | df-fin4 10392 |
| [Levy58] p. 4 | Definition VI | df-fin6 10395 |
| [Levy58] p. 4 | Definition VII | df-fin7 10396 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10520 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 28073 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 28084 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 28116 nosupbnd1 28101 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 28118 nosupbnd2 28103 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 28122 noetasuplem4 28123 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 28119 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1801 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1802 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1804 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 33040 |
| [Maeda] p. 168 | Lemma 5 | mdsym 33044 mdsymi 33043 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 33038 mdsymlem6 33040 mdsymlem7 33041 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 33042 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32945 ssdmd2 32946 ssmd1 32943 ssmd2 32944 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32941 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32913 df-md 32912 mdbr 32926 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32963 mdslj1i 32951 mdslj2i 32952 mdslle1i 32949 mdslle2i 32950 mdslmd1i 32961 mdslmd2i 32962 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32953 mdsl2bi 32955 mdsl2i 32954 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32967 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32964 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32965 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32942 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32947 mdsl3 32948 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32966 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 33061 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 40570 hlrelat1 40649 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 40288 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32968 cvmdi 32956 cvnbtwn4 32921 cvrnbtwn4 40528 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32969 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 40589 cvp 33007 cvrp 40665 lcvp 40289 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 33031 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 33030 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 40582 hlexch4N 40641 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 33033 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 40692 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 40998 atpsubN 41002 df-pointsN 40751 pointpsubN 41000 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 40753 pmap11 41011 pmaple 41010 pmapsub 41017 pmapval 41006 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 41014 pmap1N 41016 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 41019 pmapglb2N 41020 pmapglb2xN 41021 pmapglbx 41018 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 41101 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 40726 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 41045 paddclN 41091 paddidm 41090 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 40727 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 41087 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 40726 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 40727 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19919 lsmmod2 19920 lssats 40261 shatomici 32990 shatomistici 32993 shmodi 32022 shmodsi 32021 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32932 mdsymlem7 33041 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 32221 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 32125 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 33047 |
| [Margaris] p. 40 | Rule C | exlimiv 1965 |
| [Margaris] p. 49 | Axiom A1 | ax-1 6 |
| [Margaris] p. 49 | Axiom A2 | ax-2 7 |
| [Margaris] p. 49 | Axiom A3 | ax-3 8 |
| [Margaris] p. 49 | Definition | df-an 402 df-ex 1813 df-or 862 dfbi2 480 |
| [Margaris] p. 51 | Theorem 1 | idALT 24 |
| [Margaris] p. 56 | Theorem 3 | conventions 31031 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 46088 |
| [Margaris] p. 60 | Theorem 8 | jcn 163 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 46089 |
| [Margaris] p. 79 | Rule C | exinst01 45799 exinst11 45800 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 2011 19.2g 2228 r19.2z 4458 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2242 rr19.3v 3624 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2199 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1859 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1814 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2221 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2245 19.9h 2323 exlimd 2258 exlimdh 2327 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2202 excomim 2203 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2361 |
| [Margaris] p. 90 | Section 19 | conventions-labels 31032 conventions-labels 31032 conventions-labels 31032 conventions-labels 31032 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1860 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 45554 albi 1851 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2265 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2266 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 45556 exbi 1880 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2269 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 45553 2alimdv 1953 alimd 2252 alimdh 1850 alimdv 1951 ax-4 1842 ralimdaa 3267 ralimdv 3180 ralimdva 3178 ralimdvva 3213 sbcimdv 3810 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2247 19.21h 2324 19.21t 2246 19.21vv 45552 alrimd 2255 alrimdd 2254 alrimdh 1896 alrimdv 1964 alrimi 2253 alrimih 1857 alrimiv 1962 alrimivv 1963 bj-alrimdh 37672 hbralrimi 3156 r19.21be 3259 r19.21bi 3258 ralrimd 3271 ralrimdv 3164 ralrimdva 3166 ralrimdvv 3210 ralrimdvva 3221 ralrimi 3264 ralrimia 3265 ralrimiv 3157 ralrimiva 3158 ralrimivv 3207 ralrimivva 3209 ralrimivvva 3212 ralrimivw 3162 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 45555 2eximdv 1954 bj-exim 37687 exim 1867 eximd 2256 eximdh 1897 eximdv 1952 rexim 3107 reximd2a 3276 reximdai 3268 reximdd 46368 reximddv 3182 reximddv2 3225 reximddv3 3183 reximdv 3181 reximdv2 3176 reximdva 3179 reximdvai 3177 reximdvva 3214 reximi2 3099 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2251 19.23bi 2231 19.23h 2325 19.23t 2250 exlimdv 1968 exlimdvv 1969 exlimexi 45698 exlimiv 1965 exlimivv 1967 rexlimd3 46364 rexlimdv 3165 rexlimdv3a 3171 rexlimdva 3167 rexlimdva2 3169 rexlimdvaa 3168 rexlimdvv 3222 rexlimdvva 3223 rexlimdvvva 3224 rexlimdvw 3172 rexlimiv 3160 rexlimiva 3159 rexlimivv 3208 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 2026 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1915 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1903 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2267 r19.27z 4469 r19.27zv 4470 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2268 19.28vv 45562 r19.28z 4461 r19.28zf 46379 r19.28zv 4465 rr19.28v 3625 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1908 r19.29d2r 3153 r19.29imd 3131 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1916 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2274 19.31vv 45560 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2273 r19.32 48374 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 45558 19.33 1919 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 2027 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1912 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2270 19.36vv 45559 r19.36zv 4471 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2272 19.37vv 45561 r19.37zv 4466 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1872 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 2025 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1922 19.40 1921 r19.40 3132 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2275 19.41rg 45724 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2276 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1917 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2277 r19.44zv 4468 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2278 r19.45zv 4467 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2638 |
| [Mayet] p. 370 | Remark | jpi 32902 largei 32899 stri 32889 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32844 ishst 32846 |
| [Mayet3] p. 10 | Theorem | hstrbi 32898 hstri 32897 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 32360 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 32361 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32910 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31964 chsupcl 31972 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32992 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32986 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 33013 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 41232 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18690 latj32 18688 latjass 18686 |
| [Megill] p. 444 | Axiom C5 | ax-5 1945 ax5ALT 40156 |
| [Megill] p. 444 | Section 7 | conventions 31031 |
| [Megill] p. 445 | Lemma L12 | aecom-o 40150 ax-c11n 40137 axc11n 2458 |
| [Megill] p. 446 | Lemma L17 | equtrr 2057 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 40145 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 40177 hbnae 2464 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2513 sbid 2294 sbidd-misc 51092 sbidd 51091 |
| [Megill] p. 448 | Remark 9.6 | axc14 2495 |
| [Megill] p. 448 | Scheme C4' | ax-c4 40133 |
| [Megill] p. 448 | Scheme C5' | ax-c5 40132 sp 2223 |
| [Megill] p. 448 | Scheme C6' | ax-11 2197 |
| [Megill] p. 448 | Scheme C7' | ax-c7 40134 |
| [Megill] p. 448 | Scheme C8' | ax-7 2043 |
| [Megill] p. 448 | Scheme C9' | ax-c9 40139 |
| [Megill] p. 448 | Scheme C10' | ax-6 2002 ax-c10 40135 |
| [Megill] p. 448 | Scheme C11' | ax-c11 40136 |
| [Megill] p. 448 | Scheme C12' | ax-8 2149 |
| [Megill] p. 448 | Scheme C13' | ax-9 2157 |
| [Megill] p. 448 | Scheme C14' | ax-c14 40140 |
| [Megill] p. 448 | Scheme C15' | ax-c15 40138 |
| [Megill] p. 448 | Scheme C16' | ax-c16 40141 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 40153 dral1 2471 dral2-o 40179 dral2 2470 drex1 2473 drex2 2474 drsb1 2527 drsb2 2304 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2212 sbequ 2122 sbid2v 2541 |
| [Megill] p. 450 | Example in Appendix | hba1-o 40146 hba1 2330 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 48167 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 24 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3830 rspsbca 3831 stdpc4 2107 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 40133 ra4 3837 stdpc5 2248 |
| [Mendelson] p. 81 | Rule C | exlimiv 1965 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2063 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2289 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3741 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5491 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4351 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4352 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4225 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4282 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4226 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4080 |
| [Mendelson] p. 231 | Definition of union | dfun3 4224 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5423 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4578 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5546 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4579 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5547 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4894 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5810 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6289 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7813 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6386 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8632 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9187 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 9108 xpsneng 9109 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9115 xpcomeng 9116 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9118 |
| [Mendelson] p. 255 | Definition | brsdom 9029 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9111 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8879 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 9093 mapsnend 9092 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9193 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9192 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8938 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 9096 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9112 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10284 djucomen 10283 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10288 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10282 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8567 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8594 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10670 |
| [Mendelson] p. 281 | Definition | df-r1 9795 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9848 |
| [Mendelson] p. 287 | Axiom system MK | ru 3741 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30890 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30925 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30927 vdgn1frgrv3 30928 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30929 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30922 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30915 2pthfrgrrn 30913 2pthfrgrrn2 30914 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31884 |
| [Monk1] p. 22 | Remark | conventions 31031 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 31031 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4138 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5764 ssrelf 33281 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5765 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5171 |
| [Monk1] p. 36 | Theorem 3.7(i) | bj-coi1 38152 coi1 6279 coi2 6280 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5909 rn0 5915 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 5870 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5673 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5918 rnxp 6174 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5755 xp0 5756 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6087 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6084 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7950 imaexg 7949 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6210 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7099 funfvop 7072 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6962 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6973 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6606 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7281 dff13f 7282 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7248 funrnex 7990 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7274 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6241 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4927 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 8042 df-1st 8025 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 8043 df-2nd 8026 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9895 ranksnb 9864 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9896 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9897 rankunb 9891 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9877 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9795 r1val2 9876 |
| [Monk1] p. 117 | Lemma | zorn2 10611 zorn2g 10608 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 10094 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10672 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 10089 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1842 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2043 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2216 ax-c15 40138 ax12v2 2218 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 40133 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2197 |
| [Monk2] p. 109 | Lemma 15 | equvini 2487 equvinv 2064 eqvinop 5460 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1945 ax5ALT 40156 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2180 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2197 |
| [Monk2] p. 114 | Lemma 21 | sp 2223 |
| [Monk2] p. 114 | Lemma 22 | axc4 2355 hba1-o 40146 hba1 2330 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2193 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2213 nfra2 3365 nfra2w 3302 |
| [Moore] p. 53 | Part I | df-mre 17785 |
| [Munkres] p. 77 | Example 2 | distop 23343 indistop 23350 indistopon 23349 |
| [Munkres] p. 77 | Example 3 | fctop 23352 fctop2 23353 |
| [Munkres] p. 77 | Example 4 | cctop 23354 |
| [Munkres] p. 78 | Definition of basis | df-bases 23294 isbasis3g 23297 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17643 tgval2 23304 |
| [Munkres] p. 79 | Remark | tgcl 23317 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 23311 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 23335 tgss3 23334 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 23336 basgen2 23337 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 38464 topdifinfeq 38465 topdifinffin 38463 topdifinfindis 38461 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23508 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 23386 topcld 23383 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 23387 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 23389 |
| [Munkres] p. 94 | Definition of closure | clsval 23385 |
| [Munkres] p. 94 | Definition of interior | ntrval 23384 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 23423 elcls 23421 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 23431 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23496 neindisj 23465 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23498 |
| [Munkres] p. 97 | Definition of limit point | islp2 23493 lpval 23487 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23663 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23575 iscn 23583 iscn2 23586 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23628 cncnp2 23629 cncnpi 23626 df-cnp 23576 iscnp 23585 iscnp2 23587 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24892 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25662 |
| [Nathanson] p. 123 | Remark | reprgt 35320 reprinfz1 35321 reprlt 35318 |
| [Nathanson] p. 123 | Definition | df-repr 35308 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 35340 |
| [Nathanson] p. 123 | Proposition | breprexp 35332 breprexpnat 35333 itgexpif 35305 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32736 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 49113 |
| [Pfenning] p. 17 | Definition XM | natded 31034 |
| [Pfenning] p. 17 | Definition NNC | natded 31034 notnotrd 134 |
| [Pfenning] p. 17 | Definition ` `C | natded 31034 |
| [Pfenning] p. 18 | Rule" | natded 31034 |
| [Pfenning] p. 18 | Definition /\I | natded 31034 |
| [Pfenning] p. 18 | Definition ` `E | natded 31034 natded 31034 natded 31034 natded 31034 natded 31034 |
| [Pfenning] p. 18 | Definition ` `I | natded 31034 natded 31034 natded 31034 natded 31034 natded 31034 |
| [Pfenning] p. 18 | Definition ` `EL | natded 31034 |
| [Pfenning] p. 18 | Definition ` `ER | natded 31034 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 31034 |
| [Pfenning] p. 18 | Definition ` `IR | natded 31034 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 31034 |
| [Pfenning] p. 127 | Definition =E | natded 31034 |
| [Pfenning] p. 127 | Definition =I | natded 31034 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25553 df-dip 31333 dip0l 31350 ip0l 21972 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25594 ipval 31335 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 31346 ipcj 21970 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25556 dipdir 31474 ipdir 21975 ipdiri 31462 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 31342 nmsq 25545 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 31457 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 31459 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 31460 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25562 dipass 31477 ipass 21981 ipassi 31473 |
| [Prugovecki] p. 186 | Definition of bra | braval 32576 df-bra 32482 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 32483 kbval 32586 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 33014 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 41137 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 33028 atcvat4i 33029 cvrat3 40691 cvrat4 40692 lsatcvat3 40301 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32914 cvrval 40518 df-cv 32911 df-lcv 40268 lspsncv0 21454 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 41149 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 41150 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2742 rabid 3436 rabidd 46375 wl-df.clab 38622 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2316 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2755 wl-df.cleq 38623 |
| [Quine] p. 19 | Definition 2.9 | conventions 31031 df-v 3456 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2903 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2900 abid2f 2956 |
| [Quine] p. 37 | Paragraph 1 | mirimanoff 36628 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2313 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2124 sbalex 2282 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2839 wl-df.clel 38626 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2763 eqid1 31098 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2770 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3743 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3744 dfsbcq2 3745 |
| [Quine] p. 43 | Theorem 6.8 | vex 3458 |
| [Quine] p. 43 | Theorem 6.9 | isset 3468 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3549 spcgv 3554 spcimgf 3517 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3755 spsbcd 3756 |
| [Quine] p. 44 | Theorem 6.12 | elex 3475 |
| [Quine] p. 44 | Theorem 6.13 | elab 3636 elabg 3633 elabgf 3631 |
| [Quine] p. 44 | Theorem 6.14 | noel 4286 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4678 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4591 df-sn 4589 |
| [Quine] p. 49 | Theorem 7.4 | snss 4745 snssg 4744 |
| [Quine] p. 49 | Theorem 7.5 | prss 4779 prssg 4778 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4723 prid1g 4721 prid2 4724 prid2g 4722 snid 4623 snidg 4621 |
| [Quine] p. 51 | Theorem 7.12 | snex 5401 |
| [Quine] p. 51 | Theorem 7.13 | prex 5400 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4889 unisnALT 46099 unisng 4888 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4893 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4902 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4899 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6526 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 48361 dfiota2 6513 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 48370 iotaval 6530 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6537 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6533 |
| [Quine] p. 58 | Definition 9.1 | df-op 4839 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5503 opabidw 5502 opelopab 5521 opelopaba 5514 opelopabaf 5523 opelopabf 5524 opelopabg 5517 opelopabga 5511 opelopabgf 5519 oprabid 7475 oprabidw 7474 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5661 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5663 |
| [Quine] p. 64 | Definition 9.15 | df-id 5550 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6627 |
| [Quine] p. 65 | Theorem 10.4 | funi 6592 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6615 funsng 6613 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6560 |
| [Quine] p. 65 | Definition 10.2 | args 6102 dffv4 6905 |
| [Quine] p. 68 | Definition 10.11 | conventions 31031 df-fv 6566 fv2 6903 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14443 nn0opth2i 14442 nn0opthi 14441 omopthi 8698 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8446 |
| [Quine] p. 232 | Equation i | carddom 10665 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6649 funimaexg 6648 |
