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 17603 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17603 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18012 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17624 0funcg 49433 df-termc 49821 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 49898 prsthinc 49812 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 49926 df-mndtc 49926 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 49922 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17647 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 49914 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 49939 oppgoppchom 49938 oppgoppcid 49940 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17717 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17705 invisoinvl 17726 |
| [Adamek] p. 28 | Example 3.13 | idinv 17725 idiso 17724 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17710 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17684 df-iso 17685 dfiso2 17708 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17691 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17742 cicerALT 49394 |
| [Adamek] p. 29 | Definition 3.15 | cic 17735 df-cic 17732 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17794 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17706 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17707 isoco 17713 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17794 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17817 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 49652 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17810 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 49922 discthing 49809 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 49766 prsthinc 49812 thincciso 49801 thincciso2 49803 thincciso3 49804 thinccisod 49802 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 49926 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17824 cofucla 49444 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 49510 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18047 catcisoi 49748 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18102 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17843 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17842 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18102 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17867 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17873 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17872 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18087 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18087 |
| [Adamek] p. 39 | Remark 3.42 | 2oppf 49480 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 49471 funcoppc 17811 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18035 elcatchom 49745 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17861 fthoppf 49512 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17860 fulloppf 49511 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18044 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 49433 df-catc 18035 |
| [Adamek] p. 45 | Exercise 3G | incat 49949 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 49952 nelsubc3 49419 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 49499 imasubc2 49500 imasubc3 49504 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17774 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17775 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 49419 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17786 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17748 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 49508 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 49507 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 49509 ressffth 17876 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 49950 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 17882 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 17903 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 17907 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 17883 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 17909 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 49433 df-inito 17920 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 49433 df-termc 49821 initc 49439 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21446 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 17921 oppctermo 49584 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 17948 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 17952 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 49585 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 17922 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21447 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 17955 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17683 |
| [Adamek] p. 107 | Example 7.20(7) | thincinv 49817 |
| [Adamek] p. 108 | Example 7.25(4) | thincsect2 49816 |
| [Adamek] p. 110 | Example 7.33(9) | thincmon 49781 |
| [Adamek] p. 110 | Proposition 7.35 | sectmon 17718 |
| [Adamek] p. 112 | Proposition 7.42 | sectepi 17720 |
| [Adamek] p. 185 | Section 10.67 | updjud 9858 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 49993 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 49993 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 49993 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 49994 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 49994 |
| [Adamek] p. 478 | Item Rng | df-ringc 20591 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 48897 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 48919 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14506 df-pfx 14607 df-substr 14577 df-word 14449 lencl 14468 wrd0 14474 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24664 df-nmoo 30832 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32240 hmopidmchi 32238 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32288 pjcmul2i 32289 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 32005 unoplin 32007 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 32006 unopadj2 32025 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 32100 lnopunii 32099 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32173 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 27935 |
| [Alling] p. 184 | Axiom B | bdayfo 27657 |
| [Alling] p. 184 | Axiom O | ltsso 27656 |
| [Alling] p. 184 | Axiom SD | nodense 27672 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27763 |
| [Alling] p. 185 | Theorem | conway 27787 |
| [Alling] p. 185 | Axiom FE | noeta 27723 |
| [Alling] p. 186 | Theorem 4 | lesrec 27807 lesrecd 27808 |
| [Alling], p. 2 | Definition | rp-brsslt 43768 |
| [Alling], p. 3 | Note | nla0001 43771 nla0002 43769 nla0003 43770 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11329 addcan2d 11349 addcan2i 11339 addcand 11348 addcani 11338 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11382 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11441 negsubd 11510 negsubi 11471 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11443 negnegd 11495 negnegi 11463 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11582 subdid 11605 subdii 11598 subdir 11583 subdird 11606 subdiri 11599 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11324 mul01d 11344 mul01i 11335 mul02 11323 mul02d 11343 mul02i 11334 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11786 mulcan2d 11783 mulcand 11782 mulcani 11788 |
| [Apostol] p. 18 | Theorem I.8 | receu 11794 xreceu 33013 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11824 divrecd 11932 divreci 11898 divreczi 11891 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11850 recreci 11885 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11789 mul0ord 11797 mul0ori 11796 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11588 mul2negd 11604 mul2negi 11597 mulneg1 11585 mulneg1d 11602 mulneg1i 11595 |
| [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 20361 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11854 divdivdivd 11976 divdivdivi 11916 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 12941 rpaddcld 12976 rpmulcl 12942 rpmulcld 12977 |
| [Apostol] p. 20 | Axiom 8 | rpneg 12951 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 12954 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11271 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11742 ltadd1dd 11760 ltadd1i 11703 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12003 ltmul1a 12002 ltmul1i 12072 ltmul1ii 12082 ltmul2 12004 ltmul2d 13003 ltmul2dd 13017 ltmul2i 12075 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11669 msqgt0d 11716 msqgt0i 11686 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11671 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11655 lt0neg1d 11718 ltneg 11649 ltnegd 11727 ltnegi 11693 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11634 lt2addd 11772 lt2addi 11711 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 12918 |
| [Apostol] p. 21 | Exercise 4 | recgt0 11999 recgt0d 12088 recgt0i 12059 recgt0ii 12060 |
| [Apostol] p. 22 | Definition of integers | df-z 12501 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12171 |
| [Apostol] p. 22 | Definition of rationals | df-q 12874 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9369 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12409 |
| [Apostol] p. 26 | Theorem I.29 | arch 12410 archd 45510 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12607 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12411 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12872 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12871 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13126 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16278 zneo 12587 zneoALTV 48018 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26707 msqsqrtd 15378 resqrtth 15190 sqrtth 15300 sqrtthi 15306 sqsqrtd 15377 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12160 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12838 |
| [Apostol] p. 361 | Remark | crreczi 14163 |
| [Apostol] p. 363 | Remark | absgt0i 15335 |
| [Apostol] p. 363 | Example | abssubd 15391 abssubi 15339 |
| [ApostolNT] p. 7 | Remark | fmtno0 47889 fmtno1 47890 fmtno2 47899 fmtno3 47900 fmtno4 47901 fmtno5fac 47931 fmtnofz04prm 47926 |
| [ApostolNT] p. 7 | Definition | df-fmtno 47877 |
| [ApostolNT] p. 8 | Definition | df-ppi 27078 |
| [ApostolNT] p. 14 | Definition | df-dvds 16192 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16208 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16233 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16228 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16221 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16223 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16209 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16210 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16215 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16250 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16252 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16254 |
| [ApostolNT] p. 15 | Definition | df-gcd 16434 dfgcd2 16485 |
| [ApostolNT] p. 16 | Definition | isprm2 16621 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16592 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16855 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16452 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16486 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16488 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16467 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16459 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16650 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16652 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16868 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16862 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16342 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16526 |
| [ApostolNT] p. 24 | Definition | df-mu 27079 |
| [ApostolNT] p. 25 | Definition | df-phi 16705 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27169 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16730 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16715 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16719 |
| [ApostolNT] p. 32 | Definition | df-vma 27076 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27171 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27195 |
| [ApostolNT] p. 38 | Remark | df-sgm 27080 |
| [ApostolNT] p. 38 | Definition | df-sgm 27080 |
| [ApostolNT] p. 75 | Definition | df-chp 27077 df-cht 27075 |
| [ApostolNT] p. 104 | Definition | congr 16603 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16195 |
| [ApostolNT] p. 106 | Definition | moddvds 16202 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16285 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16286 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13820 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13860 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14173 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16227 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16606 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17014 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16608 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16722 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16741 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16723 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27050 |
| [ApostolNT] p. 179 | Definition | df-lgs 27274 lgsprme0 27318 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27319 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27295 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27310 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27367 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27386 2lgsoddprm 27395 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27353 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27362 |
| [ApostolNT] p. 188 | Definition | df-lgs 27274 lgs1 27320 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27311 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27313 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27321 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27322 |
| [Baer] p. 40 | Property (b) | mapdord 42003 |
| [Baer] p. 40 | Property (c) | mapd11 42004 |
| [Baer] p. 40 | Property (e) | mapdin 42027 mapdlsm 42029 |
| [Baer] p. 40 | Property (f) | mapd0 42030 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 41990 mapd1o 42013 |
| [Baer] p. 41 | Property (g) | mapdat 42032 |
| [Baer] p. 44 | Part (1) | mapdpg 42071 |
| [Baer] p. 45 | Part (2) | hdmap1eq 42166 mapdheq 42093 mapdheq2 42094 mapdheq2biN 42095 |
| [Baer] p. 45 | Part (3) | baerlem3 42078 |
| [Baer] p. 46 | Part (4) | mapdheq4 42097 mapdheq4lem 42096 |
| [Baer] p. 46 | Part (5) | baerlem5a 42079 baerlem5abmN 42083 baerlem5amN 42081 baerlem5b 42080 baerlem5bmN 42082 |
| [Baer] p. 47 | Part (6) | hdmap1l6 42186 hdmap1l6a 42174 hdmap1l6e 42179 hdmap1l6f 42180 hdmap1l6g 42181 hdmap1l6lem1 42172 hdmap1l6lem2 42173 mapdh6N 42112 mapdh6aN 42100 mapdh6eN 42105 mapdh6fN 42106 mapdh6gN 42107 mapdh6lem1N 42098 mapdh6lem2N 42099 |
| [Baer] p. 48 | Part 9 | hdmapval 42193 |
| [Baer] p. 48 | Part 10 | hdmap10 42205 |
| [Baer] p. 48 | Part 11 | hdmapadd 42208 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 42182 mapdh6hN 42108 |
| [Baer] p. 48 | Part (7) | mapdh75cN 42118 mapdh75d 42119 mapdh75e 42117 mapdh75fN 42120 mapdh7cN 42114 mapdh7dN 42115 mapdh7eN 42113 mapdh7fN 42116 |
| [Baer] p. 48 | Part (8) | mapdh8 42153 mapdh8a 42140 mapdh8aa 42141 mapdh8ab 42142 mapdh8ac 42143 mapdh8ad 42144 mapdh8b 42145 mapdh8c 42146 mapdh8d 42148 mapdh8d0N 42147 mapdh8e 42149 mapdh8g 42150 mapdh8i 42151 mapdh8j 42152 |
| [Baer] p. 48 | Part (9) | mapdh9a 42154 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 42134 |
| [Baer] p. 49 | Part 12 | hdmap11 42213 hdmapeq0 42209 hdmapf1oN 42230 hdmapneg 42211 hdmaprnN 42229 hdmaprnlem1N 42214 hdmaprnlem3N 42215 hdmaprnlem3uN 42216 hdmaprnlem4N 42218 hdmaprnlem6N 42219 hdmaprnlem7N 42220 hdmaprnlem8N 42221 hdmaprnlem9N 42222 hdmapsub 42212 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 42233 hdmap14lem10 42242 hdmap14lem1a 42231 hdmap14lem2N 42234 hdmap14lem2a 42232 hdmap14lem3 42235 hdmap14lem8 42240 hdmap14lem9 42241 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 42243 hdmap14lem12 42244 hdmap14lem13 42245 hdmap14lem14 42246 hdmap14lem15 42247 hgmapval 42252 |
| [Baer] p. 50 | Part 15 | hgmapadd 42259 hgmapmul 42260 hgmaprnlem2N 42262 hgmapvs 42256 |
| [Baer] p. 50 | Part 16 | hgmaprnN 42266 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 42282 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 42283 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 42284 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 42285 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 42287 hgmapvv 42291 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 42286 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 42288 |
| [Baer] p. 111 | Line 15 | hdmapg 42295 hdmapglem7 42294 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26708 2irrexpqALT 26778 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 23 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2570 |
| [BellMachover] p. 460 | Notation | df-mo 2540 |
| [BellMachover] p. 460 | Definition | mo3 2565 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2709 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2713 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5234 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5243 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37303 sepex 5247 |
| [BellMachover] p. 466 | Problem | axpow2 5314 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5315 |
| [BellMachover] p. 466 | Axiom Union | axun2 7692 |
| [BellMachover] p. 468 | Definition | df-ord 6328 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6343 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6350 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6345 |
| [BellMachover] p. 471 | Definition of N | df-om 7819 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7756 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6330 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9563 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7834 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9688 |
| [BellMachover] p. 478 | Definition | rankval2 9742 rankval2b 35274 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9706 r1ord3g 9703 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9513 |
| [BellMachover] p. 488 | Axiom AC | ac5 10399 dfac4 10044 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10032 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 39684 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32440 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32482 chirredi 32481 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32470 |
| [Beran] p. 3 | Definition of join | sshjval3 31441 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 31703 cmcm2i 31680 cmcm2ii 31685 cmt2N 39615 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 31704 lecmi 31689 lecmii 31690 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 31678 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 31707 cm2ji 31712 cm2mi 31713 |
| [Beran] p. 95 | Definition | df-sh 31294 issh2 31296 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31173 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31186 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31177 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 31915 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 31917 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 31916 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 31918 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31169 his1i 31187 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31170 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31171 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31172 |
| [Beran] p. 96 | Definition of norm | df-hnorm 31055 dfhnorm2 31209 normval 31211 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31271 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 31060 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31328 |
| [Beran] p. 96 | Definition of converge | df-hlim 31059 hlimi 31275 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31220 norm-i 31216 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31224 norm-ii 31225 normlem0 31196 normlem1 31197 normlem2 31198 normlem3 31199 normlem4 31200 normlem5 31201 normlem6 31202 normlem7 31203 normlem7tALT 31206 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31226 norm-iii 31227 |
| [Beran] p. 98 | Remark 3.4 | bcs 31268 bcsiALT 31266 bcsiHIL 31267 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31208 normpar 31242 normpari 31241 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31233 normpyth 31232 normpythi 31229 |
| [Beran] p. 99 | Remark | lnfn0 32134 lnfn0i 32129 lnop0 32053 lnop0i 32057 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32113 nmcfnex 32140 nmcfnexi 32138 nmcopex 32116 nmcopexi 32114 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32141 nmcfnlbi 32139 nmcoplb 32117 nmcoplbi 32115 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32143 lnfnconi 32142 lnopcon 32122 lnopconi 32121 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31243 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31240 norm3adifii 31235 norm3dif 31237 norm3difi 31234 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31388 pjhth 31480 pjhtheu 31481 pjpjhth 31512 pjpjhthi 31513 pjth 25407 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31493 ococi 31492 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32148 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32149 riesz4 32151 riesz4i 32150 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32166 cnlnadjeu 32165 cnlnadjeui 32164 cnlnadji 32163 cnlnadjlem1 32154 nmopadjlei 32175 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32178 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32177 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32179 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 32023 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32189 nmopcoadji 32188 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32180 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32190 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32187 pjadj2coi 32291 pjadjcoi 32248 |
| [Beran] p. 107 | Definition | df-ch 31308 isch2 31310 |
| [Beran] p. 107 | Remark 3.12 | choccl 31393 isch3 31328 occl 31391 ocsh 31370 shoccl 31392 shocsh 31371 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31495 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31419 |
| [Beran] p. 109 | Property (i) | pjadj2 32274 pjadj3 32275 pjadji 31772 pjadjii 31761 |
| [Beran] p. 109 | Property (ii) | pjidmco 32268 pjidmcoi 32264 pjidmi 31760 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32260 |
| [Beran] p. 111 | Remark | ho0val 31837 pjch1 31757 |
| [Beran] p. 111 | Definition | df-hfmul 31821 df-hfsum 31820 df-hodif 31819 df-homul 31818 df-hosum 31817 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 31758 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 31781 pjchi 31519 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31526 pjoc2i 31525 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 31767 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32252 pjssmii 31768 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32251 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32250 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32255 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32253 pjssge0ii 31769 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32254 pjdifnormii 31770 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1778 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1776 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1779 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1774 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34469 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34477 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34475 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34479 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34499 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34530 df-sitm 34508 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34530 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34507 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29133 isuhgrop 29155 isusgrop 29247 isuspgrop 29246 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 48210 df-subgr 29353 uhgrspan1 29388 uhgrspansubgr 29376 |
| [Bollobas] p. 3 | Definition | df-gric 48230 gricuspgr 48267 isuspgrim 48245 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29540 df-clnbgr 48168 df-cusgr 29497 df-nbgr 29418 fusgrmaxsize 29550 |
| [Bollobas] p. 4 | Definition | df-upwlks 48483 df-wlks 29685 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 29636 finsumvtxdgeven 29638 fusgr1th 29637 fusgrvtxdgonume 29640 vtxdgoddnumeven 29639 |
| [Bollobas] p. 5 | Notation | df-pths 29799 |
| [Bollobas] p. 5 | Definition | df-crcts 29871 df-cycls 29872 df-trls 29776 df-wlkson 29686 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29144 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 48549 df-cllaw 48535 df-mgm 18577 df-mgm2 48568 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 48550 df-asslaw 48537 df-sgrp 18656 df-sgrp2 48570 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 48569 df-comlaw 48536 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18672 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33118 mndlactf1o 33122 mndractf1 33120 mndractf1o 33123 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20182 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20100 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 33810 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 33814 assarrginv 33813 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 33855 fldextrspunfld 33853 fldextrspunlem1 33852 fldextrspunlem2 33854 fldextrspunlsp 33851 fldextrspunlsplem 33850 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 33629 dfufd2 33642 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7243 fcofo 7244 |
| [BourbakiTop1] p. | Remark | xnegmnf 13137 xnegpnf 13136 |
| [BourbakiTop1] p. | Remark | rexneg 13138 |
| [BourbakiTop1] p. | Remark 3 | ust0 24176 ustfilxp 24169 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24046 |
| [BourbakiTop1] p. | Criterion | ishmeo 23715 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24239 iducn 24238 snfil 23820 |
| [BourbakiTop1] p. | Example 2 | neifil 23836 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 24023 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24259 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 34134 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23819 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24231 df-ust 24157 filintn0 23817 filn0 23818 istgp 24033 ucnprima 24237 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24242 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24253 df-usp 24213 df-utop 24187 trust 24185 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 34033 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23072 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23225 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24162 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24165 |
| [BourbakiTop1] p. | Property V_ii | innei 23081 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23089 neissex 23083 |
| [BourbakiTop1] p. | Proposition 1 | neips 23069 neiss 23065 ucncn 24240 ustund 24178 ustuqtop 24202 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23223 neiptopreu 23089 utop2nei 24206 utop3cls 24207 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24247 uspreg 24229 utopreg 24208 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23647 imasncls 23648 imasnopn 23646 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 23956 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24164 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24166 |
| [BourbakiTop1] p. | Property V_iii | elnei 23067 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24258 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24163 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24167 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23343 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23802 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 22850 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 34030 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 46409 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 46411 stoweid 46410 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 46348 stoweidlem10 46357 stoweidlem14 46361 stoweidlem15 46362 stoweidlem35 46382 stoweidlem36 46383 stoweidlem37 46384 stoweidlem38 46385 stoweidlem40 46387 stoweidlem41 46388 stoweidlem43 46390 stoweidlem44 46391 stoweidlem46 46393 stoweidlem5 46352 stoweidlem50 46397 stoweidlem52 46399 stoweidlem53 46400 stoweidlem55 46402 stoweidlem56 46403 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 46370 stoweidlem24 46371 stoweidlem27 46374 stoweidlem28 46375 stoweidlem30 46377 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 46381 stoweidlem59 46406 stoweidlem60 46407 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 46392 stoweidlem49 46396 stoweidlem7 46354 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 46378 stoweidlem39 46386 stoweidlem42 46389 stoweidlem48 46395 stoweidlem51 46398 stoweidlem54 46401 stoweidlem57 46404 stoweidlem58 46405 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 46372 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 46364 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 46358 stoweidlem13 46360 stoweidlem26 46373 stoweidlem61 46408 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 46365 |
| [Bruck] p. 1 | Section I.1 | df-clintop 48549 df-mgm 18577 df-mgm2 48568 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18656 df-sgrp2 48570 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 18981 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5182 |
| [Church] p. 129 | Section II.24 | df-ifp 1064 dfifp2 1065 |
| [Clemente] p. 10 | Definition IT | natded 30490 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30490 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30490 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30490 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30490 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30490 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30490 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30490 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30490 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30490 |
| [Clemente] p. 14 | Proof 5.11 | natded 30490 |
| [Clemente] p. 14 | Definition E` `n | natded 30490 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30492 ex-natded5.2 30491 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30495 ex-natded5.3 30494 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30497 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30499 ex-natded5.7 30498 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30501 ex-natded5.8 30500 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30503 ex-natded5.13 30502 |
| [Clemente] p. 32 | Definition I` `n | natded 30490 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30490 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30490 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30490 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30504 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30505 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30507 ex-natded9.26 30506 |
| [Cohen] p. 301 | Remark | relogoprlem 26568 |
| [Cohen] p. 301 | Property 2 | relogmul 26569 relogmuld 26602 |
| [Cohen] p. 301 | Property 3 | relogdiv 26570 relogdivd 26603 |
| [Cohen] p. 301 | Property 4 | relogexp 26573 |
| [Cohen] p. 301 | Property 1a | log1 26562 |
| [Cohen] p. 301 | Property 1b | loge 26563 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26765 |
| [Cohen4] p. 349 | Property | relogbf 26769 |
| [Cohen4] p. 352 | Definition | elogb 26748 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26755 |
| [Cohen4] p. 361 | Property 3 | logbrec 26760 relogbdiv 26757 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26753 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26758 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26746 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26747 |
| [Cohen4] p. 367 | Property | logbchbase 26749 |
| [Cohen4] p. 377 | Property 2 | logblt 26762 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34462 sxbrsigalem4 34464 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18492 acsinfd 18491 acsinfdimd 18493 acsmap2d 18490 acsmapd 18489 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34467 |
| [Connell] p. 57 | Definition | df-scmat 22447 df-scmatalt 48748 |
| [Conway] p. 4 | Definition | lesrec 27807 lesrecd 27808 |
| [Conway] p. 5 | Definition | addsval 27970 addsval2 27971 df-adds 27968 df-muls 28115 df-negs 28029 |
| [Conway] p. 7 | Theorem | 0lt1s 27820 |
| [Conway] p. 12 | Theorem 12 | pw2cut2 28470 |
| [Conway] p. 16 | Theorem 0(i) | sltsright 27869 |
| [Conway] p. 16 | Theorem 0(ii) | sltsleft 27868 |
| [Conway] p. 16 | Theorem 0(iii) | lesid 27747 |
| [Conway] p. 17 | Theorem 3 | addsass 28013 addsassd 28014 addscom 27974 addscomd 27975 addsrid 27972 addsridd 27973 |
| [Conway] p. 17 | Definition | df-0s 27815 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 28052 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 28049 negsidd 28050 |
| [Conway] p. 18 | Theorem 5 | leadds1 27997 leadds1d 28003 |
| [Conway] p. 18 | Definition | df-1s 27816 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 28044 negscld 28045 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 27988 |
| [Conway] p. 19 | Note | mulsunif2 28178 |
| [Conway] p. 19 | Theorem 7 | addsdi 28163 addsdid 28164 addsdird 28165 mulnegs1d 28168 mulnegs2d 28169 mulsass 28174 mulsassd 28175 mulscom 28147 mulscomd 28148 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28142 mulscld 28143 |
| [Conway] p. 19 | Theorem 8(iii) | lemulsd 28146 ltmuls 28144 ltmulsd 28145 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28152 mulsgt0d 28153 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28226 |
| [Conway] p. 23 | Theorem 11 | eqcuts3 27812 |
| [Conway] p. 24 | Definition | df-reno 28498 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28507 remulscl 28510 renegscl 28506 |
| [Conway] p. 27 | Definition | df-ons 28260 elons2 28266 |
| [Conway] p. 27 | Theorem 14 | ltonsex 28270 |
| [Conway] p. 28 | Theorem 15 | oncutlt 28272 onswe 28280 |
| [Conway] p. 29 | Remark | madebday 27908 newbday 27910 oldbday 27909 |
| [Conway] p. 29 | Definition | df-made 27835 df-new 27837 df-old 27836 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13793 |
| [Crawley] p. 1 | Definition of poset | df-poset 18248 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 39751 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 40555 dalaw 40251 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 42326 |
| [Crawley] p. 111 | Definition of set W | df-watsN 40355 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 40471 df-ldil 40469 isldil 40475 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 40470 df-trnN 40472 isltrn 40484 ltrnu 40486 |
| [Crawley] p. 112 | Lemma A | cdlema1N 40156 cdlema2N 40157 exatleN 39769 |
| [Crawley] p. 112 | Lemma B | 1cvrat 39841 cdlemb 40159 cdlemb2 40406 cdlemb3 40971 idltrn 40515 l1cvat 39420 lhpat 40408 lhpat2 40410 lshpat 39421 ltrnel 40504 ltrnmw 40516 |
| [Crawley] p. 112 | Lemma C | cdlemc1 40556 cdlemc2 40557 ltrnnidn 40539 trlat 40534 trljat1 40531 trljat2 40532 trljat3 40533 trlne 40550 trlnidat 40538 trlnle 40551 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 40356 |
| [Crawley] p. 113 | Lemma C | cdlemc 40562 cdlemc3 40558 cdlemc4 40559 |
| [Crawley] p. 113 | Lemma D | cdlemd 40572 cdlemd1 40563 cdlemd2 40564 cdlemd3 40565 cdlemd4 40566 cdlemd5 40567 cdlemd6 40568 cdlemd7 40569 cdlemd8 40570 cdlemd9 40571 cdleme31sde 40750 cdleme31se 40747 cdleme31se2 40748 cdleme31snd 40751 cdleme32a 40806 cdleme32b 40807 cdleme32c 40808 cdleme32d 40809 cdleme32e 40810 cdleme32f 40811 cdleme32fva 40802 cdleme32fva1 40803 cdleme32fvcl 40805 cdleme32le 40812 cdleme48fv 40864 cdleme4gfv 40872 cdleme50eq 40906 cdleme50f 40907 cdleme50f1 40908 cdleme50f1o 40911 cdleme50laut 40912 cdleme50ldil 40913 cdleme50lebi 40905 cdleme50rn 40910 cdleme50rnlem 40909 cdlemeg49le 40876 cdlemeg49lebilem 40904 |
| [Crawley] p. 113 | Lemma E | cdleme 40925 cdleme00a 40574 cdleme01N 40586 cdleme02N 40587 cdleme0a 40576 cdleme0aa 40575 cdleme0b 40577 cdleme0c 40578 cdleme0cp 40579 cdleme0cq 40580 cdleme0dN 40581 cdleme0e 40582 cdleme0ex1N 40588 cdleme0ex2N 40589 cdleme0fN 40583 cdleme0gN 40584 cdleme0moN 40590 cdleme1 40592 cdleme10 40619 cdleme10tN 40623 cdleme11 40635 cdleme11a 40625 cdleme11c 40626 cdleme11dN 40627 cdleme11e 40628 cdleme11fN 40629 cdleme11g 40630 cdleme11h 40631 cdleme11j 40632 cdleme11k 40633 cdleme11l 40634 cdleme12 40636 cdleme13 40637 cdleme14 40638 cdleme15 40643 cdleme15a 40639 cdleme15b 40640 cdleme15c 40641 cdleme15d 40642 cdleme16 40650 cdleme16aN 40624 cdleme16b 40644 cdleme16c 40645 cdleme16d 40646 cdleme16e 40647 cdleme16f 40648 cdleme16g 40649 cdleme19a 40668 cdleme19b 40669 cdleme19c 40670 cdleme19d 40671 cdleme19e 40672 cdleme19f 40673 cdleme1b 40591 cdleme2 40593 cdleme20aN 40674 cdleme20bN 40675 cdleme20c 40676 cdleme20d 40677 cdleme20e 40678 cdleme20f 40679 cdleme20g 40680 cdleme20h 40681 cdleme20i 40682 cdleme20j 40683 cdleme20k 40684 cdleme20l 40687 cdleme20l1 40685 cdleme20l2 40686 cdleme20m 40688 cdleme20y 40667 cdleme20zN 40666 cdleme21 40702 cdleme21d 40695 cdleme21e 40696 cdleme22a 40705 cdleme22aa 40704 cdleme22b 40706 cdleme22cN 40707 cdleme22d 40708 cdleme22e 40709 cdleme22eALTN 40710 cdleme22f 40711 cdleme22f2 40712 cdleme22g 40713 cdleme23a 40714 cdleme23b 40715 cdleme23c 40716 cdleme26e 40724 cdleme26eALTN 40726 cdleme26ee 40725 cdleme26f 40728 cdleme26f2 40730 cdleme26f2ALTN 40729 cdleme26fALTN 40727 cdleme27N 40734 cdleme27a 40732 cdleme27cl 40731 cdleme28c 40737 cdleme3 40602 cdleme30a 40743 cdleme31fv 40755 cdleme31fv1 40756 cdleme31fv1s 40757 cdleme31fv2 40758 cdleme31id 40759 cdleme31sc 40749 cdleme31sdnN 40752 cdleme31sn 40745 cdleme31sn1 40746 cdleme31sn1c 40753 cdleme31sn2 40754 cdleme31so 40744 cdleme35a 40813 cdleme35b 40815 cdleme35c 40816 cdleme35d 40817 cdleme35e 40818 cdleme35f 40819 cdleme35fnpq 40814 cdleme35g 40820 cdleme35h 40821 cdleme35h2 40822 cdleme35sn2aw 40823 cdleme35sn3a 40824 cdleme36a 40825 cdleme36m 40826 cdleme37m 40827 cdleme38m 40828 cdleme38n 40829 cdleme39a 40830 cdleme39n 40831 cdleme3b 40594 cdleme3c 40595 cdleme3d 40596 cdleme3e 40597 cdleme3fN 40598 cdleme3fa 40601 cdleme3g 40599 cdleme3h 40600 cdleme4 40603 cdleme40m 40832 cdleme40n 40833 cdleme40v 40834 cdleme40w 40835 cdleme41fva11 40842 cdleme41sn3aw 40839 cdleme41sn4aw 40840 cdleme41snaw 40841 cdleme42a 40836 cdleme42b 40843 cdleme42c 40837 cdleme42d 40838 cdleme42e 40844 cdleme42f 40845 cdleme42g 40846 cdleme42h 40847 cdleme42i 40848 cdleme42k 40849 cdleme42ke 40850 cdleme42keg 40851 cdleme42mN 40852 cdleme42mgN 40853 cdleme43aN 40854 cdleme43bN 40855 cdleme43cN 40856 cdleme43dN 40857 cdleme5 40605 cdleme50ex 40924 cdleme50ltrn 40922 cdleme51finvN 40921 cdleme51finvfvN 40920 cdleme51finvtrN 40923 cdleme6 40606 cdleme7 40614 cdleme7a 40608 cdleme7aa 40607 cdleme7b 40609 cdleme7c 40610 cdleme7d 40611 cdleme7e 40612 cdleme7ga 40613 cdleme8 40615 cdleme8tN 40620 cdleme9 40618 cdleme9a 40616 cdleme9b 40617 cdleme9tN 40622 cdleme9taN 40621 cdlemeda 40663 cdlemedb 40662 cdlemednpq 40664 cdlemednuN 40665 cdlemefr27cl 40768 cdlemefr32fva1 40775 cdlemefr32fvaN 40774 cdlemefrs32fva 40765 cdlemefrs32fva1 40766 cdlemefs27cl 40778 cdlemefs32fva1 40788 cdlemefs32fvaN 40787 cdlemesner 40661 cdlemeulpq 40585 |
| [Crawley] p. 114 | Lemma E | 4atex 40441 4atexlem7 40440 cdleme0nex 40655 cdleme17a 40651 cdleme17c 40653 cdleme17d 40863 cdleme17d1 40654 cdleme17d2 40860 cdleme18a 40656 cdleme18b 40657 cdleme18c 40658 cdleme18d 40660 cdleme4a 40604 |
| [Crawley] p. 115 | Lemma E | cdleme21a 40690 cdleme21at 40693 cdleme21b 40691 cdleme21c 40692 cdleme21ct 40694 cdleme21f 40697 cdleme21g 40698 cdleme21h 40699 cdleme21i 40700 cdleme22gb 40659 |
| [Crawley] p. 116 | Lemma F | cdlemf 40928 cdlemf1 40926 cdlemf2 40927 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 40932 cdlemg16 41022 cdlemg28 41069 cdlemg28a 41058 cdlemg28b 41068 cdlemg3a 40962 cdlemg42 41094 cdlemg43 41095 cdlemg44 41098 cdlemg44a 41096 cdlemg46 41100 cdlemg47 41101 cdlemg9 40999 ltrnco 41084 ltrncom 41103 tgrpabl 41116 trlco 41092 |
| [Crawley] p. 116 | Definition of G | df-tgrp 41108 |
| [Crawley] p. 117 | Lemma G | cdlemg17 41042 cdlemg17b 41027 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 41121 df-edring 41122 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 41125 |
| [Crawley] p. 118 | Remark | tendopltp 41145 |
| [Crawley] p. 118 | Lemma H | cdlemh 41182 cdlemh1 41180 cdlemh2 41181 |
| [Crawley] p. 118 | Lemma I | cdlemi 41185 cdlemi1 41183 cdlemi2 41184 |
| [Crawley] p. 118 | Lemma J | cdlemj1 41186 cdlemj2 41187 cdlemj3 41188 tendocan 41189 |
| [Crawley] p. 118 | Lemma K | cdlemk 41339 cdlemk1 41196 cdlemk10 41208 cdlemk11 41214 cdlemk11t 41311 cdlemk11ta 41294 cdlemk11tb 41296 cdlemk11tc 41310 cdlemk11u-2N 41254 cdlemk11u 41236 cdlemk12 41215 cdlemk12u-2N 41255 cdlemk12u 41237 cdlemk13-2N 41241 cdlemk13 41217 cdlemk14-2N 41243 cdlemk14 41219 cdlemk15-2N 41244 cdlemk15 41220 cdlemk16-2N 41245 cdlemk16 41222 cdlemk16a 41221 cdlemk17-2N 41246 cdlemk17 41223 cdlemk18-2N 41251 cdlemk18-3N 41265 cdlemk18 41233 cdlemk19-2N 41252 cdlemk19 41234 cdlemk19u 41335 cdlemk1u 41224 cdlemk2 41197 cdlemk20-2N 41257 cdlemk20 41239 cdlemk21-2N 41256 cdlemk21N 41238 cdlemk22-3 41266 cdlemk22 41258 cdlemk23-3 41267 cdlemk24-3 41268 cdlemk25-3 41269 cdlemk26-3 41271 cdlemk26b-3 41270 cdlemk27-3 41272 cdlemk28-3 41273 cdlemk29-3 41276 cdlemk3 41198 cdlemk30 41259 cdlemk31 41261 cdlemk32 41262 cdlemk33N 41274 cdlemk34 41275 cdlemk35 41277 cdlemk36 41278 cdlemk37 41279 cdlemk38 41280 cdlemk39 41281 cdlemk39u 41333 cdlemk4 41199 cdlemk41 41285 cdlemk42 41306 cdlemk42yN 41309 cdlemk43N 41328 cdlemk45 41312 cdlemk46 41313 cdlemk47 41314 cdlemk48 41315 cdlemk49 41316 cdlemk5 41201 cdlemk50 41317 cdlemk51 41318 cdlemk52 41319 cdlemk53 41322 cdlemk54 41323 cdlemk55 41326 cdlemk55u 41331 cdlemk56 41336 cdlemk5a 41200 cdlemk5auN 41225 cdlemk5u 41226 cdlemk6 41202 cdlemk6u 41227 cdlemk7 41213 cdlemk7u-2N 41253 cdlemk7u 41235 cdlemk8 41203 cdlemk9 41204 cdlemk9bN 41205 cdlemki 41206 cdlemkid 41301 cdlemkj-2N 41247 cdlemkj 41228 cdlemksat 41211 cdlemksel 41210 cdlemksv 41209 cdlemksv2 41212 cdlemkuat 41231 cdlemkuel-2N 41249 cdlemkuel-3 41263 cdlemkuel 41230 cdlemkuv-2N 41248 cdlemkuv2-2 41250 cdlemkuv2-3N 41264 cdlemkuv2 41232 cdlemkuvN 41229 cdlemkvcl 41207 cdlemky 41291 cdlemkyyN 41327 tendoex 41340 |
| [Crawley] p. 120 | Remark | dva1dim 41350 |
| [Crawley] p. 120 | Lemma L | cdleml1N 41341 cdleml2N 41342 cdleml3N 41343 cdleml4N 41344 cdleml5N 41345 cdleml6 41346 cdleml7 41347 cdleml8 41348 cdleml9 41349 dia1dim 41426 |
| [Crawley] p. 120 | Lemma M | dia11N 41413 diaf11N 41414 dialss 41411 diaord 41412 dibf11N 41526 djajN 41502 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 41397 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 41483 dia2dimlem1 41429 dia2dimlem2 41430 dia2dimlem3 41431 dia2dimlem4 41432 dia2dimlem5 41433 diaf1oN 41495 diarnN 41494 dvheveccl 41477 dvhopN 41481 |
| [Crawley] p. 121 | Lemma N | cdlemn 41577 cdlemn10 41571 cdlemn11 41576 cdlemn11a 41572 cdlemn11b 41573 cdlemn11c 41574 cdlemn11pre 41575 cdlemn2 41560 cdlemn2a 41561 cdlemn3 41562 cdlemn4 41563 cdlemn4a 41564 cdlemn5 41566 cdlemn5pre 41565 cdlemn6 41567 cdlemn7 41568 cdlemn8 41569 cdlemn9 41570 diclspsn 41559 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 41538 |
| [Crawley] p. 122 | Lemma N | dih11 41630 dihf11 41632 dihjust 41582 dihjustlem 41581 dihord 41629 dihord1 41583 dihord10 41588 dihord11b 41587 dihord11c 41589 dihord2 41592 dihord2a 41584 dihord2b 41585 dihord2cN 41586 dihord2pre 41590 dihord2pre2 41591 dihordlem6 41578 dihordlem7 41579 dihordlem7b 41580 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 41595 dihfval 41596 dihval 41597 |
| [Diestel] p. 3 | Definition | df-gric 48230 df-grim 48227 isuspgrim 48245 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29497 df-nbgr 29418 |
| [Diestel] p. 3 | Definition by | df-grisom 48226 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 48210 df-subgr 29353 uhgrspan1 29388 uhgrspansubgr 29376 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 29640 vtxdgoddnumeven 29639 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29144 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 34041 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 34053 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 34045 zarcls1 34046 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 34056 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 34059 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 34062 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3906 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9568 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8777 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9576 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9904 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10477 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5252 |
| [Enderton] p. 19 | Definition | df-tp 4587 |
| [Enderton] p. 26 | Exercise 5 | unissb 4898 |
| [Enderton] p. 26 | Exercise 10 | pwel 5328 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5525 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5036 iinin2 5035 iinun2 5030 iunin1 5029 iunin1f 32643 iunin2 5028 uniin1 32637 uniin2 32638 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5034 iundif2 5031 |
| [Enderton] p. 32 | Exercise 20 | unineq 4242 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5055 |
| [Enderton] p. 33 | Exercise 25 | iununi 5056 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5063 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7726 iunpwss 5064 |
| [Enderton] p. 36 | Definition | opthwiener 5470 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5405 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4903 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5426 rnex 7862 rnexg 7854 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5871 rnuni 6114 |
| [Enderton] p. 42 | Definition of a function | dffun7 6527 dffun8 6528 |
| [Enderton] p. 43 | Definition of function value | funfv2 6930 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6569 |
| [Enderton] p. 44 | Definition (d) | dfima2 6029 dfima3 6030 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6939 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10395 ac7g 10396 df-ac 10038 dfac2 10054 dfac2a 10052 dfac2b 10053 dfac3 10043 dfac7 10055 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7202 |
| [Enderton] p. 52 | Definition | df-map 8777 |
| [Enderton] p. 53 | