Bibliographic Cross-References
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Metamath Proof Explorer Bibliographic Cross-References |
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| Bibliographic Reference | Description | Metamath Proof Explorer Page(s) |
|---|---|---|
| [Adamek] p. 21 | Definition 3.1 | df-cat 17632 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17632 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18041 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17653 0funcg 49576 df-termc 49964 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 50041 prsthinc 49955 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 50069 df-mndtc 50069 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 50065 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17676 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 50057 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 50082 oppgoppchom 50081 oppgoppcid 50083 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17746 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17734 invisoinvl 17755 |
| [Adamek] p. 28 | Example 3.13 | idinv 17754 idiso 17753 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17739 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17713 df-iso 17714 dfiso2 17737 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17720 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17771 cicerALT 49537 |
| [Adamek] p. 29 | Definition 3.15 | cic 17764 df-cic 17761 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17823 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17735 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17736 isoco 17742 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17823 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17846 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 49795 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17839 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 50065 discthing 49952 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 49909 prsthinc 49955 thincciso 49944 thincciso2 49946 thincciso3 49947 thinccisod 49945 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 50069 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17853 cofucla 49587 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 49653 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18076 catcisoi 49891 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18131 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17872 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17871 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18131 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17896 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17902 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17901 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18116 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18116 |
| [Adamek] p. 39 | Remark 3.42 | 2oppf 49623 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 49614 funcoppc 17840 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18064 elcatchom 49888 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17890 fthoppf 49655 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17889 fulloppf 49654 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18073 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 49576 df-catc 18064 |
| [Adamek] p. 45 | Exercise 3G | incat 50092 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 50095 nelsubc3 49562 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 49642 imasubc2 49643 imasubc3 49647 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17803 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17804 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 49562 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17815 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17777 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 49651 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 49650 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 49652 ressffth 17905 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 50093 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 17911 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 17932 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 17936 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 17912 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 17938 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 49576 df-inito 17949 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 49576 df-termc 49964 initc 49582 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21461 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 17950 oppctermo 49727 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 17977 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 17981 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 49728 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 17951 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21462 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 17984 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17712 |
| [Adamek] p. 107 | Example 7.20(7) | thincinv 49960 |
| [Adamek] p. 108 | Example 7.25(4) | thincsect2 49959 |
| [Adamek] p. 110 | Example 7.33(9) | thincmon 49924 |
| [Adamek] p. 110 | Proposition 7.35 | sectmon 17747 |
| [Adamek] p. 112 | Proposition 7.42 | sectepi 17749 |
| [Adamek] p. 185 | Section 10.67 | updjud 9856 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 50136 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 50136 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 50136 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 50137 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 50137 |
| [Adamek] p. 478 | Item Rng | df-ringc 20625 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 49040 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 49062 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14531 df-pfx 14632 df-substr 14602 df-word 14474 lencl 14493 wrd0 14499 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24698 df-nmoo 30841 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32249 hmopidmchi 32247 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32297 pjcmul2i 32298 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 32014 unoplin 32016 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 32015 unopadj2 32034 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 32109 lnopunii 32108 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32182 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 27944 |
| [Alling] p. 184 | Axiom B | bdayfo 27666 |
| [Alling] p. 184 | Axiom O | ltsso 27665 |
| [Alling] p. 184 | Axiom SD | nodense 27681 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27772 |
| [Alling] p. 185 | Theorem | conway 27796 |
| [Alling] p. 185 | Axiom FE | noeta 27732 |
| [Alling] p. 186 | Theorem 4 | lesrec 27816 lesrecd 27817 |
| [Alling], p. 2 | Definition | rp-brsslt 43868 |
| [Alling], p. 3 | Note | nla0001 43871 nla0002 43869 nla0003 43870 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11328 addcan2d 11348 addcan2i 11338 addcand 11347 addcani 11337 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11381 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11440 negsubd 11509 negsubi 11470 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11442 negnegd 11494 negnegi 11462 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11581 subdid 11604 subdii 11597 subdir 11582 subdird 11605 subdiri 11598 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11323 mul01d 11343 mul01i 11334 mul02 11322 mul02d 11342 mul02i 11333 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11785 mulcan2d 11782 mulcand 11781 mulcani 11787 |
| [Apostol] p. 18 | Theorem I.8 | receu 11793 xreceu 33007 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11823 divrecd 11932 divreci 11898 divreczi 11891 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11850 recreci 11885 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11788 mul0ord 11796 mul0ori 11795 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11587 mul2negd 11603 mul2negi 11596 mulneg1 11584 mulneg1d 11601 mulneg1i 11594 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11868 divadddivd 11973 divadddivi 11915 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11853 divmuldivd 11970 divmuldivi 11913 rdivmuldivd 20391 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11854 divdivdivd 11976 divdivdivi 11916 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 12964 rpaddcld 12999 rpmulcl 12965 rpmulcld 13000 |
| [Apostol] p. 20 | Axiom 8 | rpneg 12974 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 12977 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11270 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11741 ltadd1dd 11759 ltadd1i 11702 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12003 ltmul1a 12002 ltmul1i 12072 ltmul1ii 12082 ltmul2 12004 ltmul2d 13026 ltmul2dd 13040 ltmul2i 12075 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11668 msqgt0d 11715 msqgt0i 11685 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11670 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11654 lt0neg1d 11717 ltneg 11648 ltnegd 11726 ltnegi 11692 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11633 lt2addd 11771 lt2addi 11710 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 12941 |
| [Apostol] p. 21 | Exercise 4 | recgt0 11999 recgt0d 12088 recgt0i 12059 recgt0ii 12060 |
| [Apostol] p. 22 | Definition of integers | df-z 12523 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12186 |
| [Apostol] p. 22 | Definition of rationals | df-q 12897 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9364 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12431 |
| [Apostol] p. 26 | Theorem I.29 | arch 12432 archd 45610 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12630 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12433 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12895 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12894 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13149 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16306 zneo 12610 zneoALTV 48161 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26719 msqsqrtd 15403 resqrtth 15215 sqrtth 15325 sqrtthi 15331 sqsqrtd 15402 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12175 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12861 |
| [Apostol] p. 361 | Remark | crreczi 14188 |
| [Apostol] p. 363 | Remark | absgt0i 15360 |
| [Apostol] p. 363 | Example | abssubd 15416 abssubi 15364 |
| [ApostolNT] p. 7 | Remark | fmtno0 48019 fmtno1 48020 fmtno2 48029 fmtno3 48030 fmtno4 48031 fmtno5fac 48061 fmtnofz04prm 48056 |
| [ApostolNT] p. 7 | Definition | df-fmtno 48007 |
| [ApostolNT] p. 8 | Definition | df-ppi 27088 |
| [ApostolNT] p. 14 | Definition | df-dvds 16220 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16236 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16261 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16256 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16249 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16251 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16237 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16238 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16243 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16278 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16280 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16282 |
| [ApostolNT] p. 15 | Definition | df-gcd 16462 dfgcd2 16513 |
| [ApostolNT] p. 16 | Definition | isprm2 16649 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16620 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16884 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16480 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16514 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16516 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16495 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16487 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16679 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16681 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16897 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16891 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16370 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16554 |
| [ApostolNT] p. 24 | Definition | df-mu 27089 |
| [ApostolNT] p. 25 | Definition | df-phi 16734 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27179 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16759 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16744 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16748 |
| [ApostolNT] p. 32 | Definition | df-vma 27086 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27181 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27204 |
| [ApostolNT] p. 38 | Remark | df-sgm 27090 |
| [ApostolNT] p. 38 | Definition | df-sgm 27090 |
| [ApostolNT] p. 75 | Definition | df-chp 27087 df-cht 27085 |
| [ApostolNT] p. 104 | Definition | congr 16631 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16223 |
| [ApostolNT] p. 106 | Definition | moddvds 16230 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16313 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16314 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13845 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13885 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14198 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16255 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16634 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17043 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16636 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16751 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16770 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16752 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27060 |
| [ApostolNT] p. 179 | Definition | df-lgs 27283 lgsprme0 27327 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27328 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27304 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27319 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27376 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27395 2lgsoddprm 27404 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27362 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27371 |
| [ApostolNT] p. 188 | Definition | df-lgs 27283 lgs1 27329 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27320 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27322 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27330 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27331 |
| [Baer] p. 40 | Property (b) | mapdord 42131 |
| [Baer] p. 40 | Property (c) | mapd11 42132 |
| [Baer] p. 40 | Property (e) | mapdin 42155 mapdlsm 42157 |
| [Baer] p. 40 | Property (f) | mapd0 42158 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 42118 mapd1o 42141 |
| [Baer] p. 41 | Property (g) | mapdat 42160 |
| [Baer] p. 44 | Part (1) | mapdpg 42199 |
| [Baer] p. 45 | Part (2) | hdmap1eq 42294 mapdheq 42221 mapdheq2 42222 mapdheq2biN 42223 |
| [Baer] p. 45 | Part (3) | baerlem3 42206 |
| [Baer] p. 46 | Part (4) | mapdheq4 42225 mapdheq4lem 42224 |
| [Baer] p. 46 | Part (5) | baerlem5a 42207 baerlem5abmN 42211 baerlem5amN 42209 baerlem5b 42208 baerlem5bmN 42210 |
| [Baer] p. 47 | Part (6) | hdmap1l6 42314 hdmap1l6a 42302 hdmap1l6e 42307 hdmap1l6f 42308 hdmap1l6g 42309 hdmap1l6lem1 42300 hdmap1l6lem2 42301 mapdh6N 42240 mapdh6aN 42228 mapdh6eN 42233 mapdh6fN 42234 mapdh6gN 42235 mapdh6lem1N 42226 mapdh6lem2N 42227 |
| [Baer] p. 48 | Part 9 | hdmapval 42321 |
| [Baer] p. 48 | Part 10 | hdmap10 42333 |
| [Baer] p. 48 | Part 11 | hdmapadd 42336 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 42310 mapdh6hN 42236 |
| [Baer] p. 48 | Part (7) | mapdh75cN 42246 mapdh75d 42247 mapdh75e 42245 mapdh75fN 42248 mapdh7cN 42242 mapdh7dN 42243 mapdh7eN 42241 mapdh7fN 42244 |
| [Baer] p. 48 | Part (8) | mapdh8 42281 mapdh8a 42268 mapdh8aa 42269 mapdh8ab 42270 mapdh8ac 42271 mapdh8ad 42272 mapdh8b 42273 mapdh8c 42274 mapdh8d 42276 mapdh8d0N 42275 mapdh8e 42277 mapdh8g 42278 mapdh8i 42279 mapdh8j 42280 |
| [Baer] p. 48 | Part (9) | mapdh9a 42282 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 42262 |
| [Baer] p. 49 | Part 12 | hdmap11 42341 hdmapeq0 42337 hdmapf1oN 42358 hdmapneg 42339 hdmaprnN 42357 hdmaprnlem1N 42342 hdmaprnlem3N 42343 hdmaprnlem3uN 42344 hdmaprnlem4N 42346 hdmaprnlem6N 42347 hdmaprnlem7N 42348 hdmaprnlem8N 42349 hdmaprnlem9N 42350 hdmapsub 42340 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 42361 hdmap14lem10 42370 hdmap14lem1a 42359 hdmap14lem2N 42362 hdmap14lem2a 42360 hdmap14lem3 42363 hdmap14lem8 42368 hdmap14lem9 42369 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 42371 hdmap14lem12 42372 hdmap14lem13 42373 hdmap14lem14 42374 hdmap14lem15 42375 hgmapval 42380 |
| [Baer] p. 50 | Part 15 | hgmapadd 42387 hgmapmul 42388 hgmaprnlem2N 42390 hgmapvs 42384 |
| [Baer] p. 50 | Part 16 | hgmaprnN 42394 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 42410 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 42411 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 42412 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 42413 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 42415 hgmapvv 42419 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 42414 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 42416 |
| [Baer] p. 111 | Line 15 | hdmapg 42423 hdmapglem7 42422 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26720 2irrexpqALT 26789 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 23 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2573 |
| [BellMachover] p. 460 | Notation | df-mo 2543 |
| [BellMachover] p. 460 | Definition | mo3 2568 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2712 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2716 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5214 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5225 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37418 sepex 5229 |
| [BellMachover] p. 466 | Problem | axpow2 5303 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5304 |
| [BellMachover] p. 466 | Axiom Union | axun2 7687 |
| [BellMachover] p. 468 | Definition | df-ord 6320 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6335 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6342 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6337 |
| [BellMachover] p. 471 | Definition of N | df-om 7814 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7751 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6322 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9561 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7829 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9686 |
| [BellMachover] p. 478 | Definition | rankval2 9740 rankval2b 35289 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9704 r1ord3g 9701 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9508 |
| [BellMachover] p. 488 | Axiom AC | ac5 10397 dfac4 10042 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10030 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 39812 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32449 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32491 chirredi 32490 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32479 |
| [Beran] p. 3 | Definition of join | sshjval3 31450 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 31712 cmcm2i 31689 cmcm2ii 31694 cmt2N 39743 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 31713 lecmi 31698 lecmii 31699 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 31687 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 31716 cm2ji 31721 cm2mi 31722 |
| [Beran] p. 95 | Definition | df-sh 31303 issh2 31305 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31182 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31195 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31186 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 31924 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 31926 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 31925 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 31927 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31178 his1i 31196 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31179 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31180 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31181 |
| [Beran] p. 96 | Definition of norm | df-hnorm 31064 dfhnorm2 31218 normval 31220 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31280 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 31069 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31337 |
| [Beran] p. 96 | Definition of converge | df-hlim 31068 hlimi 31284 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31229 norm-i 31225 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31233 norm-ii 31234 normlem0 31205 normlem1 31206 normlem2 31207 normlem3 31208 normlem4 31209 normlem5 31210 normlem6 31211 normlem7 31212 normlem7tALT 31215 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31235 norm-iii 31236 |
| [Beran] p. 98 | Remark 3.4 | bcs 31277 bcsiALT 31275 bcsiHIL 31276 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31217 normpar 31251 normpari 31250 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31242 normpyth 31241 normpythi 31238 |
| [Beran] p. 99 | Remark | lnfn0 32143 lnfn0i 32138 lnop0 32062 lnop0i 32066 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32122 nmcfnex 32149 nmcfnexi 32147 nmcopex 32125 nmcopexi 32123 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32150 nmcfnlbi 32148 nmcoplb 32126 nmcoplbi 32124 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32152 lnfnconi 32151 lnopcon 32131 lnopconi 32130 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31252 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31249 norm3adifii 31244 norm3dif 31246 norm3difi 31243 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31397 pjhth 31489 pjhtheu 31490 pjpjhth 31521 pjpjhthi 31522 pjth 25431 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31502 ococi 31501 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32157 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32158 riesz4 32160 riesz4i 32159 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32175 cnlnadjeu 32174 cnlnadjeui 32173 cnlnadji 32172 cnlnadjlem1 32163 nmopadjlei 32184 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32187 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32186 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32188 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 32032 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32198 nmopcoadji 32197 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32189 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32199 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32196 pjadj2coi 32300 pjadjcoi 32257 |
| [Beran] p. 107 | Definition | df-ch 31317 isch2 31319 |
| [Beran] p. 107 | Remark 3.12 | choccl 31402 isch3 31337 occl 31400 ocsh 31379 shoccl 31401 shocsh 31380 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31504 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31428 |
| [Beran] p. 109 | Property (i) | pjadj2 32283 pjadj3 32284 pjadji 31781 pjadjii 31770 |
| [Beran] p. 109 | Property (ii) | pjidmco 32277 pjidmcoi 32273 pjidmi 31769 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32269 |
| [Beran] p. 111 | Remark | ho0val 31846 pjch1 31766 |
| [Beran] p. 111 | Definition | df-hfmul 31830 df-hfsum 31829 df-hodif 31828 df-homul 31827 df-hosum 31826 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 31767 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 31790 pjchi 31528 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31535 pjoc2i 31534 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 31776 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32261 pjssmii 31777 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32260 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32259 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32264 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32262 pjssge0ii 31778 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32263 pjdifnormii 31779 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1783 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1781 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1784 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1779 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34483 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34491 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34489 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34493 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34513 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34544 df-sitm 34522 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34544 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34521 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29142 isuhgrop 29164 isusgrop 29256 isuspgrop 29255 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 48353 df-subgr 29362 uhgrspan1 29397 uhgrspansubgr 29385 |
| [Bollobas] p. 3 | Definition | df-gric 48373 gricuspgr 48410 isuspgrim 48388 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29548 df-clnbgr 48311 df-cusgr 29506 df-nbgr 29427 fusgrmaxsize 29558 |
| [Bollobas] p. 4 | Definition | df-upwlks 48626 df-wlks 29693 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 29644 finsumvtxdgeven 29646 fusgr1th 29645 fusgrvtxdgonume 29648 vtxdgoddnumeven 29647 |
| [Bollobas] p. 5 | Notation | df-pths 29807 |
| [Bollobas] p. 5 | Definition | df-crcts 29879 df-cycls 29880 df-trls 29784 df-wlkson 29694 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29153 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 48692 df-cllaw 48678 df-mgm 18606 df-mgm2 48711 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 48693 df-asslaw 48680 df-sgrp 18685 df-sgrp2 48713 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 48712 df-comlaw 48679 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18701 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33112 mndlactf1o 33116 mndractf1 33114 mndractf1o 33117 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20214 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20132 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 33824 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 33828 assarrginv 33827 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 33869 fldextrspunfld 33867 fldextrspunlem1 33866 fldextrspunlem2 33868 fldextrspunlsp 33865 fldextrspunlsplem 33864 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 33627 dfufd2 33640 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7238 fcofo 7239 |
| [BourbakiTop1] p. | Remark | xnegmnf 13160 xnegpnf 13159 |
| [BourbakiTop1] p. | Remark | rexneg 13161 |
| [BourbakiTop1] p. | Remark 3 | ust0 24210 ustfilxp 24203 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24080 |
| [BourbakiTop1] p. | Criterion | ishmeo 23749 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24273 iducn 24272 snfil 23854 |
| [BourbakiTop1] p. | Example 2 | neifil 23870 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 24057 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24293 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 34148 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23853 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24265 df-ust 24191 filintn0 23851 filn0 23852 istgp 24067 ucnprima 24271 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24276 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24287 df-usp 24247 df-utop 24221 trust 24219 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 34047 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23106 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23259 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24196 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24199 |
| [BourbakiTop1] p. | Property V_ii | innei 23115 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23123 neissex 23117 |
| [BourbakiTop1] p. | Proposition 1 | neips 23103 neiss 23099 ucncn 24274 ustund 24212 ustuqtop 24236 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23257 neiptopreu 23123 utop2nei 24240 utop3cls 24241 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24281 uspreg 24263 utopreg 24242 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23681 imasncls 23682 imasnopn 23680 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 23990 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24198 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24200 |
| [BourbakiTop1] p. | Property V_iii | elnei 23101 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24292 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24197 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24201 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23377 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23836 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 22884 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 34044 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 46506 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 46508 stoweid 46507 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 46445 stoweidlem10 46454 stoweidlem14 46458 stoweidlem15 46459 stoweidlem35 46479 stoweidlem36 46480 stoweidlem37 46481 stoweidlem38 46482 stoweidlem40 46484 stoweidlem41 46485 stoweidlem43 46487 stoweidlem44 46488 stoweidlem46 46490 stoweidlem5 46449 stoweidlem50 46494 stoweidlem52 46496 stoweidlem53 46497 stoweidlem55 46499 stoweidlem56 46500 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 46467 stoweidlem24 46468 stoweidlem27 46471 stoweidlem28 46472 stoweidlem30 46474 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 46478 stoweidlem59 46503 stoweidlem60 46504 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 46489 stoweidlem49 46493 stoweidlem7 46451 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 46475 stoweidlem39 46483 stoweidlem42 46486 stoweidlem48 46492 stoweidlem51 46495 stoweidlem54 46498 stoweidlem57 46501 stoweidlem58 46502 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 46469 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 46461 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 46455 stoweidlem13 46457 stoweidlem26 46470 stoweidlem61 46505 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 46462 |
| [Bruck] p. 1 | Section I.1 | df-clintop 48692 df-mgm 18606 df-mgm2 48711 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18685 df-sgrp2 48713 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 19013 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5161 |
| [Church] p. 129 | Section II.24 | df-ifp 1069 dfifp2 1070 |
| [Clemente] p. 10 | Definition IT | natded 30498 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30498 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30498 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30498 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30498 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30498 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30498 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30498 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30498 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30498 |
| [Clemente] p. 14 | Proof 5.11 | natded 30498 |
| [Clemente] p. 14 | Definition E` `n | natded 30498 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30500 ex-natded5.2 30499 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30503 ex-natded5.3 30502 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30505 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30507 ex-natded5.7 30506 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30509 ex-natded5.8 30508 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30511 ex-natded5.13 30510 |
| [Clemente] p. 32 | Definition I` `n | natded 30498 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30498 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30498 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30498 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30512 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30513 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30515 ex-natded9.26 30514 |
| [Cohen] p. 301 | Remark | relogoprlem 26580 |
| [Cohen] p. 301 | Property 2 | relogmul 26581 relogmuld 26614 |
| [Cohen] p. 301 | Property 3 | relogdiv 26582 relogdivd 26615 |
| [Cohen] p. 301 | Property 4 | relogexp 26585 |
| [Cohen] p. 301 | Property 1a | log1 26574 |
| [Cohen] p. 301 | Property 1b | loge 26575 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26776 |
| [Cohen4] p. 349 | Property | relogbf 26780 |
| [Cohen4] p. 352 | Definition | elogb 26759 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26766 |
| [Cohen4] p. 361 | Property 3 | logbrec 26771 relogbdiv 26768 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26764 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26769 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26757 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26758 |
| [Cohen4] p. 367 | Property | logbchbase 26760 |
| [Cohen4] p. 377 | Property 2 | logblt 26773 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34476 sxbrsigalem4 34478 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18521 acsinfd 18520 acsinfdimd 18522 acsmap2d 18519 acsmapd 18518 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34481 |
| [Connell] p. 57 | Definition | df-scmat 22481 df-scmatalt 48891 |
| [Conway] p. 4 | Definition | lesrec 27816 lesrecd 27817 |
| [Conway] p. 5 | Definition | addsval 27979 addsval2 27980 df-adds 27977 df-muls 28124 df-negs 28038 |
| [Conway] p. 7 | Theorem | 0lt1s 27829 |
| [Conway] p. 12 | Theorem 12 | pw2cut2 28479 |
| [Conway] p. 16 | Theorem 0(i) | sltsright 27878 |
| [Conway] p. 16 | Theorem 0(ii) | sltsleft 27877 |
| [Conway] p. 16 | Theorem 0(iii) | lesid 27756 |
| [Conway] p. 17 | Theorem 3 | addsass 28022 addsassd 28023 addscom 27983 addscomd 27984 addsrid 27981 addsridd 27982 |
| [Conway] p. 17 | Definition | df-0s 27824 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 28061 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 28058 negsidd 28059 |
| [Conway] p. 18 | Theorem 5 | leadds1 28006 leadds1d 28012 |
| [Conway] p. 18 | Definition | df-1s 27825 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 28053 negscld 28054 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 27997 |
| [Conway] p. 19 | Note | mulsunif2 28187 |
| [Conway] p. 19 | Theorem 7 | addsdi 28172 addsdid 28173 addsdird 28174 mulnegs1d 28177 mulnegs2d 28178 mulsass 28183 mulsassd 28184 mulscom 28156 mulscomd 28157 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28151 mulscld 28152 |
| [Conway] p. 19 | Theorem 8(iii) | lemulsd 28155 ltmuls 28153 ltmulsd 28154 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28161 mulsgt0d 28162 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28235 |
| [Conway] p. 23 | Theorem 11 | eqcuts3 27821 |
| [Conway] p. 24 | Definition | df-reno 28507 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28516 remulscl 28519 renegscl 28515 |
| [Conway] p. 27 | Definition | df-ons 28269 elons2 28275 |
| [Conway] p. 27 | Theorem 14 | ltonsex 28279 |
| [Conway] p. 28 | Theorem 15 | oncutlt 28281 onswe 28289 |
| [Conway] p. 29 | Remark | madebday 27917 newbday 27919 oldbday 27918 |
| [Conway] p. 29 | Definition | df-made 27844 df-new 27846 df-old 27845 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13818 |
| [Crawley] p. 1 | Definition of poset | df-poset 18277 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 39879 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 40683 dalaw 40379 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 42454 |
| [Crawley] p. 111 | Definition of set W | df-watsN 40483 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 40599 df-ldil 40597 isldil 40603 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 40598 df-trnN 40600 isltrn 40612 ltrnu 40614 |
| [Crawley] p. 112 | Lemma A | cdlema1N 40284 cdlema2N 40285 exatleN 39897 |
| [Crawley] p. 112 | Lemma B | 1cvrat 39969 cdlemb 40287 cdlemb2 40534 cdlemb3 41099 idltrn 40643 l1cvat 39548 lhpat 40536 lhpat2 40538 lshpat 39549 ltrnel 40632 ltrnmw 40644 |
| [Crawley] p. 112 | Lemma C | cdlemc1 40684 cdlemc2 40685 ltrnnidn 40667 trlat 40662 trljat1 40659 trljat2 40660 trljat3 40661 trlne 40678 trlnidat 40666 trlnle 40679 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 40484 |
| [Crawley] p. 113 | Lemma C | cdlemc 40690 cdlemc3 40686 cdlemc4 40687 |
| [Crawley] p. 113 | Lemma D | cdlemd 40700 cdlemd1 40691 cdlemd2 40692 cdlemd3 40693 cdlemd4 40694 cdlemd5 40695 cdlemd6 40696 cdlemd7 40697 cdlemd8 40698 cdlemd9 40699 cdleme31sde 40878 cdleme31se 40875 cdleme31se2 40876 cdleme31snd 40879 cdleme32a 40934 cdleme32b 40935 cdleme32c 40936 cdleme32d 40937 cdleme32e 40938 cdleme32f 40939 cdleme32fva 40930 cdleme32fva1 40931 cdleme32fvcl 40933 cdleme32le 40940 cdleme48fv 40992 cdleme4gfv 41000 cdleme50eq 41034 cdleme50f 41035 cdleme50f1 41036 cdleme50f1o 41039 cdleme50laut 41040 cdleme50ldil 41041 cdleme50lebi 41033 cdleme50rn 41038 cdleme50rnlem 41037 cdlemeg49le 41004 cdlemeg49lebilem 41032 |
| [Crawley] p. 113 | Lemma E | cdleme 41053 cdleme00a 40702 cdleme01N 40714 cdleme02N 40715 cdleme0a 40704 cdleme0aa 40703 cdleme0b 40705 cdleme0c 40706 cdleme0cp 40707 cdleme0cq 40708 cdleme0dN 40709 cdleme0e 40710 cdleme0ex1N 40716 cdleme0ex2N 40717 cdleme0fN 40711 cdleme0gN 40712 cdleme0moN 40718 cdleme1 40720 cdleme10 40747 cdleme10tN 40751 cdleme11 40763 cdleme11a 40753 cdleme11c 40754 cdleme11dN 40755 cdleme11e 40756 cdleme11fN 40757 cdleme11g 40758 cdleme11h 40759 cdleme11j 40760 cdleme11k 40761 cdleme11l 40762 cdleme12 40764 cdleme13 40765 cdleme14 40766 cdleme15 40771 cdleme15a 40767 cdleme15b 40768 cdleme15c 40769 cdleme15d 40770 cdleme16 40778 cdleme16aN 40752 cdleme16b 40772 cdleme16c 40773 cdleme16d 40774 cdleme16e 40775 cdleme16f 40776 cdleme16g 40777 cdleme19a 40796 cdleme19b 40797 cdleme19c 40798 cdleme19d 40799 cdleme19e 40800 cdleme19f 40801 cdleme1b 40719 cdleme2 40721 cdleme20aN 40802 cdleme20bN 40803 cdleme20c 40804 cdleme20d 40805 cdleme20e 40806 cdleme20f 40807 cdleme20g 40808 cdleme20h 40809 cdleme20i 40810 cdleme20j 40811 cdleme20k 40812 cdleme20l 40815 cdleme20l1 40813 cdleme20l2 40814 cdleme20m 40816 cdleme20y 40795 cdleme20zN 40794 cdleme21 40830 cdleme21d 40823 cdleme21e 40824 cdleme22a 40833 cdleme22aa 40832 cdleme22b 40834 cdleme22cN 40835 cdleme22d 40836 cdleme22e 40837 cdleme22eALTN 40838 cdleme22f 40839 cdleme22f2 40840 cdleme22g 40841 cdleme23a 40842 cdleme23b 40843 cdleme23c 40844 cdleme26e 40852 cdleme26eALTN 40854 cdleme26ee 40853 cdleme26f 40856 cdleme26f2 40858 cdleme26f2ALTN 40857 cdleme26fALTN 40855 cdleme27N 40862 cdleme27a 40860 cdleme27cl 40859 cdleme28c 40865 cdleme3 40730 cdleme30a 40871 cdleme31fv 40883 cdleme31fv1 40884 cdleme31fv1s 40885 cdleme31fv2 40886 cdleme31id 40887 cdleme31sc 40877 cdleme31sdnN 40880 cdleme31sn 40873 cdleme31sn1 40874 cdleme31sn1c 40881 cdleme31sn2 40882 cdleme31so 40872 cdleme35a 40941 cdleme35b 40943 cdleme35c 40944 cdleme35d 40945 cdleme35e 40946 cdleme35f 40947 cdleme35fnpq 40942 cdleme35g 40948 cdleme35h 40949 cdleme35h2 40950 cdleme35sn2aw 40951 cdleme35sn3a 40952 cdleme36a 40953 cdleme36m 40954 cdleme37m 40955 cdleme38m 40956 cdleme38n 40957 cdleme39a 40958 cdleme39n 40959 cdleme3b 40722 cdleme3c 40723 cdleme3d 40724 cdleme3e 40725 cdleme3fN 40726 cdleme3fa 40729 cdleme3g 40727 cdleme3h 40728 cdleme4 40731 cdleme40m 40960 cdleme40n 40961 cdleme40v 40962 cdleme40w 40963 cdleme41fva11 40970 cdleme41sn3aw 40967 cdleme41sn4aw 40968 cdleme41snaw 40969 cdleme42a 40964 cdleme42b 40971 cdleme42c 40965 cdleme42d 40966 cdleme42e 40972 cdleme42f 40973 cdleme42g 40974 cdleme42h 40975 cdleme42i 40976 cdleme42k 40977 cdleme42ke 40978 cdleme42keg 40979 cdleme42mN 40980 cdleme42mgN 40981 cdleme43aN 40982 cdleme43bN 40983 cdleme43cN 40984 cdleme43dN 40985 cdleme5 40733 cdleme50ex 41052 cdleme50ltrn 41050 cdleme51finvN 41049 cdleme51finvfvN 41048 cdleme51finvtrN 41051 cdleme6 40734 cdleme7 40742 cdleme7a 40736 cdleme7aa 40735 cdleme7b 40737 cdleme7c 40738 cdleme7d 40739 cdleme7e 40740 cdleme7ga 40741 cdleme8 40743 cdleme8tN 40748 cdleme9 40746 cdleme9a 40744 cdleme9b 40745 cdleme9tN 40750 cdleme9taN 40749 cdlemeda 40791 cdlemedb 40790 cdlemednpq 40792 cdlemednuN 40793 cdlemefr27cl 40896 cdlemefr32fva1 40903 cdlemefr32fvaN 40902 cdlemefrs32fva 40893 cdlemefrs32fva1 40894 cdlemefs27cl 40906 cdlemefs32fva1 40916 cdlemefs32fvaN 40915 cdlemesner 40789 cdlemeulpq 40713 |
| [Crawley] p. 114 | Lemma E | 4atex 40569 4atexlem7 40568 cdleme0nex 40783 cdleme17a 40779 cdleme17c 40781 cdleme17d 40991 cdleme17d1 40782 cdleme17d2 40988 cdleme18a 40784 cdleme18b 40785 cdleme18c 40786 cdleme18d 40788 cdleme4a 40732 |
| [Crawley] p. 115 | Lemma E | cdleme21a 40818 cdleme21at 40821 cdleme21b 40819 cdleme21c 40820 cdleme21ct 40822 cdleme21f 40825 cdleme21g 40826 cdleme21h 40827 cdleme21i 40828 cdleme22gb 40787 |
| [Crawley] p. 116 | Lemma F | cdlemf 41056 cdlemf1 41054 cdlemf2 41055 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 41060 cdlemg16 41150 cdlemg28 41197 cdlemg28a 41186 cdlemg28b 41196 cdlemg3a 41090 cdlemg42 41222 cdlemg43 41223 cdlemg44 41226 cdlemg44a 41224 cdlemg46 41228 cdlemg47 41229 cdlemg9 41127 ltrnco 41212 ltrncom 41231 tgrpabl 41244 trlco 41220 |
| [Crawley] p. 116 | Definition of G | df-tgrp 41236 |
| [Crawley] p. 117 | Lemma G | cdlemg17 41170 cdlemg17b 41155 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 41249 df-edring 41250 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 41253 |
| [Crawley] p. 118 | Remark | tendopltp 41273 |
| [Crawley] p. 118 | Lemma H | cdlemh 41310 cdlemh1 41308 cdlemh2 41309 |
| [Crawley] p. 118 | Lemma I | cdlemi 41313 cdlemi1 41311 cdlemi2 41312 |
| [Crawley] p. 118 | Lemma J | cdlemj1 41314 cdlemj2 41315 cdlemj3 41316 tendocan 41317 |
| [Crawley] p. 118 | Lemma K | cdlemk 41467 cdlemk1 41324 cdlemk10 41336 cdlemk11 41342 cdlemk11t 41439 cdlemk11ta 41422 cdlemk11tb 41424 cdlemk11tc 41438 cdlemk11u-2N 41382 cdlemk11u 41364 cdlemk12 41343 cdlemk12u-2N 41383 cdlemk12u 41365 cdlemk13-2N 41369 cdlemk13 41345 cdlemk14-2N 41371 cdlemk14 41347 cdlemk15-2N 41372 cdlemk15 41348 cdlemk16-2N 41373 cdlemk16 41350 cdlemk16a 41349 cdlemk17-2N 41374 cdlemk17 41351 cdlemk18-2N 41379 cdlemk18-3N 41393 cdlemk18 41361 cdlemk19-2N 41380 cdlemk19 41362 cdlemk19u 41463 cdlemk1u 41352 cdlemk2 41325 cdlemk20-2N 41385 cdlemk20 41367 cdlemk21-2N 41384 cdlemk21N 41366 cdlemk22-3 41394 cdlemk22 41386 cdlemk23-3 41395 cdlemk24-3 41396 cdlemk25-3 41397 cdlemk26-3 41399 cdlemk26b-3 41398 cdlemk27-3 41400 cdlemk28-3 41401 cdlemk29-3 41404 cdlemk3 41326 cdlemk30 41387 cdlemk31 41389 cdlemk32 41390 cdlemk33N 41402 cdlemk34 41403 cdlemk35 41405 cdlemk36 41406 cdlemk37 41407 cdlemk38 41408 cdlemk39 41409 cdlemk39u 41461 cdlemk4 41327 cdlemk41 41413 cdlemk42 41434 cdlemk42yN 41437 cdlemk43N 41456 cdlemk45 41440 cdlemk46 41441 cdlemk47 41442 cdlemk48 41443 cdlemk49 41444 cdlemk5 41329 cdlemk50 41445 cdlemk51 41446 cdlemk52 41447 cdlemk53 41450 cdlemk54 41451 cdlemk55 41454 cdlemk55u 41459 cdlemk56 41464 cdlemk5a 41328 cdlemk5auN 41353 cdlemk5u 41354 cdlemk6 41330 cdlemk6u 41355 cdlemk7 41341 cdlemk7u-2N 41381 cdlemk7u 41363 cdlemk8 41331 cdlemk9 41332 cdlemk9bN 41333 cdlemki 41334 cdlemkid 41429 cdlemkj-2N 41375 cdlemkj 41356 cdlemksat 41339 cdlemksel 41338 cdlemksv 41337 cdlemksv2 41340 cdlemkuat 41359 cdlemkuel-2N 41377 cdlemkuel-3 41391 cdlemkuel 41358 cdlemkuv-2N 41376 cdlemkuv2-2 41378 cdlemkuv2-3N 41392 cdlemkuv2 41360 cdlemkuvN 41357 cdlemkvcl 41335 cdlemky 41419 cdlemkyyN 41455 tendoex 41468 |
| [Crawley] p. 120 | Remark | dva1dim 41478 |
| [Crawley] p. 120 | Lemma L | cdleml1N 41469 cdleml2N 41470 cdleml3N 41471 cdleml4N 41472 cdleml5N 41473 cdleml6 41474 cdleml7 41475 cdleml8 41476 cdleml9 41477 dia1dim 41554 |
| [Crawley] p. 120 | Lemma M | dia11N 41541 diaf11N 41542 dialss 41539 diaord 41540 dibf11N 41654 djajN 41630 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 41525 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 41611 dia2dimlem1 41557 dia2dimlem2 41558 dia2dimlem3 41559 dia2dimlem4 41560 dia2dimlem5 41561 diaf1oN 41623 diarnN 41622 dvheveccl 41605 dvhopN 41609 |
| [Crawley] p. 121 | Lemma N | cdlemn 41705 cdlemn10 41699 cdlemn11 41704 cdlemn11a 41700 cdlemn11b 41701 cdlemn11c 41702 cdlemn11pre 41703 cdlemn2 41688 cdlemn2a 41689 cdlemn3 41690 cdlemn4 41691 cdlemn4a 41692 cdlemn5 41694 cdlemn5pre 41693 cdlemn6 41695 cdlemn7 41696 cdlemn8 41697 cdlemn9 41698 diclspsn 41687 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 41666 |
| [Crawley] p. 122 | Lemma N | dih11 41758 dihf11 41760 dihjust 41710 dihjustlem 41709 dihord 41757 dihord1 41711 dihord10 41716 dihord11b 41715 dihord11c 41717 dihord2 41720 dihord2a 41712 dihord2b 41713 dihord2cN 41714 dihord2pre 41718 dihord2pre2 41719 dihordlem6 41706 dihordlem7 41707 dihordlem7b 41708 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 41723 dihfval 41724 dihval 41725 |
| [Diestel] p. 3 | Definition | df-gric 48373 df-grim 48370 isuspgrim 48388 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29506 df-nbgr 29427 |
| [Diestel] p. 3 | Definition by | df-grisom 48369 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 48353 df-subgr 29362 uhgrspan1 29397 uhgrspansubgr 29385 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 29648 vtxdgoddnumeven 29647 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29153 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 34055 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 34067 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 34059 zarcls1 34060 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 34070 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 34073 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 34076 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3893 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9566 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8772 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9574 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9902 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10475 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5234 |
| [Enderton] p. 19 | Definition | df-tp 4567 |
| [Enderton] p. 26 | Exercise 5 | unissb 4878 |
| [Enderton] p. 26 | Exercise 10 | pwel 5317 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5518 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5015 iinin2 5014 iinun2 5009 iunin1 5008 iunin1f 32653 iunin2 5007 uniin1 32647 uniin2 32648 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5013 iundif2 5010 |
| [Enderton] p. 32 | Exercise 20 | unineq 4223 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5034 |
| [Enderton] p. 33 | Exercise 25 | iununi 5035 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5042 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7721 iunpwss 5043 |
| [Enderton] p. 36 | Definition | opthwiener 5462 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5396 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4883 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5417 rnex 7857 rnexg 7849 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5863 rnuni 6106 |
| [Enderton] p. 42 | Definition of a function | dffun7 6519 dffun8 6520 |
| [Enderton] p. 43 | Definition of function value | funfv2 6922 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6561 |
| [Enderton] p. 44 | Definition (d) | dfima2 6021 dfima3 6022 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6931 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10393 ac7g 10394 df-ac 10036 dfac2 10052 dfac2a 10050 dfac2b 10051 dfac3 10041 dfac7 10053 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7197 |
| [Enderton] p. 52 | Definition | df-map 8772 |
| [Enderton] p. 53 | Exercise 21 | coass 6224 |
| [Enderton] p. 53 | Exercise 27 | dmco 6213 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6568 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6061 |
| [Enderton] p. 54 | Remark | ixpf 8865 ixpssmap 8877 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8843 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10403 ac9s 10413 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 39062 erref 8661 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 39065 erthi 8697 |
| [Enderton] p. 57 | Definition | df-ec 8642 |
| [Enderton] p. 58 | Definition | df-qs 8646 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8642 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5859 |
| [Enderton] p. 68 | Definition of successor | df-suc 6323 |
| [Enderton] p. 71 | Definition | df-tr 5187 dftr4 5192 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6398 unisucg 6397 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6398 unisucg 6397 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5202 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5204 trintALT 45325 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8537 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8539 onasuc 8460 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7366 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8538 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8540 onmsuc 8461 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8555 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8542 nnacom 8550 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8556 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8557 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8559 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8543 nnmsucr 8558 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8571 |
| [Enderton] p. 129 | Definition | df-en 8891 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7317 |
| [Enderton] p. 133 | Exercise 1 | xpomen 9935 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16178 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9138 |
| [Enderton] p. 135 | Corollary 6C | php3 9140 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9137 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9169 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9171 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9100 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9104 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9076 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10100 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10101 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10096 dju1en 10092 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9250 unifi 9251 unifi2 9252 |
| [Enderton] p. 144 | Corollary 6K | undif2 4412 unfi 9102 unfi2 9217 |
| [Enderton] p. 145 | Figure 38 | ffoss 7895 |
| [Enderton] p. 145 | Definition | df-dom 8892 |
| [Enderton] p. 146 | Example 1 | domen 8905 domeng 8906 |
| [Enderton] p. 146 | Example 3 | nndomo 9149 nnsdom 9573 nnsdomg 9206 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10104 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9077 xpdom1 9011 xpdom1g 9009 xpdom2g 9008 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9083 |
| [Enderton] p. 151 | Theorem 6M | zorn 10427 zorng 10424 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10412 dfac5 10049 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10496 |
| [Enderton] p. 164 | Example | infdif 10128 |
| [Enderton] p. 168 | Definition | df-po 5533 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6432 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6364 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6431 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6372 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7786 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7731 |
| [Enderton] p. 194 | Remark | onprc 7728 |
| [Enderton] p. 194 | Exercise 16 | suc11 6426 |
| [Enderton] p. 197 | Definition | df-card 9861 |
| [Enderton] p. 197 | Theorem 7P | carden 10471 |
| [Enderton] p. 200 | Exercise 25 | tfis 7802 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9698 |
| [Enderton] p. 202 | Definition | df-r1 9686 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9708 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9789 rankval4b 35290 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9525 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9779 rankprb 9773 rankpw 9765 rankpwi 9745 rankuniss 9788 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9537 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9538 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10030 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 9996 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10010 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8278 |
| [Enderton] p. 222 | Definition of kard | karden 9817 kardex 9816 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8530 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8532 |
| [Enderton] p. 240 | Exercise 25 | oarec 8494 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10170 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17606 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17548 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18517 mrieqv2d 17603 mrieqvd 17602 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17607 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17612 mreexexlem2d 17609 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18523 mreexfidimd 17614 |
| [Frege1879] p. 11 | Statement | df3or2 44213 |
| [Frege1879] p. 12 | Statement | df3an2 44214 dfxor4 44211 dfxor5 44212 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 44235 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 44236 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 44240 |
| [Frege1879] p. 31 | Proposition 4 | frege4 44244 |
| [Frege1879] p. 32 | Proposition 5 | frege5 44245 |
| [Frege1879] p. 33 | Proposition 6 | frege6 44251 |
| [Frege1879] p. 34 | Proposition 7 | frege7 44253 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 44254 axfrege8 44252 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 90 wl-luk-pm2.04 37808 |
| [Frege1879] p. 35 | Proposition 9 | frege9 44257 |
| [Frege1879] p. 36 | Proposition 10 | frege10 44265 |
| [Frege1879] p. 36 | Proposition 11 | frege11 44259 |
| [Frege1879] p. 37 | Proposition 12 | frege12 44258 |
| [Frege1879] p. 37 | Proposition 13 | frege13 44267 |
| [Frege1879] p. 37 | Proposition 14 | frege14 44268 |
| [Frege1879] p. 38 | Proposition 15 | frege15 44271 |
| [Frege1879] p. 38 | Proposition 16 | frege16 44261 |
| [Frege1879] p. 39 | Proposition 17 | frege17 44266 |
| [Frege1879] p. 39 | Proposition 18 | frege18 44263 |
| [Frege1879] p. 39 | Proposition 19 | frege19 44269 |
| [Frege1879] p. 40 | Proposition 20 | frege20 44273 |
| [Frege1879] p. 40 | Proposition 21 | frege21 44272 |
| [Frege1879] p. 41 | Proposition 22 | frege22 44264 |
| [Frege1879] p. 42 | Proposition 23 | frege23 44270 |
| [Frege1879] p. 42 | Proposition 24 | frege24 44260 |
| [Frege1879] p. 42 | Proposition 25 | frege25 44262 rp-frege25 44250 |
| [Frege1879] p. 42 | Proposition 26 | frege26 44255 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 44275 |
| [Frege1879] p. 43 | Proposition 27 | frege27 44256 |
| [Frege1879] p. 43 | Proposition 28 | con3 153 |
| [Frege1879] p. 43 | Proposition 29 | frege29 44276 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 44279 axfrege31 44278 |
| [Frege1879] p. 44 | Proposition 30 | frege30 44277 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 130 |
| [Frege1879] p. 44 | Proposition 32 | frege32 44280 |
| [Frege1879] p. 44 | Proposition 33 | frege33 44281 |
| [Frege1879] p. 45 | Proposition 34 | frege34 44282 |
| [Frege1879] p. 45 | Proposition 35 | frege35 44283 |
| [Frege1879] p. 45 | Proposition 36 | frege36 44284 |
| [Frege1879] p. 46 | Proposition 37 | frege37 44285 |
| [Frege1879] p. 46 | Proposition 38 | frege38 44286 |
| [Frege1879] p. 46 | Proposition 39 | frege39 44287 |
| [Frege1879] p. 46 | Proposition 40 | frege40 44288 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 44290 axfrege41 44289 |
| [Frege1879] p. 47 | Proposition 41 | notnot 142 |
| [Frege1879] p. 47 | Proposition 42 | frege42 44291 |
| [Frege1879] p. 47 | Proposition 43 | frege43 44292 |
| [Frege1879] p. 47 | Proposition 44 | frege44 44293 |
| [Frege1879] p. 47 | Proposition 45 | frege45 44294 |
| [Frege1879] p. 48 | Proposition 46 | frege46 44295 |
| [Frege1879] p. 48 | Proposition 47 | frege47 44296 |
| [Frege1879] p. 49 | Proposition 48 | frege48 44297 |
| [Frege1879] p. 49 | Proposition 49 | frege49 44298 |
| [Frege1879] p. 49 | Proposition 50 | frege50 44299 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 44302 ax-frege52c 44333 frege52aid 44303 frege52b 44334 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 44307 ax-frege54c 44337 frege54b 44338 |
| [Frege1879] p. 50 | Proposition 51 | frege51 44300 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3732 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 44305 frege53aid 44304 frege53b 44335 frege53c 44359 |
| [Frege1879] p. 50 | Proposition 54 | biid 262 eqid 2740 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 44313 frege55aid 44310 frege55b 44342 frege55c 44363 frege55cor1a 44314 frege55lem2a 44312 frege55lem2b 44341 frege55lem2c 44362 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 44316 frege56aid 44315 frege56b 44343 frege56c 44364 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 44320 ax-frege58b 44346 frege58bid 44347 frege58c 44366 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 44318 frege57aid 44317 frege57b 44344 frege57c 44365 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3743 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 44322 frege59b 44349 frege59c 44367 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 44323 frege60b 44350 frege60c 44368 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 44324 frege61b 44351 frege61c 44369 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 44325 frege62b 44352 frege62c 44370 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 44326 frege63b 44353 frege63c 44371 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 44327 frege64b 44354 frege64c 44372 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 44328 frege65b 44355 frege65c 44373 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 44329 frege66b 44356 frege66c 44374 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 44330 frege67b 44357 frege67c 44375 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 44331 frege68b 44358 frege68c 44376 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 44377 |
| [Frege1879] p. 58 | Proposition 70 | frege70 44378 |
| [Frege1879] p. 59 | Proposition 71 | frege71 44379 |
| [Frege1879] p. 59 | Proposition 72 | frege72 44380 |
| [Frege1879] p. 59 | Proposition 73 | frege73 44381 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 44384 |
| [Frege1879] p. 60 | Proposition 74 | frege74 44382 |
| [Frege1879] p. 60 | Proposition 75 | frege75 44383 |
| [Frege1879] p. 62 | Proposition 77 | frege77 44385 frege77d 44191 |
| [Frege1879] p. 63 | Proposition 78 | frege78 44386 |
| [Frege1879] p. 63 | Proposition 79 | frege79 44387 |
| [Frege1879] p. 63 | Proposition 80 | frege80 44388 |
| [Frege1879] p. 63 | Proposition 81 | frege81 44389 frege81d 44192 |
| [Frege1879] p. 64 | Proposition 82 | frege82 44390 |
| [Frege1879] p. 65 | Proposition 83 | frege83 44391 frege83d 44193 |
| [Frege1879] p. 65 | Proposition 84 | frege84 44392 |
| [Frege1879] p. 66 | Proposition 85 | frege85 44393 |
| [Frege1879] p. 66 | Proposition 86 | frege86 44394 |
| [Frege1879] p. 66 | Proposition 87 | frege87 44395 frege87d 44195 |
| [Frege1879] p. 67 | Proposition 88 | frege88 44396 |
| [Frege1879] p. 68 | Proposition 89 | frege89 44397 |
| [Frege1879] p. 68 | Proposition 90 | frege90 44398 |
| [Frege1879] p. 68 | Proposition 91 | frege91 44399 frege91d 44196 |
| [Frege1879] p. 69 | Proposition 92 | frege92 44400 |
| [Frege1879] p. 70 | Proposition 93 | frege93 44401 |
| [Frege1879] p. 70 | Proposition 94 | frege94 44402 |
| [Frege1879] p. 70 | Proposition 95 | frege95 44403 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 44407 |
| [Frege1879] p. 71 | Proposition 96 | frege96 44404 frege96d 44194 |
| [Frege1879] p. 71 | Proposition 97 | frege97 44405 frege97d 44197 |
| [Frege1879] p. 71 | Proposition 98 | frege98 44406 frege98d 44198 |
| [Frege1879] p. 72 | Proposition 100 | frege100 44408 |
| [Frege1879] p. 72 | Proposition 101 | frege101 44409 |
| [Frege1879] p. 72 | Proposition 102 | frege102 44410 frege102d 44199 |
| [Frege1879] p. 73 | Proposition 103 | frege103 44411 |
| [Frege1879] p. 73 | Proposition 104 | frege104 44412 |
| [Frege1879] p. 73 | Proposition 105 | frege105 44413 |
| [Frege1879] p. 73 | Proposition 106 | frege106 44414 frege106d 44200 |
| [Frege1879] p. 74 | Proposition 107 | frege107 44415 |
| [Frege1879] p. 74 | Proposition 108 | frege108 44416 frege108d 44201 |
| [Frege1879] p. 74 | Proposition 109 | frege109 44417 frege109d 44202 |
| [Frege1879] p. 75 | Proposition 110 | frege110 44418 |
| [Frege1879] p. 75 | Proposition 111 | frege111 44419 frege111d 44204 |
| [Frege1879] p. 76 | Proposition 112 | frege112 44420 |
| [Frege1879] p. 76 | Proposition 113 | frege113 44421 |
| [Frege1879] p. 76 | Proposition 114 | frege114 44422 frege114d 44203 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 44423 |
| [Frege1879] p. 77 | Proposition 116 | frege116 44424 |
| [Frege1879] p. 78 | Proposition 117 | frege117 44425 |
| [Frege1879] p. 78 | Proposition 118 | frege118 44426 |
| [Frege1879] p. 78 | Proposition 119 | frege119 44427 |
| [Frege1879] p. 78 | Proposition 120 | frege120 44428 |
| [Frege1879] p. 79 | Proposition 121 | frege121 44429 |
| [Frege1879] p. 79 | Proposition 122 | frege122 44430 frege122d 44205 |
| [Frege1879] p. 79 | Proposition 123 | frege123 44431 |
| [Frege1879] p. 80 | Proposition 124 | frege124 44432 frege124d 44206 |
| [Frege1879] p. 81 | Proposition 125 | frege125 44433 |
| [Frege1879] p. 81 | Proposition 126 | frege126 44434 frege126d 44207 |
| [Frege1879] p. 82 | Proposition 127 | frege127 44435 |
| [Frege1879] p. 83 | Proposition 128 | frege128 44436 |
| [Frege1879] p. 83 | Proposition 129 | frege129 44437 frege129d 44208 |
| [Frege1879] p. 84 | Proposition 130 | frege130 44438 |
| [Frege1879] p. 85 | Proposition 131 | frege131 44439 frege131d 44209 |
| [Frege1879] p. 86 | Proposition 132 | frege132 44440 |
| [Frege1879] p. 86 | Proposition 133 | frege133 44441 frege133d 44210 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 46757 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 47080 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 46780 |
| [Fremlin1] p. 14 | Definition 112A | ismea 46895 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 46915 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 46906 meadjunre 46920 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 46907 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 46908 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 46904 meaiunle 46913 meaiunlelem 46912 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 46925 meaiuninc2 46926 meaiuninc3 46929 meaiuninc3v 46928 meaiunincf 46927 meaiuninclem 46924 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 46931 meaiininc2 46932 meaiininclem 46930 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 46950 caragendifcl 46958 caratheodory 46972 omelesplit 46962 |
| [Fremlin1] p. 19 | Definition 113A | isome 46938 isomennd 46975 isomenndlem 46974 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 46960 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 46979 voncmpl 47065 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 46942 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 46967 carageniuncllem1 46965 carageniuncllem2 46966 caragenuncl 46957 caragenuncllem 46956 caragenunicl 46968 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 46976 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 46970 caratheodorylem2 46971 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 46979 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 47038 hoidmv1lelem1 47035 hoidmv1lelem2 47036 hoidmv1lelem3 47037 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 47082 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 47038 hoidmvle 47044 hoidmvlelem1 47039 hoidmvlelem2 47040 hoidmvlelem3 47041 hoidmvlelem4 47042 hoidmvlelem5 47043 hsphoidmvle2 47029 hsphoif 47020 hsphoival 47023 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 46992 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 47000 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 47027 hoidmvn0val 47028 hoidmvval 47021 hoidmvval0 47031 hoidmvval0b 47034 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 47032 hsphoidmvle 47030 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 46981 df-voln 46983 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 47048 ovn0 47010 ovn0lem 47009 ovnf 47007 ovnome 47017 ovnssle 47005 ovnsslelem 47004 ovnsupge0 47001 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 47047 ovnhoilem1 47045 ovnhoilem2 47046 vonhoi 47111 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 47064 hoidifhspf 47062 hoidifhspval 47052 hoidifhspval2 47059 hoidifhspval3 47063 hspmbl 47073 hspmbllem1 47070 hspmbllem2 47071 hspmbllem3 47072 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 47065 vonmea 47018 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 47016 ovnsubadd2 47090 ovnsubadd2lem 47089 ovnsubaddlem1 47014 ovnsubaddlem2 47015 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 47075 hoimbl2 47109 hoimbllem 47074 hspdifhsp 47060 opnvonmbl 47078 opnvonmbllem2 47077 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 47080 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 47123 iccvonmbllem 47122 ioovonmbl 47121 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 47129 vonicclem2 47128 vonioo 47126 vonioolem2 47125 vonn0icc 47132 vonn0icc2 47136 vonn0ioo 47131 vonn0ioo2 47134 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 47133 snvonmbl 47130 vonct 47137 vonsn 47135 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 46803 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 46802 subsaliuncllem 46801 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 47169 salpreimalegt 47153 salpreimaltle 47170 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 47172 issmff 47178 issmflem 47171 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 47189 issmflelem 47188 smfpreimale 47198 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 47200 issmfgtlem 47199 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 47140 issmf 47172 issmff 47178 issmfge 47214 issmfgelem 47213 issmfgt 47200 issmfgtlem 47199 issmfle 47189 issmflelem 47188 issmflem 47171 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 47151 salpreimagtlt 47174 salpreimalelt 47173 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 47214 issmfgelem 47213 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 47197 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 47195 cnfsmf 47184 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 47211 decsmflem 47210 incsmf 47186 incsmflem 47185 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 47145 pimconstlt1 47146 smfconst 47193 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 47209 smfaddlem1 47207 smfaddlem2 47208 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 47240 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 47239 smfmullem1 47235 smfmullem2 47236 smfmullem3 47237 smfmullem4 47238 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 47241 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 47244 smfpimbor1lem2 47243 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 47246 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 47234 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 47233 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 47242 smfresal 47232 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 47221 smflim2 47250 smflimlem1 47215 smflimlem2 47216 smflimlem3 47217 smflimlem4 47218 smflimlem5 47219 smflimlem6 47220 smflimmpt 47254 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 47258 smfsuplem1 47255 smfsuplem2 47256 smfsuplem3 47257 smfsupmpt 47259 smfsupxr 47260 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 47262 smfinflem 47261 smfinfmpt 47263 |
| [Fremlin1] p. 39 | Remark 121G | smflim 47221 smflim2 47250 smflimmpt 47254 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 47252 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 47282 smfdivdmmbl2 47285 smfinfdmmbl 47293 smfinfdmmbllem 47292 smfsupdmmbl 47289 smfsupdmmbllem 47288 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 47272 smflimsuplem2 47265 smflimsuplem6 47269 smflimsuplem7 47270 smflimsuplem8 47271 smflimsupmpt 47273 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 47275 smfliminflem 47274 smfliminfmpt 47276 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 47140 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 47286 fsupdm2 47287 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 47277 adddmmbl2 47278 finfdm 47290 finfdm2 47291 fsupdm 47286 fsupdm2 47287 muldmmbl 47279 muldmmbl2 47280 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 47290 finfdm2 47291 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25528 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25571 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25581 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 38066 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 38069 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9557 inf1 9541 inf2 9542 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10832 enqer 10842 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10837 df-nq 10833 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10829 df-plq 10835 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7600 df-mpq 10830 df-mq 10836 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10838 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10896 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10897 ltbtwnnq 10899 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10892 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10893 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10900 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10902 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 10914 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 10916 |
| [Gleason] p. 122 | Definition | df-1p 10903 |
| [Gleason] p. 122 | Remark (1) | prub 10915 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 10954 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10906 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 10953 psslinpr 10952 supexpr 10975 suplem1pr 10973 suplem2pr 10974 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 10939 addclprlem1 10937 addclprlem2 10938 df-plp 10904 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 10943 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 10942 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 10955 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 10964 ltexprlem1 10957 ltexprlem2 10958 ltexprlem3 10959 ltexprlem4 10960 ltexprlem5 10961 ltexprlem6 10962 ltexprlem7 10963 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 10966 ltaprlem 10965 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 10967 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 10968 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10905 mulclpr 10941 mulclprlem 10940 reclem2pr 10969 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 10950 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 10945 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 10944 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 10949 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 10972 reclem3pr 10970 reclem4pr 10971 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 10976 enrer 10984 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 10981 df-1r 10982 df-nr 10977 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 10979 df-plr 10978 negexsr 11023 recexsr 11028 recexsrlem 11024 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 10980 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12152 creur 12151 cru 12149 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11109 axcnre 11085 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15075 crimd 15192 crimi 15153 crre 15074 crred 15191 crrei 15152 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15077 remimd 15158 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15244 absval2d 15408 absval2i 15358 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15101 cjaddd 15180 cjaddi 15148 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15102 cjmuld 15181 cjmuli 15149 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15100 cjcjd 15159 cjcji 15131 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15099 cjreb 15083 cjrebd 15162 cjrebi 15134 cjred 15186 rere 15082 rereb 15080 rerebd 15161 rerebi 15133 rered 15184 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15108 addcjd 15172 addcji 15143 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15198 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15239 abscjd 15413 abscji 15362 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15249 abs00d 15409 abs00i 15359 absne0d 15410 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15282 releabsd 15414 releabsi 15363 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15254 absmuld 15417 absmuli 15365 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15242 sqabsaddi 15366 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15291 abstrid 15419 abstrii 15369 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14022 exp0 14025 expp1 14028 expp1d 14107 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26668 cxpaddd 26706 expadd 14064 expaddd 14108 expaddz 14066 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26677 cxpmuld 26726 expmul 14067 expmuld 14109 expmulz 14068 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26674 mulcxpd 26717 mulexp 14061 mulexpd 14121 mulexpz 14062 |
| [Gleason] p. 140 | Exercise 1 | znnen 16177 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13461 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15592 rlimadd 15603 rlimdiv 15606 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15594 rlimsub 15604 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15593 rlimmul 15605 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15597 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15543 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15564 climcj 15565 climim 15567 climre 15566 rlimabs 15569 rlimcj 15570 rlimim 15572 rlimre 15571 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11182 df-xr 11181 ltxr 13064 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15431 limsupval 15434 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15630 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15639 caucvgb 15640 caucvgbf 45933 caucvgr 15636 climcau 15631 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15777 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15846 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15296 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13785 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21348 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24333 xmet0 24332 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24349 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24340 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24342 mstri 24459 xmettri 24341 xmstri 24458 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24372 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23638 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25302 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24530 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24856 addcn2 15554 mulcn 24858 mulcn2 15556 subcn 24857 subcn2 15555 |
| [Gleason] p. 295 | Remark | bcval3 14266 bcval4 14267 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14281 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14264 df-bc 14263 |
| [Gleason] p. 296 | Remark | bcn0 14270 bcnn 14272 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15793 |
| [Gleason] p. 308 | Equation 2 | ef0 16054 |
| [Gleason] p. 308 | Equation 3 | efcj 16055 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16061 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16066 |
| [Gleason] p. 310 | Equation 14 | sinadd 16129 |
| [Gleason] p. 310 | Equation 15 | cosadd 16130 |
| [Gleason] p. 311 | Equation 17 | sincossq 16141 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16146 sinbnd 16145 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14176 sqeqori 14174 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16035 |
| [Godowski] p. 730 | Equation SF | goeqi 32369 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 31764 |
| [Golan] p. 1 | Remark | srgisid 20188 |
| [Golan] p. 1 | Definition | df-srg 20166 |
| [Golan] p. 149 | Definition | df-slmd 33289 |
| [Gonshor] p. 7 | Definition | df-cuts 27777 |
| [Gonshor] p. 9 | Theorem 2.5 | lesrec 27816 lesrecd 27817 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 27937 cofcut1d 27938 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 27939 cofcut2d 27940 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 27941 cofcutr1d 27942 cofcutr2d 27943 |
| [Gonshor] p. 13 | Definition | df-adds 27977 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 27993 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 28019 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28147 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28167 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28475 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28477 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28476 |
| [Gonshor] p. 39 | Theorem 4.4(b) | elreno2 28512 |
| [Gonshor] p. 95 | Theorem 6.1 | addbday 28035 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36388 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17546 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17548 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 48680 df-cllaw 48678 df-comlaw 48679 |
| [Hall] p. 2 | Section 1.2 | df-clintop 48692 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 48713 |
| [Halmos] p. 28 | Partition ` ` | df-parts 39236 dfmembpart2 39241 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32161 riesz2 32162 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 32037 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32269 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32281 elpjidm 32280 pjnmopi 32244 |
| [Halmos] p. 44 | Remark | pjinormi 31783 pjinormii 31772 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32285 pjrn 31803 pjrni 31798 pjvec 31792 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 31823 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32250 hmopidmpji 32248 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32287 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32276 pjocvec 31793 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32265 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32268 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32271 pjssdif2i 32270 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 31951 |
| [Hamilton] p. 28 | Definition 2.1 | ax-1 6 |
| [Hamilton] p. 31 | Example 2.7(a) | idALT 23 |
| [Hamilton] p. 73 | Rule 1 | ax-mp 5 |
| [Hamilton] p. 74 | Rule 2 | ax-gen 1802 |
| [Hatcher] p. 25 | Definition | df-phtpc 24984 df-phtpy 24963 |
| [Hatcher] p. 26 | Definition | df-pco 24997 df-pi1 25000 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 24987 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 25042 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22480 df-dmatalt 48890 |
| [Helfgott] p. 2 | Theorem | tgoldbach 48309 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 48294 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 48306 bgoldbtbnd 48301 bgoldbtbnd 48301 tgblthelfgott 48307 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 34833 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 34834 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 34848 hgt750lemb 34847 hgt750leme 34849 hgt750lemf 34844 hgt750lemg 34845 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 48303 tgoldbachgt 34854 tgoldbachgtALTV 48304 tgoldbachgtd 34853 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 34835 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30589 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 18918 grpoideu 30605 mndideu 18711 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 18948 grpoinveu 30615 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 18979 grpo2inv 30627 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 18992 grpoinvop 30629 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 19014 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1775 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1776 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1778 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32516 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32529 cdj3i 32537 cdj3lem1 32530 cdjreui 32528 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32527 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 42454 |
| [Holland95] p. 14 | Line 15 | hgmapvs 42384 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 42406 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 42407 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 42404 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 42410 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 42329 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 42424 |
| [Holland95] p. 204 | Definition of involution | df-srng 20819 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 39996 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 42021 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 41974 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 40426 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 41870 poml4N 40446 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 41961 pexmidALTN 40471 pexmidN 40462 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 42026 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 39617 ldualset 39618 |
| [Holland95] p. 222 | Item 1 | df-lines 39994 df-pointsN 39995 |
| [Holland95] p. 222 | Item 2 | df-polarityN 40396 |
| [Holland95] p. 223 | Remark | ispsubcl2N 40440 omllaw4 39739 pol1N 40403 polcon3N 40410 |
| [Holland95] p. 223 | Definition | df-psubclN 40428 |
| [Holland95] p. 223 | Equation for polarity | polval2N 40399 |
| [Holmes] p. 40 | Definition | df-xrn 38748 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31180 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32278 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 32059 eigre 31931 eigrei 31930 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 32060 eigorth 31934 eigorthi 31933 |
| [Hughes] p. 137 | Remark (ii) | eigposi 31932 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30404 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30400 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30401 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30402 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30420 frgrregorufr0 30419 frgrregorufrg 30421 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30427 frrusgrord 30436 frrusgrord0 30435 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30183 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30410 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30413 frgrwopreg2 30414 frgrwopregasn 30411 frgrwopregbsn 30412 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30416 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30430 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30433 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30181 numclwlk1 30466 numclwlk1lem1 30464 numclwlk1lem2 30465 numclwwlk1 30456 numclwwlk8 30487 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30407 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 29864 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30442 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30468 numclwwlkovh0 30467 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30476 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 30073 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30480 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30483 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30486 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30498 natded 30498 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30498 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30498 natded 30498 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30498 |
| [Jech] p. 4 | Definition of class | cv 1546 cvjust 2734 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10500 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10498 alephmul 10499 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10497 infmap2 10137 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9736 |
| [Jech] p. 72 | Equation 9.3 | scott0 9808 scottex 9807 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9789 rankval4b 35290 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9813 |
| [Jech] p. 78 | Note | opthprc 5689 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 43361 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 43449 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 43450 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 43373 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 43377 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 43378 rmyp1 43379 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 43380 rmym1 43381 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 43371 rmx1 43372 rmxluc 43382 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 43375 rmy1 43376 rmyluc 43383 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 43385 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 43386 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 43406 jm2.17b 43407 jm2.17c 43408 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 43439 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 43443 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 43434 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 43409 jm2.24nn 43405 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 43448 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 43454 rmygeid 43410 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 43466 |
| [Juillerat] p. 11 | Section *5 | etransc 46727 etransclem47 46725 etransclem48 46726 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 46722 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 46724 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 46710 |
| [Juillerat] p. 13 | Proof | etransclem35 46713 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 46716 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 46702 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 46719 |
| [Juillerat] p. 14 | Proof | etransclem23 46701 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1974 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2019 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2024 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2014 cbvaliw 2013 wl-cbvmotv 37885 wl-motae 37887 wl-moteq 37886 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 1993 spimw 1977 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2040 spw 2041 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31612 chabs1i 31614 chabs2 31613 chabs2i 31615 chjass 31629 chjassi 31582 latabs1 18439 latabs2 18440 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32434 ela 32435 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32379 cvrval2 39767 |
| [Kalmbach] p. 16 | Definition | df-ol 39671 df-oml 39672 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 31680 cmbri 31686 cmtvalN 39704 df-cm 31679 df-cmtN 39670 |
| [Kalmbach] p. 22 | Remark | omllaw5N 39740 pjoml5 31709 pjoml5i 31684 |
| [Kalmbach] p. 22 | Definition | pjoml2 31707 pjoml2i 31681 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 31710 cmcmi 31688 cmcmii 31693 cmtcomN 39742 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 39738 omlsi 31500 pjoml 31532 pjomli 31531 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 39737 |
| [Kalmbach] p. 23 | Remark | cmbr2i 31692 cmcm3 31711 cmcm3i 31690 cmcm3ii 31695 cmcm4i 31691 cmt3N 39744 cmt4N 39745 cmtbr2N 39746 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 31704 cmbr3i 31696 cmtbr3N 39747 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 31714 fh1i 31717 fh2 31715 fh2i 31718 omlfh1N 39751 |
| [Kalmbach] p. 65 | Remark | chjatom 32453 chslej 31594 chsleji 31554 shslej 31476 shsleji 31466 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31591 chocini 31550 chsupcl 31436 chsupval2 31506 h0elch 31351 helch 31339 hsupval2 31505 ocin 31392 ococss 31389 shococss 31390 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31408 |
| [Kalmbach] p. 66 | Remark | df-pjh 31491 pjssmi 32261 pjssmii 31777 |
| [Kalmbach] p. 67 | Lemma 3 | osum 31741 osumi 31738 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32296 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32496 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32406 |
| [Kalmbach] p. 140 | Remark | hatomic 32456 hatomici 32455 hatomistici 32458 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 39812 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32477 lsatexch 39536 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32451 cvlcvr1 39832 cvr1 39903 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32470 cvexchi 32465 cvrexch 39913 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32460 hlrelat 39895 hlrelat5N 39894 lrelat 39507 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21141 lsmsatcv 39503 spansncv 31749 spansncvi 31748 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 39522 spansncv2 32389 |
| [Kalmbach] p. 266 | Definition | df-st 32307 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 31945 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10567 fpwwe2 10564 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10568 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10575 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10570 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10572 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10585 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10589 gchxpidm 10590 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10601 gchhar 10600 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10135 unxpwdom 9501 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10591 |
| [Kreyszig] p. 3 | Property M1 | metcl 24322 xmetcl 24321 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24329 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24562 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11870 muleqadd 11792 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24428 |
| [Kreyszig] p. 19 | Remark | mopntopon 24429 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24488 mopnm 24434 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24486 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24491 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24532 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23248 lmmbr 25250 lmmbr2 25251 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23370 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25305 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25268 iscmet2 25286 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25308 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23451 metelcls 25297 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25298 metcld2 25299 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25091 lmodvneg1 20902 nvinv 30735 vcm 30672 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25087 lmod0vs 20892 slmd0vs 33312 vc0 30670 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20893 slmdvs0 33313 vcz 30671 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 30787 ngpmet 24593 nrmmetd 24564 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 30782 imsdval2 30783 ncvspds 25153 ngpds 24594 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24579 nvnd 30784 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24608 nmge0 24607 nvge0 30769 nvz 30765 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24614 nvabs 30768 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 30897 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 30841 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 30903 blocni 30901 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 30902 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25196 ipeq0 21620 ipz 30815 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25208 pythi 30946 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 30950 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25230 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15819 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25428 minveco 30980 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 30846 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25321 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 30969 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32219 leopg 32218 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32237 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 31014 |
| [Kulpa] p. 547 | Theorem | poimir 38021 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 38020 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 38019 |
| [Kulpa] p. 548 | Theorem | broucube 38022 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 38014 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 38015 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2391 axnul 5234 |
| [Kunen] p. 11 | Axiom 3 | axnul 5234 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 5218 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8782 mapvalg 8780 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10442 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7888 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9686 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9728 r1elssi 9727 |
| [Kunen] p. 107 | Exercise 4 | rankop 9780 rankopb 9774 rankuni 9785 rankxplim 9801 rankxpsuc 9804 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 45399 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 45407 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 45406 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 45408 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 45413 rexabso 45414 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 45420 n0abso 45421 ssabso 45419 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 45422 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 45432 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 45427 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 45430 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 45431 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 45426 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 45438 wfaxpr 45443 wfaxreg 45445 wfaxrep 45439 wfaxsep 45440 wfaxun 45444 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 45429 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 45442 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 45438 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 45437 omelaxinf2 45434 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 45447 wfaxinf2 45446 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 45460 permaxext 45450 permaxinf2 45458 permaxnul 45453 permaxpow 45454 permaxpr 45455 permaxrep 45451 permaxsep 45452 permaxun 45456 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 45448 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 45459 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4941 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 33856 |
| [Lang] p. | Definition | df-rn 5636 |
| [Lang] p. 3 | Statement | lidrideqd 18635 mndbn0 18716 |
| [Lang] p. 3 | Definition | df-mnd 18701 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18653 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18807 |
| [Lang] p. 5 | Equation | gsumreidx 19890 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 48674 |
| [Lang] p. 6 | Example | nn0mnd 48671 |
| [Lang] p. 6 | Equation | gsumxp2 19953 |
| [Lang] p. 6 | Statement | cycsubm 19175 |
| [Lang] p. 6 | Definition | mulgnn0gsum 19054 |
| [Lang] p. 6 | Observation | mndlsmidm 19643 |
| [Lang] p. 7 | Definition | dfgrp2e 18937 |
| [Lang] p. 30 | Definition | df-tocyc 33195 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33240 |
| [Lang] p. 32 | Property (b) | cyc3conja 33245 cycpmconjv 33230 |
| [Lang] p. 53 | Definition | df-cat 17632 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18062 cat1lem 18061 |
| [Lang] p. 54 | Definition | df-iso 17714 |
| [Lang] p. 57 | Definition | df-inito 17949 df-termo 17950 |
| [Lang] p. 58 | Example | irinitoringc 21461 |
| [Lang] p. 58 | Statement | initoeu1 17976 termoeu1 17983 |
| [Lang] p. 62 | Definition | df-func 17823 |
| [Lang] p. 65 | Definition | df-nat 17911 |
| [Lang] p. 91 | Note | df-ringc 20625 |
| [Lang] p. 92 | Statement | mxidlprm 33560 |
| [Lang] p. 92 | Definition | isprmidlc 33537 |
| [Lang] p. 128 | Remark | dsmmlmod 21727 |
| [Lang] p. 129 | Proof | lincscm 48922 lincscmcl 48924 lincsum 48921 lincsumcl 48923 |
| [Lang] p. 129 | Statement | lincolss 48926 |
| [Lang] p. 129 | Observation | dsmmfi 21720 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 33818 qusdimsum 33819 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 33799 |
| [Lang] p. 147 | Definition | snlindsntor 48963 |
| [Lang] p. 504 | Statement | mat1 22437 matring 22433 |
| [Lang] p. 504 | Definition | df-mamu 22381 |
| [Lang] p. 505 | Statement | mamuass 22392 mamutpos 22448 matassa 22434 mattposvs 22445 tposmap 22447 |
| [Lang] p. 513 | Definition | mdet1 22591 mdetf 22585 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22681 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22577 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22601 |
| [Lang] p. 515 | Definition | df-minmar1 22625 smadiadetr 22665 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22600 mdetralt 22598 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22613 |
| [Lang] p. 518 | Definition | df-madu 22624 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22635 madurid 22634 matinv 22667 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 22880 |
| [Lang], p. 190 | Chapter 6 | vieta 33771 |
| [Lang], p. 224 | Proposition 1.1 | extdgfialg 33885 finextalg 33889 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 33854 fedgmul 33822 |
| [Lang], p. 225 | Proposition 1.4 | algextdeg 33916 |
| [Lang], p. 561 | Remark | chpmatply1 22822 |
| [Lang], p. 561 | Definition | df-chpmat 22817 |
| [Lang2] p. 3 | Notations | df-ind 12158 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 44779 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 44774 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 44780 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5234 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2719 wl-df.clab 37870 |
| [Levy] p. 59 | Definition | df-ttrcl 9627 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9673 |
| [Levy] p. 338 | Axiom | df-clel 2815 df-cleq 2732 wl-df.cleq 37871 |
| [Levy] p. 338 | Axiom. See also comments under ~ df-clab , ~ df-cleq , and ~ eqabb . Alternate characterizations | wl-df.clel 37874 |
| [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 37874 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2815 df-cleq 2732 wl-df.cleq 37871 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2719 wl-df.clab 37870 |
| [Levy] p. 358 | Axiom | df-clab 2719 wl-df.clab 37870 |
| [Levy58] p. 2 | Definition I | isfin1-3 10306 |
| [Levy58] p. 2 | Definition II | df-fin2 10206 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10205 |
| [Levy58] p. 2 | Definition III | df-fin3 10208 |
| [Levy58] p. 3 | Definition V | df-fin5 10209 |
| [Levy58] p. 3 | Definition IV | df-fin4 10207 |
| [Levy58] p. 4 | Definition VI | df-fin6 10210 |
| [Levy58] p. 4 | Definition VII | df-fin7 10211 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10335 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27675 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27686 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27718 nosupbnd1 27703 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27720 nosupbnd2 27705 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27724 noetasuplem4 27725 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27721 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1775 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1776 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1778 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32504 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32508 mdsymi 32507 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32502 mdsymlem6 32504 mdsymlem7 32505 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32506 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32409 ssdmd2 32410 ssmd1 32407 ssmd2 32408 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32405 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32377 df-md 32376 mdbr 32390 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32427 mdslj1i 32415 mdslj2i 32416 mdslle1i 32413 mdslle2i 32414 mdslmd1i 32425 mdslmd2i 32426 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32417 mdsl2bi 32419 mdsl2i 32418 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32431 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32428 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32429 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32406 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32411 mdsl3 32412 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32430 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32525 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 39814 hlrelat1 39893 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 39532 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32432 cvmdi 32420 cvnbtwn4 32385 cvrnbtwn4 39772 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32433 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 39833 cvp 32471 cvrp 39909 lcvp 39533 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32495 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32494 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 39826 hlexch4N 39885 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32497 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 39936 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 40242 atpsubN 40246 df-pointsN 39995 pointpsubN 40244 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 39997 pmap11 40255 pmaple 40254 pmapsub 40261 pmapval 40250 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 40258 pmap1N 40260 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 40263 pmapglb2N 40264 pmapglb2xN 40265 pmapglbx 40262 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 40345 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 39970 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 40289 paddclN 40335 paddidm 40334 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 39971 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 40331 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 39970 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 39971 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19648 lsmmod2 19649 lssats 39505 shatomici 32454 shatomistici 32457 shmodi 31486 shmodsi 31485 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32396 mdsymlem7 32505 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 31685 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31589 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32511 |
| [Margaris] p. 40 | Rule C | exlimiv 1937 |
| [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 397 df-ex 1787 df-or 854 dfbi2 475 |
| [Margaris] p. 51 | Theorem 1 | idALT 23 |
| [Margaris] p. 56 | Theorem 3 | conventions 30495 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 45359 |
| [Margaris] p. 60 | Theorem 8 | jcn 162 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 45360 |
| [Margaris] p. 79 | Rule C | exinst01 45070 exinst11 45071 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1983 19.2g 2200 r19.2z 4434 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2214 rr19.3v 3612 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2170 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1833 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1788 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2193 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2217 19.9h 2297 exlimd 2230 exlimdh 2301 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2173 excomim 2174 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2336 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30496 conventions-labels 30496 conventions-labels 30496 conventions-labels 30496 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1834 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 44823 albi 1825 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2237 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2238 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 44825 exbi 1854 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2241 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 44822 2alimdv 1925 alimd 2224 alimdh 1824 alimdv 1923 ax-4 1816 ralimdaa 3241 ralimdv 3154 ralimdva 3152 ralimdvva 3187 sbcimdv 3798 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2219 19.21h 2298 19.21t 2218 19.21vv 44821 alrimd 2227 alrimdd 2226 alrimdh 1870 alrimdv 1936 alrimi 2225 alrimih 1831 alrimiv 1934 alrimivv 1935 bj-alrimdh 36936 hbralrimi 3130 r19.21be 3233 r19.21bi 3232 ralrimd 3245 ralrimdv 3138 ralrimdva 3140 ralrimdvv 3184 ralrimdvva 3195 ralrimi 3238 ralrimia 3239 ralrimiv 3131 ralrimiva 3132 ralrimivv 3181 ralrimivva 3183 ralrimivvva 3186 ralrimivw 3136 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 44824 2eximdv 1926 bj-exim 36951 exim 1841 eximd 2228 eximdh 1871 eximdv 1924 rexim 3081 reximd2a 3250 reximdai 3242 reximdd 45596 reximddv 3156 reximddv2 3199 reximddv3 3157 reximdv 3155 reximdv2 3150 reximdva 3153 reximdvai 3151 reximdvva 3188 reximi2 3073 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2223 19.23bi 2203 19.23h 2299 19.23t 2222 exlimdv 1940 exlimdvv 1941 exlimexi 44969 exlimiv 1937 exlimivv 1939 rexlimd3 45592 rexlimdv 3139 rexlimdv3a 3145 rexlimdva 3141 rexlimdva2 3143 rexlimdvaa 3142 rexlimdvv 3196 rexlimdvva 3197 rexlimdvvva 3198 rexlimdvw 3146 rexlimiv 3134 rexlimiva 3133 rexlimivv 3182 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 1998 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1887 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1877 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2239 r19.27z 4445 r19.27zv 4446 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2240 19.28vv 44831 r19.28z 4437 r19.28zf 45607 r19.28zv 4441 rr19.28v 3613 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1880 r19.29d2r 3127 r19.29imd 3105 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1888 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2246 19.31vv 44829 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2245 r19.32 47562 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 44827 19.33 1891 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 1999 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1884 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2242 19.36vv 44828 r19.36zv 4447 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2244 19.37vv 44830 r19.37zv 4442 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1846 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 1997 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1894 19.40 1893 r19.40 3106 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2247 19.41rg 44995 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2248 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1889 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2249 r19.44zv 4444 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2250 r19.45zv 4443 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2614 |
| [Mayet] p. 370 | Remark | jpi 32366 largei 32363 stri 32353 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32308 ishst 32310 |
| [Mayet3] p. 10 | Theorem | hstrbi 32362 hstri 32361 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 31824 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 31825 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32374 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31428 chsupcl 31436 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32456 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32450 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32477 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 40476 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18451 latj32 18449 latjass 18447 |
| [Megill] p. 444 | Axiom C5 | ax-5 1917 ax5ALT 39400 |
| [Megill] p. 444 | Section 7 | conventions 30495 |
| [Megill] p. 445 | Lemma L12 | aecom-o 39394 ax-c11n 39381 axc11n 2434 |
| [Megill] p. 446 | Lemma L17 | equtrr 2029 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 39389 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 39421 hbnae 2440 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2489 sbid 2267 sbidd-misc 50210 sbidd 50209 |
| [Megill] p. 448 | Remark 9.6 | axc14 2471 |
| [Megill] p. 448 | Scheme C4' | ax-c4 39377 |
| [Megill] p. 448 | Scheme C5' | ax-c5 39376 sp 2195 |
| [Megill] p. 448 | Scheme C6' | ax-11 2168 |
| [Megill] p. 448 | Scheme C7' | ax-c7 39378 |
| [Megill] p. 448 | Scheme C8' | ax-7 2015 |
| [Megill] p. 448 | Scheme C9' | ax-c9 39383 |
| [Megill] p. 448 | Scheme C10' | ax-6 1974 ax-c10 39379 |
| [Megill] p. 448 | Scheme C11' | ax-c11 39380 |
| [Megill] p. 448 | Scheme C12' | ax-8 2121 |
| [Megill] p. 448 | Scheme C13' | ax-9 2129 |
| [Megill] p. 448 | Scheme C14' | ax-c14 39384 |
| [Megill] p. 448 | Scheme C15' | ax-c15 39382 |
| [Megill] p. 448 | Scheme C16' | ax-c16 39385 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 39397 dral1 2447 dral2-o 39423 dral2 2446 drex1 2449 drex2 2450 drsb1 2503 drsb2 2278 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2183 sbequ 2094 sbid2v 2517 |
| [Megill] p. 450 | Example in Appendix | hba1-o 39390 hba1 2304 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 47356 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 23 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3818 rspsbca 3819 stdpc4 2079 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 39377 ra4 3825 stdpc5 2220 |
| [Mendelson] p. 81 | Rule C | exlimiv 1937 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2035 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2262 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3728 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5462 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4333 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4334 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4212 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4269 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4213 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4078 |
| [Mendelson] p. 231 | Definition of union | dfun3 4211 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5397 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4842 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5516 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4554 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5517 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4869 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5776 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6227 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7725 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6323 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8528 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9075 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 8996 xpsneng 8997 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9003 xpcomeng 9004 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9006 |
| [Mendelson] p. 255 | Definition | brsdom 8918 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 8999 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8774 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 8981 mapsnend 8980 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9081 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9080 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8827 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 8984 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9000 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10099 djucomen 10098 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10103 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10097 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8463 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8490 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10479 |
| [Mendelson] p. 281 | Definition | df-r1 9686 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9735 |
| [Mendelson] p. 287 | Axiom system MK | ru 3728 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30354 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30389 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30391 vdgn1frgrv3 30392 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30393 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30386 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30379 2pthfrgrrn 30377 2pthfrgrrn2 30378 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31348 |
| [Monk1] p. 22 | Remark | conventions 30495 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30495 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4174 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5733 ssrelf 32714 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5734 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5142 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6221 coi2 6222 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5869 rn0 5875 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 6099 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5643 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5878 rnxp 6128 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5724 xp0 5725 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6036 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6033 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7861 imaexg 7860 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6030 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7023 funfvop 6998 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6888 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6899 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6538 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7205 dff13f 7206 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7170 funrnex 7903 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7198 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6185 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4901 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 7955 df-1st 7938 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 7956 df-2nd 7939 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9776 ranksnb 9749 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9777 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9778 rankunb 9772 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9760 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9686 r1val2 9759 |
| [Monk1] p. 117 | Lemma | zorn2 10426 zorn2g 10423 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9908 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10481 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9903 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1816 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2015 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2189 ax-c15 39382 ax12v2 2191 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 39377 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2168 |
| [Monk2] p. 109 | Lemma 15 | equvini 2463 equvinv 2036 eqvinop 5434 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1917 ax5ALT 39400 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2152 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2168 |
| [Monk2] p. 114 | Lemma 21 | sp 2195 |
| [Monk2] p. 114 | Lemma 22 | axc4 2330 hba1-o 39390 hba1 2304 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2164 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2186 nfra2 3341 nfra2w 3276 |
| [Moore] p. 53 | Part I | df-mre 17546 |
| [Munkres] p. 77 | Example 2 | distop 22985 indistop 22992 indistopon 22991 |
| [Munkres] p. 77 | Example 3 | fctop 22994 fctop2 22995 |
| [Munkres] p. 77 | Example 4 | cctop 22996 |
| [Munkres] p. 78 | Definition of basis | df-bases 22936 isbasis3g 22939 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17404 tgval2 22946 |
| [Munkres] p. 79 | Remark | tgcl 22959 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 22953 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 22977 tgss3 22976 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 22978 basgen2 22979 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 37712 topdifinfeq 37713 topdifinffin 37711 topdifinfindis 37709 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23150 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 23028 topcld 23025 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 23029 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 23031 |
| [Munkres] p. 94 | Definition of closure | clsval 23027 |
| [Munkres] p. 94 | Definition of interior | ntrval 23026 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 23065 elcls 23063 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 23073 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23138 neindisj 23107 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23140 |
| [Munkres] p. 97 | Definition of limit point | islp2 23135 lpval 23129 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23305 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23217 iscn 23225 iscn2 23228 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23270 cncnp2 23271 cncnpi 23268 df-cnp 23218 iscnp 23227 iscnp2 23229 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24533 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25303 |
| [Nathanson] p. 123 | Remark | reprgt 34812 reprinfz1 34813 reprlt 34810 |
| [Nathanson] p. 123 | Definition | df-repr 34800 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 34832 |
| [Nathanson] p. 123 | Proposition | breprexp 34824 breprexpnat 34825 itgexpif 34797 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32200 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 48302 |
| [Pfenning] p. 17 | Definition XM | natded 30498 |
| [Pfenning] p. 17 | Definition NNC | natded 30498 notnotrd 133 |
| [Pfenning] p. 17 | Definition ` `C | natded 30498 |
| [Pfenning] p. 18 | Rule" | natded 30498 |
| [Pfenning] p. 18 | Definition /\I | natded 30498 |
| [Pfenning] p. 18 | Definition ` `E | natded 30498 natded 30498 natded 30498 natded 30498 natded 30498 |
| [Pfenning] p. 18 | Definition ` `I | natded 30498 natded 30498 natded 30498 natded 30498 natded 30498 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30498 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30498 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30498 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30498 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30498 |
| [Pfenning] p. 127 | Definition =E | natded 30498 |
| [Pfenning] p. 127 | Definition =I | natded 30498 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25194 df-dip 30797 dip0l 30814 ip0l 21618 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25235 ipval 30799 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 30810 ipcj 21616 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25197 dipdir 30938 ipdir 21621 ipdiri 30926 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 30806 nmsq 25186 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 30921 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 30923 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 30924 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25203 dipass 30941 ipass 21627 ipassi 30937 |
| [Prugovecki] p. 186 | Definition of bra | braval 32040 df-bra 31946 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 31947 kbval 32050 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32478 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 40381 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32492 atcvat4i 32493 cvrat3 39935 cvrat4 39936 lsatcvat3 39545 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32378 cvrval 39762 df-cv 32375 df-lcv 39512 lspsncv0 21146 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 40393 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 40394 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2719 rabid 3413 rabidd 45603 wl-df.clab 37870 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2290 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2732 wl-df.cleq 37871 |
| [Quine] p. 19 | Definition 2.9 | conventions 30495 df-v 3434 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2879 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2876 abid2f 2932 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2287 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2096 sbalex 2254 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2815 wl-df.clel 37874 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2740 eqid1 30562 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2747 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3731 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3732 dfsbcq2 3733 |
| [Quine] p. 43 | Theorem 6.8 | vex 3436 |
| [Quine] p. 43 | Theorem 6.9 | isset 3446 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3536 spcgv 3541 spcimgf 3498 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3743 spsbcd 3744 |
| [Quine] p. 44 | Theorem 6.12 | elex 3453 |
| [Quine] p. 44 | Theorem 6.13 | elab 3624 elabg 3621 elabgf 3619 |
| [Quine] p. 44 | Theorem 6.14 | noel 4273 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4656 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4565 df-sn 4563 |
| [Quine] p. 49 | Theorem 7.4 | snss 4723 snssg 4722 |
| [Quine] p. 49 | Theorem 7.5 | prss 4758 prssg 4757 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4701 prid1g 4699 prid2 4702 prid2g 4700 snid 4601 snidg 4599 |
| [Quine] p. 51 | Theorem 7.12 | snex 5375 |
| [Quine] p. 51 | Theorem 7.13 | prex 5374 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4864 unisnALT 45370 unisng 4863 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4868 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4876 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4873 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6462 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 47550 dfiota2 6449 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 47559 iotaval 6466 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6472 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6468 |
| [Quine] p. 58 | Definition 9.1 | df-op 4569 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5474 opabidw 5473 opelopab 5491 opelopaba 5485 opelopabaf 5493 opelopabf 5494 opelopabg 5487 opelopabga 5482 opelopabgf 5489 oprabid 7395 oprabidw 7394 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5631 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5633 |
| [Quine] p. 64 | Definition 9.15 | df-id 5520 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6557 |
| [Quine] p. 65 | Theorem 10.4 | funi 6524 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6545 funsng 6543 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6494 |
| [Quine] p. 65 | Definition 10.2 | args 6051 dffv4 6831 |
| [Quine] p. 68 | Definition 10.11 | conventions 30495 df-fv 6500 fv2 6829 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14232 nn0opth2i 14231 nn0opthi 14230 omopthi 8594 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8346 |
| [Quine] p. 232 | Equation i | carddom 10474 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6580 funimaexg 6579 |
| [Quine] p. 331 | Axiom system NF | ru 3728 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31180 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 30797 polid 31255 polid2i 31253 polidi 31254 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 30909 |
| [ReedSimon] p. 195 | Remark | lnophm 32115 lnophmi 32114 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32228 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32230 leopmuli 32229 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32233 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 31948 leoppos 32222 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32232 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32221 |
| [Ribenboim] p. 181 | Remark | nprmdvdsfacm1 48103 |
| [Ribenboim], p. 181 | Statement | ppivalnn 48111 |
| [Roman] p. 4 | Definition | df-dmat 22480 df-dmatalt 48890 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20132 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20214 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 48977 |
| [Roman] p. 112 | Note | isldepslvec2 48977 ldepsnlinc 49000 zlmodzxznm 48989 |
| [Roman] p. 112 | Example | zlmodzxzequa 48988 zlmodzxzequap 48991 zlmodzxzldep 48996 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 22880 |
| [Rosenlicht] p. 80 | Theorem | heicant 38023 |
| [Rosser] p. 281 | Definition | df-op 4569 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 34836 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 34837 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 48858 pmtr3ncom 19448 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19444 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19387 cayleyth 19388 |
| [Rudin] p. 164 | Equation 27 | efcan 16059 |
| [Rudin] p. 164 | Equation 30 | efzval 16067 |
| [Rudin] p. 167 | Equation 48 | absefi 16161 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 198 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1778 |
| [Sanford] p. 39 | Rule 4 | mptxor 1776 |
| [Sanford] p. 40 | Rule 1 | mptnan 1775 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6072 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6075 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6071 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6069 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17546 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17547 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17547 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17549 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10057 |
| [Schechter] p. 141 | Definition (MC) | dfac11 43508 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10366 axdc3 10374 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20216 isrngo 38265 |
| [Schechter] p. 276 | Remark 11.6.e | span0 31638 |
| [Schechter] p. 276 | Definition of span | df-span 31405 spanval 31429 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 22983 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6342 onelord 43697 ordelon 6341 ordelord 6339 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 43698 sucidg 6400 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6372 onsuc 7760 ord0 6371 ordsuci 7758 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 43699 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5190 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 43474 elon2 6328 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6323 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5528 epelg 5526 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9512 epirron 43700 ordirr 6335 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 43702 oneptr 43701 ontr1 6364 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6360 oneptri 43703 ordtri3or 6349 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8433 ord0eln0 6373 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6386 onsucss 43712 trsucss 6407 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7765 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6413 ordnbtwn 6412 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 43714 ordnexbtwnsuc 43713 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10321 onsucf1lem 43715 onsucf1o 43718 onsucf1olem 43716 onsucrn 43717 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 43719 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7792 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 43708 ordne0gt0 43707 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 43710 limnsuc 43711 onsucelab 43709 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9562 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7807 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9565 ordom 7823 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9566 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8573 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7730 ssorduni 7729 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8463 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9569 limom 7829 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8402 df1o2 8409 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8448 oa0suclim 43721 oalim 8464 oasuc 8456 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8449 om0suclim 43722 omlim 8465 omsuc 8458 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8454 oe0m1 8453 oe0suclim 43723 oelim 8466 oesuc 8459 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 43675 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 43725 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 43726 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 43727 limexissupab 43729 limiun 43728 limuni 6379 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8470 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8474 om1om1r 43730 om1r 8475 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8467 oaomoecl 43724 oecl 8469 omcl 8468 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 43677 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8476 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8477 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 43731 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 43732 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8544 nnamecl 43733 nnecl 8546 nnmcl 8545 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 43734 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8484 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8485 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8492 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 43736 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 43737 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 43739 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8491 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 43743 omword1 8505 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 43742 oaordnrex 43741 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 43738 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 43744 omword2 8506 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 43745 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 43746 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 43747 omordi 8498 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8500 omord2com 43748 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 43749 df-2o 8403 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 43752 oewordi 8524 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 43753 oeworde 8526 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 43754 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 43755 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 43751 omnord1ex 43750 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 43756 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 43758 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 43762 oenord1ex 43761 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 43763 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8493 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 43757 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8511 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8512 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 43765 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8530 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 43766 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 43767 cantnfub2 43768 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 43771 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 29008 axtgcgrrflx 28555 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 29009 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 29010 axtgcgrid 28556 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28541 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 29021 axtgsegcon 28557 df-trkgcb 28543 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 29032 axtg5seg 28558 df-trkgcb 28543 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 29033 axtgbtwnid 28559 df-trkgb 28542 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 29035 axtgpasch 28560 df-trkgb 28542 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 29054 df-trkg2d 34856 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28563 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28564 df-trkg2d 34856 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 29057 axtgeucl 28565 df-trkge 28544 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 29070 axtgcont 28562 axtgcont1 28561 df-trkgb 28542 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 36216 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 36218 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 36221 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 36225 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 36226 tgcgrcomimp 28570 tgcgrcoml 28572 tgcgrcomr 28571 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 36231 tgcgrtriv 28577 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 36235 tg5segofs 34864 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 34861 df-ofs 36212 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 36237 tgcgrextend 28578 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 36239 tgsegconeq 28579 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36251 btwntriv2 36241 tgbtwntriv2 28580 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 36242 tgbtwncom 28581 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36245 tgbtwntriv1 28584 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36246 tgbtwnswapid 28585 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36252 btwnintr 36248 tgbtwnexch2 28589 tgbtwnintr 28586 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36254 btwnexch3 36249 tgbtwnexch 28591 tgbtwnexch3 28587 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36253 tgbtwnouttr 28590 tgbtwnouttr2 28588 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 29053 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36256 tgbtwndiff 28599 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28592 trisegint 36257 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36273 tgifscgr 28601 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28651 colrot1 28652 colrot2 28653 lncom 28715 lnrot1 28716 lnrot2 28717 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36269 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36274 tgcgrsub 28602 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36284 tgcgrxfr 28611 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28610 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36270 df-cgrg 28604 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28604 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36285 tgbtwnxfr 28623 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36291 colinearperm2 36293 colinearperm3 36292 colinearperm4 36294 colinearperm5 36295 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28626 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36268 tgellng 28646 tglng 28639 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36296 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36304 lnxfr 28659 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36305 lnext 28660 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36309 tgfscgr 28661 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36310 lncgr 28662 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36271 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36312 lnid 28663 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36313 tgidinside 28664 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36330 tgbtwnconn1 28668 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36331 tgbtwnconn2 28669 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36332 tgbtwnconn3 28670 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36338 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36336 legov 28678 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28679 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28692 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36339 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36341 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36343 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36344 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36345 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36342 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36347 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28680 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28682 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28683 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28684 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28685 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36354 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36355 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36350 df-outsideof 36349 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36351 ishlg 28695 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28700 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28702 outsideofrflx 36356 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28696 hlcomd 28697 outsideofcom 36357 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28703 outsideoftr 36358 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 28711 outsideofeu 36360 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36367 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36368 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36361 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36376 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36377 tglineelsb2 28725 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36379 linerflx1 36378 linerflx2 36380 tglinecom 28728 tglinerflx1 28726 tglinerflx2 28727 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36382 tglinethru 28729 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36366 tglng 28639 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28687 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36385 tglinethrueu 28732 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36386 tglineineq 28736 tglineinteq 28738 tglineintmo 28735 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28742 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28743 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 28744 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 28759 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 28755 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 28747 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 28746 ismir 28752 mirbtwn 28751 mircgr 28750 mirfv 28749 mirval 28748 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 28757 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 28758 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 28759 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 28762 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 28763 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 28768 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 28765 mirbtwni 28764 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 28766 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 28778 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 28782 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 28779 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 28780 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 28781 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 28784 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 28785 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 28791 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 28787 israg 28790 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 28792 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 28793 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 28795 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 28796 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 28797 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 28798 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 28799 ragncol 28802 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 28800 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 28806 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 28810 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 28807 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 28789 isperp 28805 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 28808 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 28815 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 28823 colperpexlem2 28824 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 28826 colperpexlem3 28825 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 28831 midex 28830 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 28828 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 28837 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 28832 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 28841 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 28844 opphllem6 28845 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 28847 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28560 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 28848 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 28856 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 28851 hpgbr 28853 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 28858 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 28857 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 28859 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 28860 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 28861 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 28862 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 28863 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 28877 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 28867 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 28881 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 28882 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 28883 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 28884 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 28885 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 28888 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 28890 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 28868 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 28891 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 28894 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 28895 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 28896 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 28897 trgcopyeu 28899 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 28923 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 28902 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 28911 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 28909 cgrahl2 28910 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 28912 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 28913 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 28915 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 28916 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 28919 cgrahl 28920 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 28924 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 28925 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 28926 acopyeu 28927 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 28934 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 28938 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 28931 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 28946 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 28939 isleag 28940 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 28948 tgsas1 28947 tgsas2 28949 tgsas3 28950 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 28952 tgasa1 28951 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 28953 tgsss2 28954 tgsss3 28955 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27259 dchrsum 27257 dchrsum2 27256 sumdchr 27260 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27261 sum2dchr 27262 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 20041 ablfacrp2 20042 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27204 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27205 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27212 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27470 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27473 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27527 vmalogdivsum2 27526 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27517 dirith2 27516 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27515 rpvmasum 27514 rpvmasum2 27500 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27475 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27513 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27480 dchrisumlem1 27477 dchrisumlem2 27478 dchrisumlem3 27479 dchrisumlema 27476 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27483 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27512 dchrmusumlem 27510 dchrvmasumlem 27511 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27482 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27484 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27508 dchrisum0re 27501 dchrisumn0 27509 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27494 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27498 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27499 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27554 pntrsumbnd2 27555 pntrsumo1 27553 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27518 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27520 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27522 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27525 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27530 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27531 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27536 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27538 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27539 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27547 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27548 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27545 selberg3lem2 27546 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27549 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27543 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27556 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27557 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27558 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27572 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27584 pntlemb 27585 pntlemc 27583 pntlemd 27582 pntlemg 27586 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27584 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27576 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27581 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27584 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27597 pntleml 27599 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 33934 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 33921 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 33953 constrinvcl 33964 constrmulcl 33962 constrnegcl 33954 constrsqrtcl 33970 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 33940 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 33950 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 33972 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 33982 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4241 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4340 dif0 4313 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4426 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4410 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4232 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4233 |
| [Stoll] p. 20 | Remark | invdif 4214 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4571 |
| [Stoll] p. 43 | Definition | uniiun 4995 |
| [Stoll] p. 44 | Definition | intiin 4996 |
| [Stoll] p. 45 | Definition | df-iin 4931 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4930 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 402 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4241 |
| [Strang] p. 242 | Section 6.3 | expgrowth 44780 |
| [Suppes] p. 22 | Theorem 2 | eq0 4285 eq0f 4282 |
| [Suppes] p. 22 | Theorem 4 | eqss 3937 eqssd 3939 eqssi 3938 |
| [Suppes] p. 23 | Theorem 5 | ss0 4337 ss0b 4336 |
| [Suppes] p. 23 | Theorem 6 | sstr 3930 sstrALT2 45279 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4041 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4042 |
| [Suppes] p. 23 | Theorem 9 | psstr 4045 |
| [Suppes] p. 23 | Theorem 10 | pssss 4036 |
| [Suppes] p. 25 | Theorem 12 | elin 3906 elun 4090 |
| [Suppes] p. 26 | Theorem 15 | inidm 4162 |
| [Suppes] p. 26 | Theorem 16 | in0 4330 |
| [Suppes] p. 27 | Theorem 23 | unidm 4094 |
| [Suppes] p. 27 | Theorem 24 | un0 4329 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4114 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4122 |
| [Suppes] p. 27 | Theorem 27 | unss 4126 |
| [Suppes] p. 27 | Theorem 28 | indir 4221 |
| [Suppes] p. 27 | Theorem 29 | undir 4222 |
| [Suppes] p. 28 | Theorem 32 | difid 4311 |
| [Suppes] p. 29 | Theorem 33 | difin 4207 |
| [Suppes] p. 29 | Theorem 34 | indif 4215 |
| [Suppes] p. 29 | Theorem 35 | undif1 4411 |
| [Suppes] p. 29 | Theorem 36 | difun2 4416 |
| [Suppes] p. 29 | Theorem 37 | difin0 4409 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4407 |
| [Suppes] p. 29 | Theorem 39 | difundi 4225 |
| [Suppes] p. 29 | Theorem 40 | difindi 4227 |
| [Suppes] p. 30 | Theorem 41 | nalset 5243 |
| [Suppes] p. 39 | Theorem 61 | uniss 4853 |
| [Suppes] p. 39 | Theorem 65 | uniop 5463 |
| [Suppes] p. 41 | Theorem 70 | intsn 4921 |
| [Suppes] p. 42 | Theorem 71 | intpr 4919 intprg 4918 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5418 |
| [Suppes] p. 42 | Theorem 78 | intun 4917 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4968 dfiun2g 4966 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4969 |
| [Suppes] p. 47 | Theorem 86 | elpw 4540 elpw2 5269 elpw2g 5268 elpwg 4539 elpwgdedVD 45361 |
| [Suppes] p. 47 | Theorem 87 | pwid 4558 |
| [Suppes] p. 47 | Theorem 89 | pw0 4750 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4751 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5640 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5782 xpindir 5783 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5694 xpundir 5695 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9509 |
| [Suppes] p. 58 | Theorem 2 | relss 5732 |
| [Suppes] p. 59 | Theorem 4 | eldm 5849 eldm2 5850 eldm2g 5848 eldmg 5847 |
| [Suppes] p. 59 | Definition 3 | df-dm 5635 |
| [Suppes] p. 60 | Theorem 6 | dmin 5860 |
| [Suppes] p. 60 | Theorem 8 | rnun 6103 |
| [Suppes] p. 60 | Theorem 9 | rnin 6104 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5837 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5831 brcnvg 5828 |
| [Suppes] p. 62 | Equation 5 | elcnv 5825 elcnv2 5826 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6063 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6102 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6100 |
| [Suppes] p. 63 | Definition | dftrrels2 39027 |
| [Suppes] p. 63 | Theorem 20 | co02 6219 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5924 |
| [Suppes] p. 63 | Definition 7 | df-co 5634 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5834 |
| [Suppes] p. 64 | Theorem 27 | coass 6224 |
| [Suppes] p. 65 | Theorem 31 | resundi 5952 |
| [Suppes] p. 65 | Theorem 34 | elima 6024 elima2 6025 elima3 6026 elimag 6023 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6107 |
| [Suppes] p. 66 | Theorem 40 | dminss 6111 |
| [Suppes] p. 66 | Theorem 41 | imainss 6112 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6115 |
| [Suppes] p. 81 | Definition 34 | dfec2 8643 |
| [Suppes] p. 82 | Theorem 72 | elec 8687 elecALTV 38639 elecg 8685 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 39063 erth 8695 erth2 8696 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 39066 erdisj 8698 |
| [Suppes] p. 83 | Definition 35, | df-parts 39236 dfmembpart2 39241 |
| [Suppes] p. 89 | Theorem 96 | map0b 8828 |
| [Suppes] p. 89 | Theorem 97 | map0 8832 map0g 8829 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8833 mapsnd 8831 |
| [Suppes] p. 89 | Theorem 99 | mapss 8834 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 9988 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 9987 |
| [Suppes] p. 92 | Theorem 1 | enref 8929 enrefg 8928 |
| [Suppes] p. 92 | Theorem 2 | ensym 8947 ensymb 8946 ensymi 8948 |
| [Suppes] p. 92 | Theorem 3 | entr 8950 |
| [Suppes] p. 92 | Theorem 4 | unen 8989 |
| [Suppes] p. 94 | Theorem 15 | endom 8923 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 8944 |
| [Suppes] p. 94 | Theorem 17 | domtr 8951 |
| [Suppes] p. 95 | Theorem 18 | sbth 9032 |
| [Suppes] p. 97 | Theorem 23 | canth2 9065 canth2g 9066 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9036 df-sdom 8893 dfsdom2 9035 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9049 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9038 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9037 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9047 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8926 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9050 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9045 |
| [Suppes] p. 98 | Exercise 4 | fundmen 8975 fundmeng 8976 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9010 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9046 |
| [Suppes] p. 104 | Theorem 37 | fofi 9220 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9226 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9226 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10471 |
| [Suppes] p. 130 | Definition 3 | df-tr 5187 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7730 |
| [Suppes] p. 134 | Definition 6 | df-suc 6323 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7847 finds 7843 finds1 7846 finds2 7845 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9571 isfinite2 9205 isfiniteg 9207 unbnn 9203 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10839 df-ltpq 10831 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7810 tfinds 7807 tfinds2 7811 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8483 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8485 |
| [Suppes] p. 211 | Theorem 25 | oaass 8493 |
| [Suppes] p. 225 | Definition 8 | iscard2 9898 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10483 |
| [Suppes] p. 228 | Theorem 59 | harcard 9900 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 9986 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6369 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7743 onminsb 7744 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10493 |
| [Suppes] p. 229 | Theorem 65 | alephcard 9990 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 9997 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 9991 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9862 |
| [Suppes] p. 242 | Theorem 6 | weth 10415 |
| [Suppes] p. 242 | Theorem 8 | entric 10477 |
| [Suppes] p. 242 | Theorem 9 | carden 10471 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 35925 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 35929 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2712 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2732 wl-df.cleq 37871 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2815 wl-df.clel 37874 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2734 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2760 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7367 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3728 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5357 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4587 elpr2 4589 elpr2g 4588 elprg 4585 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4577 elsn2 4604 elsn2g 4603 elsng 4576 velsn 4578 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5414 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4572 sneqr 4778 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4583 dfsn2 4575 dfsn2ALT 4584 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7691 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5423 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5410 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5394 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7694 unexg 7693 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4630 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4846 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3897 df-un 3895 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4862 uniprg 4861 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5313 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4628 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6389 elsucg 6387 sstr2 3929 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4095 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4145 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4108 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4163 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4219 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4220 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3910 df-ss 3907 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4538 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4123 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3908 sseqin2 4159 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3944 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4172 inss2 4173 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 3986 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4856 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5395 sspwimp 45362 sspwimpALT 45369 sspwimpALT2 45372 sspwimpcf 45364 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5402 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5206 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3393 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5236 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3893 |
| [TakeutiZaring] p. 20 | Definition 5.14 | bj-dfnul2 36882 dfnul2 4271 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4311 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4288 n0f 4284 neq0 4287 neq0f 4283 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9508 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9651 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9666 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3434 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5249 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4335 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5256 ssexg 5258 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5252 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9520 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9512 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4301 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4072 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4235 undif3VD 45326 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4073 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4080 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3055 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3065 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7703 xpexg 7700 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5632 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6563 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6739 fun11 6566 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6505 svrelfun 6564 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5836 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5838 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5637 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5638 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5634 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6152 dfrel2 6147 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5641 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5761 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5768 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5781 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 5964 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5944 opelresi 5946 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 5971 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5960 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 5965 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6534 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6067 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6532 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6741 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2613 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30495 df-fv 6500 fv3 6852 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7872 cnvexg 7871 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7856 dmexg 7848 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7857 rnexg 7849 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 44898 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7867 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6847 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 47638 tz6.12-1-afv2 47705 tz6.12-1 6857 tz6.12-afv 47637 tz6.12-afv2 47704 tz6.12 6858 tz6.12c-afv2 47706 tz6.12c 6856 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 47701 tz6.12-2 6821 tz6.12i-afv2 47707 tz6.12i 6860 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6495 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6496 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6498 wfo 6490 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6497 wf1 6489 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6499 wf1o 6491 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 6978 eqfnfv2 6979 eqfnfv2f 6982 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6932 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7168 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7166 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6580 funimaexg 6579 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5080 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5534 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5586 dffr3 6058 eliniseg 6053 iniseg 6056 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5525 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5602 fr3nr 7722 frirr 5601 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5578 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7724 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5589 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5611 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6305 tz6.26i 6306 wefrc 5619 wereu2 5622 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6307 wfii 6308 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6501 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7280 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7281 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7287 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7288 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7289 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7293 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7300 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7302 |
| [TakeutiZaring] p. 35 | Notation | wtr 5186 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 44899 tz7.2 5608 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5191 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6330 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6338 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6339 ordelordALT 44982 ordelordALTVD 45311 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6345 ordelssne 6344 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6343 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6347 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7732 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7733 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6321 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6349 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 44994 ordon 7727 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7728 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7800 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6365 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5188 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7742 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7778 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6423 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6422 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7729 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4876 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6323 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6399 sucidg 6400 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7760 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6413 ordnbtwn 6412 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7775 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6322 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7828 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7833 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7788 ordelsuc 7767 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7769 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7798 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7815 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7836 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7837 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7838 |
| [TakeutiZaring] p. 43 | Remark | omon 7825 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9554 omex 9562 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7823 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7842 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7839 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7840 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7818 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4899 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5205 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4900 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5279 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7745 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6368 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4885 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9579 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7740 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8312 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8333 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8334 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8335 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8342 tz7.44-2 8343 tz7.44-3 8344 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8304 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8299 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8283 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8381 tz7.49c 8382 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8379 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8378 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8380 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2660 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 9931 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 9932 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8464 oasuc 8456 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7808 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8467 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8448 oa0r 8470 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8468 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8480 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8552 nnaordi 8551 oaord 8479 oaordi 8478 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 4986 uniss2 4879 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8482 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8487 oawordex 8489 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8544 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8581 |
| [TakeutiZaring] p. 60 | Remark | oancom 9570 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8492 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8549 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8484 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8451 omlim 8465 omsuc 8458 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8449 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8546 nnmcl 8545 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8565 nnmordi 8564 omord 8500 omordi 8498 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8501 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8569 omwordri 8504 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8471 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8474 om1r 8475 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8507 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8509 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8510 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8511 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8512 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8541 oe0 8454 oelim 8466 oesuc 8459 onesuc 8462 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8452 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8519 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8520 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8453 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8477 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8521 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8527 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8525 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8526 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8530 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8532 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9647 tz9.1 9648 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9686 r10 9690 r1lim 9694 r1limg 9693 r1suc 9692 r1sucg 9691 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9702 r1ord2 9703 r1ordg 9700 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9712 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9737 tz9.13 9713 tz9.13g 9714 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9687 rankval 9738 rankvalb 9719 rankvalg 9739 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9761 rankelb 9746 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9775 rankval3 9762 rankval3b 9748 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9751 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9717 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9756 rankr1c 9743 rankr1g 9754 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9757 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9771 rankssb 9770 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9764 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9763 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10395 dfac3 10041 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 9950 numth 10392 numth2 10391 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10466 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10467 cardid2 9875 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9882 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10471 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9881 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9866 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9887 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9879 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9085 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 8962 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9090 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9014 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9885 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10018 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9137 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9145 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10019 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9142 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10008 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 9986 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9894 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10136 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9230 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8894 isfi 8919 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9146 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10454 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9007 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10446 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10106 unxpdom 9166 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9896 cardsdomelir 9895 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9168 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 9934 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8772 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10482 infxpidm2 9937 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10127 infxp 10134 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9019 pw2f1o 9017 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9078 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10407 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10402 ac6s5 10411 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10463 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10464 uniimadomf 10465 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10194 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10189 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10174 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10171 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10177 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10184 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10193 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10503 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10172 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10196 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10017 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10016 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10028 alephfp2 10029 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10620 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10032 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10490 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10504 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10505 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 39376 |
| [Tarski] p. 67 | Scheme B5 | sp 2195 |
| [Tarski] p. 68 | Lemma 6 | avril1 30558 equid 2019 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2024 |
| [Tarski] p. 70 | Lemma 14 | spim 2395 spime 2397 spimew 1978 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2189 ax-c15 39382 ax12i 1973 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2096 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1975 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1917 ax5ALT 39400 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2015 ax-8 2121 ax-9 2129 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28557 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28558 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28560 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28560 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28561 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16208 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 38027 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 38029 |
| [Weierstrass] p. 272 | Definition | df-mdet 22575 mdetuni 22612 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 909 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 874 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 875 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 925 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 975 |
| [WhiteheadRussell] p. 100 | Theorem *2.01 | pm2.01 189 |
| [WhiteheadRussell] p. 100 | Theorem *2.02 | ax-1 6 |
| [WhiteheadRussell] p. 100 | Theorem *2.03 | con2 135 |
| [WhiteheadRussell] p. 100 | Theorem *2.04 | pm2.04 90 wl-luk-pm2.04 37808 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 44245 imim2 58 wl-luk-imim2 37803 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 47483 imim1 83 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 902 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2667 syl 17 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 908 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 22 wl-luk-id 37806 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 900 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 142 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 903 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 130 notnotrALT2 45371 wl-luk-notnotr 37807 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 146 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 44275 axfrege28 44274 con3 153 |
| [WhiteheadRussell] p. 103 | Theorem *2.17 | ax-3 8 |
| [WhiteheadRussell] p. 103 | Theorem *2.18 | pm2.18 128 |
| [WhiteheadRussell] p. 104 | Theorem *2.2 | orc 873 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 930 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 123 wl-luk-pm2.21 37800 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 124 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 895 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 947 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 30496 pm2.27 42 wl-luk-pm2.27 37798 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 928 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 38739 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 929 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 977 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 978 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 976 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1093 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 912 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 913 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 950 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 56 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 887 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 888 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5 169 pm2.5g 168 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6 192 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 889 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 890 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 891 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 172 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 857 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 858 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 894 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 896 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 193 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 905 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 948 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 949 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 194 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 897 pm2.67 898 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 176 pm2.521g 174 pm2.521g2 175 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 904 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 980 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 906 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 204 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 981 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 982 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 939 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 937 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 979 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 983 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 84 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 938 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 109 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 999 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 470 pm3.2im 160 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 1000 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 1001 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 1002 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 1003 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 472 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 460 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 403 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 808 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 449 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 450 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 483 simplim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 485 simprim 166 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 770 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 771 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 813 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 628 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 815 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 493 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 494 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 968 pm3.44 967 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 814 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 474 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 971 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34b 317 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 262 |
| [WhiteheadRussell] p. 117 | Theorem *4.11 | notbi 320 |
| [WhiteheadRussell] p. 117 | Theorem *4.12 | con2bi 354 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotb 316 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14 812 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 838 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 223 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 811 bitr 810 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 568 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 910 pm4.25 911 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 461 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1015 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 876 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 469 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 927 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 639 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 923 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 643 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 984 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1094 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1013 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1059 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1030 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 1004 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 1006 pm4.45 1005 pm4.45im 833 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 990 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 859 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 550 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 989 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 992 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 993 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 994 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 995 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 991 pm4.56 996 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 997 pm4.57 998 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 405 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 862 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 398 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 855 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 406 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 856 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67 399 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 562 pm4.71d 566 pm4.71i 564 pm4.71r 563 pm4.71rd 567 pm4.71ri 565 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 957 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 532 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 942 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 522 pm4.76 523 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 969 pm4.77 970 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 940 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1011 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 393 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81 394 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 1031 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1032 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 348 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 349 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 352 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 388 impexp 451 pm4.87 849 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 829 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 952 pm5.11g 951 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 953 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 955 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 954 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1020 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1021 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1019 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbn 384 pm5.18 382 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 387 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 830 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1022 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1055 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1056 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 907 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 577 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 389 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 362 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6 1009 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 961 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 836 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 578 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 841 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 831 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 839 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 390 pm5.41 391 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 548 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 547 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 1012 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1025 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 956 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1008 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1026 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1027 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1035 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 367 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 271 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 1036 |
| [WhiteheadRussell] p. 145 | Theorem *10.3 | bj-alsyl 36933 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 44803 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 44804 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1877 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 44805 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 44806 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 44807 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1900 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 44808 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 44809 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 44810 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 44811 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 44812 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 44814 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 44815 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 44816 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 44813 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2101 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 44819 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 44820 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2081 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2171 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1836 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1837 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 44821 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 44822 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 44823 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 44824 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 44826 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 44825 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1894 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 44828 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 44829 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 44827 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1835 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 44830 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 44831 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1853 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 44832 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2354 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1867 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 44837 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 44833 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 44834 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 44835 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 44836 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 44841 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 44838 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 44839 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 44840 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 44842 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2573 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 44852 pm13.13b 44853 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 44854 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3016 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3017 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3611 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 44860 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 44861 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 44855 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 44997 pm13.193 44856 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 44857 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 44858 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 44859 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 44866 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 44865 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 44864 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3792 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 44867 pm14.122b 44868 pm14.122c 44869 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 44870 pm14.123b 44871 pm14.123c 44872 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 44874 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 44873 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 44875 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6473 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 44876 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6474 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 44877 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 44879 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2637 eupickbi 2640 sbaniota 44880 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 44878 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2588 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 44881 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30495 df-fv 6500 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 9923 pm54.43lem 9922 |
| [Young] p. 141 | Definition of operator ordering | leop2 32220 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32226 idleop 32227 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 43274 |
| [vandenDries] p. 43 | Theorem 62 | pellex 43281 pellexlem1 43275 |