| [Quine] p. 331 | Axiom system NF | ru 3741 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31716 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 31333 polid 31791 polid2i 31789 polidi 31790 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 31445 |
| [ReedSimon] p. 195 | Remark | lnophm 32651 lnophmi 32650 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32764 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32766 leopmuli 32765 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32769 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 32484 leoppos 32758 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32768 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32757 |
| [Ribenboim] p. 181 | Remark | nprmdvdsfacm1 48914 |
| [Ribenboim], p. 181 | Statement | ppivalnn 48922 |
| [Roman] p. 4 | Definition | df-dmat 22835 df-dmatalt 49715 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20405 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20491 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 49802 |
| [Roman] p. 112 | Note | isldepslvec2 49802 ldepsnlinc 49825 zlmodzxznm 49814 |
| [Roman] p. 112 | Example | zlmodzxzequa 49813 zlmodzxzequap 49816 zlmodzxzldep 49821 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 23238 |
| [Rosenlicht] p. 80 | Theorem | heicant 38765 |
| [Rosser] p. 281 | Definition | df-op 4839 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 35344 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 35345 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 49683 pmtr3ncom 19719 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19715 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19658 cayleyth 19659 |
| [Rudin] p. 164 | Equation 27 | efcan 16291 |
| [Rudin] p. 164 | Equation 30 | efzval 16299 |
| [Rudin] p. 167 | Equation 48 | absefi 16393 |
| [Russell1905] p. 482 | Example of "the father | dfalseu2 51212 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 200 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1804 |
| [Sanford] p. 39 | Rule 4 | mptxor 1802 |
| [Sanford] p. 40 | Rule 1 | mptnan 1801 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6121 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6124 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6120 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6118 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17785 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17786 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17786 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17788 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10242 |
| [Schechter] p. 141 | Definition (MC) | dfac11 44257 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10551 axdc3 10559 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20493 isrngo 39023 |
| [Schechter] p. 276 | Remark 11.6.e | span0 32174 |
| [Schechter] p. 276 | Definition of span | df-span 31941 spanval 31965 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 23341 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6405 onelond 37126 onelord 44445 ordelon 6404 ordelord 6402 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 44446 sucidg 6464 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6436 onsuc 7848 ord0 6435 ordsuci 7846 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 44447 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5219 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 44228 elon2 6391 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6386 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5558 epelg 5556 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9621 epirron 44448 ordirr 6398 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 44450 oneptr 44449 ontr1 6428 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6424 oneptri 44451 ordtri3or 6413 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8537 ord0eln0 6437 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6450 onsucss 44460 trsucss 6471 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7853 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6477 ordnbtwn 6476 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 44462 ordnexbtwnsuc 44461 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10506 onsucf1lem 44463 onsucf1o 44466 onsucf1olem 44464 onsucrn 44465 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 44467 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7880 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 44456 ordne0gt0 44455 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 44458 limnsuc 44459 onsucelab 44457 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9671 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7895 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9674 ordom 7911 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9675 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8677 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7818 ssorduni 7817 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8567 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9678 limom 7917 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8504 df1o2 8511 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8552 oa0suclim 44469 oalim 8568 oasuc 8560 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8553 om0suclim 44470 omlim 8569 omsuc 8562 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8558 oe0m1 8557 oe0suclim 44471 oelim 8570 oesuc 8563 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 44423 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 44473 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 44474 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 44475 limexissupab 44477 limiun 44476 limuni 6443 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8574 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8578 om1om1r 44478 om1r 8579 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8571 oaomoecl 44472 oecl 8573 omcl 8572 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 44425 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8580 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8581 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 44479 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 44480 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8648 nnamecl 44481 nnecl 8650 nnmcl 8649 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 44482 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8588 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8589 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8596 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 44484 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 44485 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 44487 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8595 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 44491 omword1 8609 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 44490 oaordnrex 44489 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 44486 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 44492 omword2 8610 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 44493 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 44494 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 44495 omordi 8602 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8604 omord2com 44496 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 44497 df-2o 8505 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 44500 oewordi 8628 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 44501 oeworde 8630 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 44502 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 44503 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 44499 omnord1ex 44498 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 44504 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 44506 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 44510 oenord1ex 44509 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 44511 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8597 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 44505 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8615 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8616 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 44513 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8634 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 44514 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 44515 cantnfub2 44516 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 44519 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 29522 axtgcgrrflx 28954 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 29523 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 29524 axtgcgrid 28955 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28940 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 29535 axtgsegcon 28956 df-trkgcb 28942 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 29546 axtg5seg 28957 df-trkgcb 28942 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 29547 axtgbtwnid 28958 df-trkgb 28941 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 29549 axtgpasch 28959 df-trkgb 28941 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 29568 df-trkg2d 35364 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28962 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28963 df-trkg2d 35364 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 29571 axtgeucl 28964 df-trkge 28943 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 29584 axtgcont 28961 axtgcont1 28960 df-trkgb 28941 |
| [Schwabhauser] p. 24 | Theorem A10 | prlngmo 29462 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 36930 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 36932 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 36935 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 36939 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 36940 tgcgrcomimp 28969 tgcgrcoml 28971 tgcgrcomr 28970 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 36945 tgcgrtriv 28976 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 36949 tg5segofs 35375 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 35372 df-ofs 36926 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 36951 tgcgrextend 28977 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 36953 tgsegconeq 28978 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36965 btwntriv2 36955 tgbtwntriv2 28980 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 36956 tgbtwncom 28981 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36959 tgbtwntriv1 28984 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36960 tgbtwnswapid 28985 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36966 btwnintr 36962 tgbtwnexch2 28989 tgbtwnintr 28986 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36968 btwnexch3 36963 tgbtwnexch 28991 tgbtwnexch3 28987 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36967 tgbtwnouttr 28990 tgbtwnouttr2 28988 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 29567 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36970 tgbtwndiff 28999 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28992 trisegint 36971 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36987 tgifscgr 29001 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 29051 colrot1 29052 colrot2 29053 lncom 29120 lnrot1 29121 lnrot2 29122 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36983 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36988 tgcgrsub 29002 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36998 tgcgrxfr 29011 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 29010 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36984 df-cgrg 29004 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 29004 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36999 tgbtwnxfr 29023 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 37005 colinearperm2 37007 colinearperm3 37006 colinearperm4 37008 colinearperm5 37009 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 29026 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36982 tgellng 29046 tglng 29039 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 37010 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 37018 lnxfr 29059 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 37019 lnext 29060 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 37023 tgfscgr 29061 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 37024 lncgr 29062 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36985 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 37026 lnid 29063 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 37027 tgidinside 29064 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 37044 tgbtwnconn1 29068 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 37045 tgbtwnconn2 29069 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 37046 tgbtwnconn3 29070 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 37052 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 37050 legov 29078 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 29079 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 29092 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 37053 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 37055 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 37057 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 37058 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 37059 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 37056 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 37061 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 29080 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 29082 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 29083 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 29084 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 29085 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 37068 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 37069 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 37064 df-outsideof 37063 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 37065 ishlg 29098 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 29103 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 29105 outsideofrflx 37070 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 29099 hlcomd 29100 outsideofcom 37071 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 29106 outsideoftr 37072 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreq 29115 hlcgreu 29114 outsideofeu 37074 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 37081 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 37082 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 37075 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 37090 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 37091 tglineelsb2 29130 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 37093 linerflx1 37092 linerflx2 37094 tglinecom 29133 tglinerflx1 29131 tglinerflx2 29132 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 37096 tglinethru 29134 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 37080 tglng 29039 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 29087 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 37099 tglinethrueu 29137 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 37100 tglineineq 29141 tglineinsn 29142 tglineinteq 29144 tglineintmo 29140 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 29148 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 29149 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 29150 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 29168 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 29164 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 29156 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 29155 ismir 29161 mirbtwn 29160 mircgr 29159 mirfv 29158 mirval 29157 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 29166 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 29167 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 29168 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 29171 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 29172 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 29177 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 29174 mirbtwni 29173 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 29175 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 29187 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 29191 symquadmid 29334 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 29188 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 29189 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 29190 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 29193 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 29194 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 29203 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 29199 israg 29202 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 29204 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 29205 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 29207 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 29208 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 29209 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 29210 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 29211 ragncol 29214 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 29212 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 29218 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 29222 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 29219 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 29201 isperp 29217 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 29220 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 29227 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 29236 colperpexlem2 29237 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 29239 colperpexlem3 29238 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 29244 midex 29243 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 29241 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 29250 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 29245 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 29254 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 29257 opphllem6 29258 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 29260 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28959 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 29263 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 29271 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 29266 hpgbr 29268 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 29273 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 29272 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 29274 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 29275 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 29276 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 29277 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 29278 |
| [Schwabhauser] p. 74 | Lemma 9.22 | lnincplng 29292 |
| [Schwabhauser] p. 74 | Theorem 9.21 | plngcp 29294 |
| [Schwabhauser] p. 74 | Theorem 9.24 | plngrot 29298 |
| [Schwabhauser] p. 74 | Definition 9.20 | df-plng 29282 elplng 29288 |
| [Schwabhauser] p. 75 | Theorem 9.25 | lnssplng 29300 lnssplng1 29301 |
| [Schwabhauser] p. 76 | Theorem 9.26 | plng3p 29305 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 29319 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 29309 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 29323 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 29324 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 29325 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 29326 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 29327 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 29330 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 29332 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 29310 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 29333 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 29337 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 29338 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 29339 lnperpexs 29340 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 29341 trgcopyeu 29343 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 29368 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 29346 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 29355 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 29353 cgrahl2 29354 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 29356 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 29357 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 29359 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 29360 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 29364 cgrahl 29365 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 29369 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 29370 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 29371 acopyeu 29372 |
| [Schwabhauser] p. 98 | Theorem 11.16 | ragcgra 29373 |
| [Schwabhauser] p. 98 | Theorem 11.17 | cgrarag 29374 |
| [Schwabhauser] p. 98 | Theorem 11.18 | ragsupplcgra 29375 |
| [Schwabhauser] p. 99 | Theorem 11.19 | ragraghl 29376 |
| [Schwabhauser] p. 99 | Theorem 11.20 | perpeq 29378 |
| [Schwabhauser] p. 99 | Theorem 11.22 | tgaaddcpbl 29382 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 29390 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 29394 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 29387 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 29402 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 29395 isleag 29396 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 29430 tgsas1 29429 tgsas2 29431 tgsas3 29432 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 29434 tgasa1 29433 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 29435 tgsss2 29436 tgsss3 29437 |
| [Schwabhauser] p. 121 | Definition 12.2 | df-prlng 29445 |
| [Schwabhauser] p. 122 | Theorem 12.4 | prlngref 29448 |
| [Schwabhauser] p. 122 | Theorem 12.5 | prlngsym 29449 |
| [Schwabhauser] p. 122 | Theorem 12.6 | prlnghpg 29454 |
| [Schwabhauser] p. 122 | Theorem 12.7 | dfprlng2 29455 dfprlng3 29456 |
| [Schwabhauser] p. 122 | Theorem 12.9 | perpprlng 29458 |
| [Schwabhauser] p. 122 | Theorem 12.10 | prlngex 29459 |
| [Schwabhauser] p. 123 | Theorem 12.11 | prlngmo 29462 prlngmo2 29464 |
| [Schwabhauser] p. 124 | Theorem 12.13 | prlngeu 29463 |
| [Schwabhauser] p. 124 | Theorem 12.14 | prlngpln4 29466 |
| [Schwabhauser] p. 124 | Theorem 12.15 | prlngplngtr 29467 |
| [Schwabhauser] p. 125 | Theorem 12.16 | prlnginn0 29468 |
| [Schwabhauser] p. 125 | Theorem 12.17 | prlngmid2 29469 |
| [Schwabhauser] p. 126 | Theorem 12.18 | symquadprlng 29470 |
| [Schwabhauser] p. 126 | Theorem 12.19 | prlngsymquad 29472 prlngsymquadopp 29473 |
| [Schwabhauser] p. 126 | Theorem 12.20 | quadcgrprlng 29474 |
| [Schwabhauser] p. 126 | Theorem 12.21 | tgaltai 29475 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27628 dchrsum 27626 dchrsum2 27625 sumdchr 27629 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27630 sum2dchr 27631 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 20312 ablfacrp2 20313 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27573 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27574 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27581 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27839 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27842 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27896 vmalogdivsum2 27895 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27886 dirith2 27885 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27884 rpvmasum 27883 rpvmasum2 27869 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27844 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27882 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27849 dchrisumlem1 27846 dchrisumlem2 27847 dchrisumlem3 27848 dchrisumlema 27845 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27852 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27881 dchrmusumlem 27879 dchrvmasumlem 27880 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27851 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27853 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27877 dchrisum0re 27870 dchrisumn0 27878 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27863 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27867 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27868 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27923 pntrsumbnd2 27924 pntrsumo1 27922 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27887 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27889 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27891 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27894 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27899 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27900 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27905 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27907 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27908 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27916 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27917 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27914 selberg3lem2 27915 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27918 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27912 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27925 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27926 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27927 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27941 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27953 pntlemb 27954 pntlemc 27952 pntlemd 27951 pntlemg 27955 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27953 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27945 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27950 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27953 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27966 pntleml 27968 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 34445 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 34432 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 34464 constrinvcl 34475 constrmulcl 34473 constrnegcl 34465 constrsqrtcl 34481 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 34451 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 34461 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 34483 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 34493 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4254 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4359 dif0 4330 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4450 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4432 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4245 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4246 |
| [Stoll] p. 20 | Remark | invdif 4227 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4862 |
| [Stoll] p. 43 | Definition | uniiun 5020 |
| [Stoll] p. 44 | Definition | intiin 5021 |
| [Stoll] p. 45 | Definition | df-iin 4957 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4956 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 407 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4254 |
| [Strang] p. 242 | Section 6.3 | expgrowth 45511 |
| [Suppes] p. 22 | Theorem 2 | eq0 4300 eq0f 4297 |
| [Suppes] p. 22 | Theorem 4 | eqss 3928 eqssd 3930 eqssi 3929 |
| [Suppes] p. 23 | Theorem 5 | ss0 4355 ss0b 4354 |
| [Suppes] p. 23 | Theorem 6 | sstr 3921 sstrALT2 46008 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4033 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4035 |
| [Suppes] p. 23 | Theorem 9 | psstr 4038 |
| [Suppes] p. 23 | Theorem 10 | pssss 4028 |
| [Suppes] p. 25 | Theorem 12 | elin 4096 elun 4155 |
| [Suppes] p. 26 | Theorem 15 | inidm 4126 |
| [Suppes] p. 26 | Theorem 16 | in0 4348 |
| [Suppes] p. 27 | Theorem 23 | unidm 4159 |
| [Suppes] p. 27 | Theorem 24 | un0 4347 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4179 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4187 |
| [Suppes] p. 27 | Theorem 27 | unss 4191 |
| [Suppes] p. 27 | Theorem 28 | indir 4234 |
| [Suppes] p. 27 | Theorem 29 | undir 4235 |
| [Suppes] p. 28 | Theorem 32 | difid 4328 |
| [Suppes] p. 29 | Theorem 33 | difin 4220 |
| [Suppes] p. 29 | Theorem 34 | indif 4228 |
| [Suppes] p. 29 | Theorem 35 | undif1 4433 |
| [Suppes] p. 29 | Theorem 36 | difun2 4440 |
| [Suppes] p. 29 | Theorem 37 | difin0 4431 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4429 |
| [Suppes] p. 29 | Theorem 39 | difundi 4238 |
| [Suppes] p. 29 | Theorem 40 | difindi 4240 |
| [Suppes] p. 30 | Theorem 41 | nalset 5271 |
| [Suppes] p. 39 | Theorem 61 | uniss 4878 |
| [Suppes] p. 39 | Theorem 65 | uniop 5492 |
| [Suppes] p. 41 | Theorem 70 | intsn 4947 |
| [Suppes] p. 42 | Theorem 71 | intpr 4945 intprg 4944 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5444 |
| [Suppes] p. 42 | Theorem 78 | intun 4943 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4993 dfiun2g 4991 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4994 |
| [Suppes] p. 47 | Theorem 86 | elpw 4564 elpw2 5300 elpw2g 5299 elpwg 4563 elpwgdedVD 46090 |
| [Suppes] p. 47 | Theorem 87 | pwid 4584 |
| [Suppes] p. 47 | Theorem 89 | pw0 4833 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4834 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5670 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5816 xpindir 5817 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5724 xpundir 5725 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9618 |
| [Suppes] p. 58 | Theorem 2 | relss 5763 |
| [Suppes] p. 59 | Theorem 4 | eldm 5889 eldm2 5890 eldm2g 5888 eldmg 5887 |
| [Suppes] p. 59 | Definition 3 | df-dm 5665 |
| [Suppes] p. 60 | Theorem 6 | dmin 5900 |
| [Suppes] p. 60 | Theorem 8 | rnun 6148 |
| [Suppes] p. 60 | Theorem 9 | rnin 6149 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5877 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5867 brcnvg 5864 |
| [Suppes] p. 62 | Equation 5 | elcnv 5861 elcnv2 5862 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6112 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6147 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6145 |
| [Suppes] p. 63 | Definition | dftrrels2 39783 |
| [Suppes] p. 63 | Theorem 20 | co02 6277 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5964 |
| [Suppes] p. 63 | Definition 7 | df-co 5664 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5874 |
| [Suppes] p. 64 | Theorem 27 | coass 6284 |
| [Suppes] p. 65 | Theorem 31 | resundi 5995 |
| [Suppes] p. 65 | Theorem 34 | elima 6073 elima2 6074 elima3 6075 elimag 6072 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6153 |
| [Suppes] p. 66 | Theorem 40 | dminss 6155 |
| [Suppes] p. 66 | Theorem 41 | imainss 6156 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6159 |
| [Suppes] p. 81 | Definition 34 | dfec2 8748 |
| [Suppes] p. 82 | Theorem 72 | elec 8792 elecALTV 39395 elecg 8790 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 39819 erth 8800 erth2 8801 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 39822 erdisj 8803 |
| [Suppes] p. 83 | Definition 35, | df-parts 39992 dfmembpart2 39997 |
| [Suppes] p. 89 | Theorem 96 | map0b 8939 |
| [Suppes] p. 89 | Theorem 97 | map0 8943 map0g 8940 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8944 mapsnd 8942 |
| [Suppes] p. 89 | Theorem 99 | mapss 8945 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 10174 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 10173 |
| [Suppes] p. 92 | Theorem 1 | enref 9040 enrefg 9039 |
| [Suppes] p. 92 | Theorem 2 | ensym 9058 ensymb 9057 ensymi 9059 |
| [Suppes] p. 92 | Theorem 3 | entr 9061 |
| [Suppes] p. 92 | Theorem 4 | unen 9101 |
| [Suppes] p. 94 | Theorem 15 | endom 9034 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 9055 |
| [Suppes] p. 94 | Theorem 17 | domtr 9062 |
| [Suppes] p. 95 | Theorem 18 | sbth 9144 |
| [Suppes] p. 97 | Theorem 23 | canth2 9177 canth2g 9178 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9148 df-sdom 9004 dfsdom2 9147 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9161 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9150 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9149 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9159 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 9037 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9162 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9157 |
| [Suppes] p. 98 | Exercise 4 | fundmen 9087 fundmeng 9088 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9122 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9158 |
| [Suppes] p. 104 | Theorem 37 | fofi 9333 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9338 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9338 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10662 |
| [Suppes] p. 130 | Definition 3 | df-tr 5216 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7818 |
| [Suppes] p. 134 | Definition 6 | df-suc 6386 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7936 finds 7932 finds1 7935 finds2 7934 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9680 isfinite2 9318 isfiniteg 9320 unbnn 9316 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 11030 df-ltpq 11022 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7898 tfinds 7895 tfinds2 7899 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8587 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8589 |
| [Suppes] p. 211 | Theorem 25 | oaass 8597 |
| [Suppes] p. 225 | Definition 8 | iscard2 10084 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10674 |
| [Suppes] p. 228 | Theorem 59 | harcard 10086 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 10172 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6433 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7831 onminsb 7832 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10684 |
| [Suppes] p. 229 | Theorem 65 | alephcard 10176 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 10183 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 10177 |
| [Suppes] p. 229 | Definition 12 | df-aleph 10048 |
| [Suppes] p. 242 | Theorem 6 | weth 10600 |
| [Suppes] p. 242 | Theorem 8 | entric 10668 |
| [Suppes] p. 242 | Theorem 9 | carden 10662 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 36639 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 36643 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2735 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2755 wl-df.cleq 38623 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2839 wl-df.clel 38626 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2757 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2783 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7447 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3741 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5387 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4609 elpr2 4611 elpr2g 4610 elprg 4607 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4599 elsn2 4626 elsn2g 4625 elsng 4598 velsn 4600 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5440 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4594 sneqr 4798 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4605 dfsn2 4597 dfsn2ALT 4606 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7782 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5449 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5436 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5420 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7785 unexg 7784 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4652 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4871 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 4094 df-un 4154 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4887 uniprg 4886 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5343 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4650 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6453 elsucg 6451 sstr2 3920 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4160 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4109 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4173 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4127 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4232 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4233 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 4017 df-ss 3901 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4562 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4188 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 4097 sseqin2 4123 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3935 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4136 inss2 4137 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 3977 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4881 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5421 sspwimp 46091 sspwimpALT 46098 sspwimpALT2 46101 sspwimpcf 46093 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5428 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5235 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3417 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5264 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 4050 |
| [TakeutiZaring] p. 20 | Definition 5.14 | bj-dfnul2 37618 dfnul2 4284 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4328 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4303 n0f 4299 neq0 4302 neq0f 4298 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9617 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9760 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9775 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3456 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5278 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4353 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5286 ssexg 5285 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5281 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9629 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9621 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4317 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4074 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4248 undif3VD 46055 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4075 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4082 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3081 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3091 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7791 xpexg 7788 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5662 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6633 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6811 fun11 6636 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6571 svrelfun 6634 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5876 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5878 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5667 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5668 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5664 |
| [TakeutiZaring] p. 25 | Exercise 2 | bj-dfrel2 38147 cnvcnvss 6198 dfrel2 6193 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5671 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5794 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5801 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5815 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 6007 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5987 opelresi 5989 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 6015 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 6003 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 6009 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6602 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6116 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6600 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6813 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2637 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 31031 df-fv 6566 fv3 6926 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7961 cnvexg 7960 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7945 dmexg 7937 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7946 rnexg 7938 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 45627 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7956 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6921 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 48449 tz6.12-1-afv2 48516 tz6.12-1 6931 tz6.12-afv 48448 tz6.12-afv2 48515 tz6.12 6932 tz6.12c-afv2 48517 tz6.12c 6930 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 48512 tz6.12-2 6895 tz6.12i-afv2 48518 tz6.12i 6934 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6561 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6562 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6564 wfo 6556 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6563 wf1 6555 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6565 wf1o 6557 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 7052 eqfnfv2 7053 eqfnfv2f 7056 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 7006 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7246 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7244 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6649 funimaexg 6648 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5107 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5564 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5616 dffr3 6109 eliniseg 6104 iniseg 6107 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5555 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5632 fr3nr 7810 frirr 5631 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5608 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7812 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5619 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5641 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6368 tz6.26i 6369 wefrc 5649 wereu2 5652 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6370 wfii 6371 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6567 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7360 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7361 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7367 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7368 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7369 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7373 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7380 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7382 |
| [TakeutiZaring] p. 35 | Notation | wtr 5215 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 45628 tz7.2 5638 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5220 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6393 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6401 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6402 ordelordALT 45711 ordelordALTVD 46040 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6408 ordelssne 6407 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6406 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6411 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7820 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7821 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6384 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6413 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 45723 ordon 7815 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7816 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7888 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6429 ontr2d 37127 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5217 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7830 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7866 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6487 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6486 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7817 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4902 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6386 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6463 sucidg 6464 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7848 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6477 ordnbtwn 6476 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7863 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6385 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7916 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7921 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7876 ordelsuc 7855 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7857 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7886 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7903 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7924 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7925 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7926 |
| [TakeutiZaring] p. 43 | Remark | omon 7913 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9663 omex 9671 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7911 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7931 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7928 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7929 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7906 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4925 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5234 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4926 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5309 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7833 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6432 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4911 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9688 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7828 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8411 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8433 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8434 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8435 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8442 tz7.44-2 8443 tz7.44-3 8444 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8403 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8398 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8382 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8483 tz7.49c 8484 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8481 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8480 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8482 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2683 |
| [TakeutiZaring] p. 54 | Definition 7.55 | df-lexo 35989 |
| [TakeutiZaring] p. 54 | Definition 7.57 | df-r0 35990 |
| [TakeutiZaring] p. 54 | Proposition 7.58 | r0weseon 36000 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 10117 lexoweon 35998 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 10118 |
| [TakeutiZaring] p. 55 | Definition 7.59 | df-j0 35991 j0iso 36004 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8568 oasuc 8560 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7896 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8571 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8552 oa0r 8574 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8572 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8584 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8656 nnaordi 8655 oaord 8583 oaordi 8582 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5011 uniss2 4905 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8586 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8591 oawordex 8593 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8648 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8685 |
| [TakeutiZaring] p. 60 | Remark | oancom 9679 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8596 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8653 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8588 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8555 omlim 8569 omsuc 8562 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8553 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8650 nnmcl 8649 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8669 nnmordi 8668 omord 8604 omordi 8602 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8605 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8673 omwordri 8608 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8575 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8578 om1r 8579 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8611 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8613 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8614 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8615 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8616 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8645 oe0 8558 oelim 8570 oesuc 8563 onesuc 8566 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8556 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8623 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8624 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8557 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8581 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8625 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8631 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8629 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8630 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8634 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8636 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9756 tz9.1 9757 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9795 r10 9802 r1lim 9806 r1limg 9805 r1suc 9804 r1sucg 9803 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9814 r1ord2 9815 r1ordg 9812 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9824 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9851 tz9.13 9825 tz9.13g 9826 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9796 rankval 9852 rankvalb 9832 rankvalg 9853 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9878 rankelb 9860 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9894 rankval3 9880 rankval3b 9863 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9866 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9830 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9873 rankr1c 9857 rankr1g 9871 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9874 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9890 rankssb 9889 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9882 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9881 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10580 dfac3 10227 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 10136 numth 10577 numth2 10576 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10657 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10658 cardid2 10061 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 10068 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10662 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 10067 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 10052 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 10073 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 10065 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9197 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 9073 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9202 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9126 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 10071 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10204 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9249 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9257 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10205 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9254 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10194 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 10172 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 10080 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10321 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9342 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 9005 isfi 9030 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9258 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10640 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9119 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10632 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10291 unxpdom 9278 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 10082 cardsdomelir 10081 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9280 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 10120 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8877 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10673 infxpidm2 10123 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10312 infxp 10319 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9131 pw2f1o 9129 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9190 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10592 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10587 ac6s5 10596 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10654 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10655 uniimadomf 10656 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10379 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10374 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10358 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10355 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10362 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10369 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10378 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10694 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10356 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10381 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10203 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10202 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10214 alephfp2 10215 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10811 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10218 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10681 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10695 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10696 |
| [TakeutiZaring] p. 143 | Definition 14.1(1) | df-cnv2 35952 |
| [TakeutiZaring] p. 143 | Definition 14.1(2) | df-cnv3 35953 |
| [TakeutiZaring] p. 144 | Definition 14.2 | df-gdlop1 35954 df-gdlop2 35955 df-gdlop3 35956 df-gdlop4 35957 df-gdlop5 35958 df-gdlop6 35959 df-gdlop7 35960 df-gdlop8 35961 df-gdlopc 35962 |
| [TakeutiZaring] p. 154 | Proposition 15.1(1) | maxssj0 36006 |
| [TakeutiZaring] p. 154 | Proposition 15.1(2) | j0ltaleph 36008 |
| [TakeutiZaring] p. 155 | Definition 15.2 | df-j 35992 |
| [TakeutiZaring] p. 155 | Proposition 15.3 | jf1 36010 jf1o 36011 |
| [TakeutiZaring] p. 156 | Definition 15.7 | df-k1 35993 df-k2 35994 df-k3 35995 |
| [TakeutiZaring] p. 156 | Proposition 15.8 | jk1k2k3 36018 |
| [TakeutiZaring] p. 156 | Proposition 15.11 | jltaleph 36026 |
| [TakeutiZaring] p. 156 | Proposition 15.10(1) | k1le 36021 k2le 36022 |
| [TakeutiZaring] p. 156 | Proposition 15.10(2) | k3n0k1lt 36023 k3n0k2lt 36024 |
| [TakeutiZaring] p. 158 | Definition 15.13 | df-fnl 35996 |
| [TakeutiZaring] p. 158 | Definition 15.15 | df-l 35997 |
| [TakeutiZaring] p. 158 | Proposition 15.14 | fnlfvk30 36027 fnlfvk3n0 36028 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 40132 |
| [Tarski] p. 67 | Scheme B5 | sp 2223 |
| [Tarski] p. 68 | Lemma 6 | avril1 31094 equid 2047 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2052 |
| [Tarski] p. 70 | Lemma 14 | spim 2419 spime 2421 spimew 2006 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2216 ax-c15 40138 ax12i 2001 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2124 |
| [Tarski] p. 75 | Axiom B7 | ax6v 2003 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1945 ax5ALT 40156 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2043 ax-8 2149 ax-9 2157 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28956 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28957 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28959 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28959 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28960 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16440 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 38769 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 38771 |
| [Weierstrass] p. 272 | Definition | df-mdet 22930 mdetuni 22967 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 917 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 882 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 883 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 933 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 983 |
| [WhiteheadRussell] p. 100 | Theorem *2.01 | pm2.01 190 |
| [WhiteheadRussell] p. 100 | Theorem *2.02 | ax-1 6 |
| [WhiteheadRussell] p. 100 | Theorem *2.03 | con2 136 |
| [WhiteheadRussell] p. 100 | Theorem *2.04 | pm2.04 91 wl-luk-pm2.04 38560 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 44992 imim2 59 wl-luk-imim2 38555 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 48294 imim1 84 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 910 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2690 syl 18 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 916 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 23 wl-luk-id 38558 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 908 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 143 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 911 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 131 notnotrALT2 46100 wl-luk-notnotr 38559 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 147 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 45022 axfrege28 45021 con3 154 |
| [WhiteheadRussell] p. 103 | Theorem *2.17 | ax-3 8 |
| [WhiteheadRussell] p. 103 | Theorem *2.18 | pm2.18 129 |
| [WhiteheadRussell] p. 104 | Theorem *2.2 | orc 881 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 938 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 124 wl-luk-pm2.21 38552 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 125 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 903 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 954 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 31032 pm2.27 43 wl-luk-pm2.27 38550 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 936 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 39495 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 937 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 985 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 986 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 984 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1104 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 920 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 921 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 957 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 57 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 895 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 896 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5 170 pm2.5g 169 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6 193 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 897 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 898 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 899 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 174 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 865 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 866 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 902 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 904 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 194 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 913 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 955 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 956 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 195 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 905 pm2.67 906 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 177 pm2.521g 175 pm2.521g2 176 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 912 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 988 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 914 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 206 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 989 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 990 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 947 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 945 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 987 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 991 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 85 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 946 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 110 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 1007 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 475 pm3.2im 161 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 1008 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 1009 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 1010 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 1011 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 477 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 465 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 408 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 815 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 454 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 455 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 488 simplim 168 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 490 simprim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 777 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 778 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 820 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 634 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 822 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 498 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 499 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 975 pm3.44 974 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 821 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 479 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 978 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34b 319 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 264 |
| [WhiteheadRussell] p. 117 | Theorem *4.11 | notbi 322 |
| [WhiteheadRussell] p. 117 | Theorem *4.12 | con2bi 356 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotb 318 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14 819 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 846 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 225 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 818 bitr 817 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 574 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 918 pm4.25 919 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 466 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1025 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 884 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 474 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 935 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 645 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 931 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 649 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 992 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1105 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1023 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1069 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1040 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 1012 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 1014 pm4.45 1013 pm4.45im 841 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 998 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 867 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 555 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 997 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 1000 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 1001 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 1002 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 1003 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 999 pm4.56 1004 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 1005 pm4.57 1006 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 410 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 870 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 403 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 863 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 411 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 864 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67 404 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 567 pm4.71d 571 pm4.71i 569 pm4.71r 568 pm4.71rd 572 pm4.71ri 570 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 964 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 537 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 950 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 527 pm4.76 528 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 976 pm4.77 977 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 948 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1021 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 398 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81 399 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 1041 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1042 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 350 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 351 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 354 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 392 impexp 456 pm4.87 857 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 836 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 959 pm5.11g 958 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 960 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 962 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 961 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1030 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1031 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1029 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbn 386 pm5.18 384 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 391 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 837 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1032 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1065 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1066 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 915 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 583 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 393 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 364 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6 1017 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 968 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 844 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 584 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 849 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 838 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 847 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 394 pm5.41 395 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 553 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 552 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 1022 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1035 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 963 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1016 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1036 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1037 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1045 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 369 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 273 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 1046 |
| [WhiteheadRussell] p. 145 | Theorem *10.3 | bj-alsyl 37669 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 45534 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 45535 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1903 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 45536 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 45537 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 45538 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1928 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 45539 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 45540 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 45541 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 45542 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 45543 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 45545 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 45546 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 45547 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 45544 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2129 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 45550 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 45551 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2109 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2200 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1862 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1863 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 45552 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 45553 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 45554 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 45555 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 45557 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 45556 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1922 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 45559 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 45560 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 45558 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1861 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 45561 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 45562 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1879 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 45563 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2379 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1893 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 45568 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 45564 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 45565 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 45566 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 45567 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 45572 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 45569 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 45570 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 45571 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 45573 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2597 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 45583 pm13.13b 45584 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 45585 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3040 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3041 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3623 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 45591 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 45592 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 45586 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 45726 pm13.193 45587 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 45588 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 45589 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 45590 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 45596 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 45595 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 45594 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3804 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 45597 pm14.122b 45598 pm14.122c 45599 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 45600 pm14.123b 45601 pm14.123c 45602 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 45604 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 45603 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 45605 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6538 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 45606 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6539 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 45607 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 45609 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2661 eupickbi 2664 sbaniota 45610 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 45608 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2612 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 45611 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 31031 df-fv 6566 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 10109 pm54.43lem 10108 |
| [Young] p. 141 | Definition of operator ordering | leop2 32756 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32762 idleop 32763 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 44028 |
| [vandenDries] p. 43 | Theorem 62 | pellex 44035 pellexlem1 44029 |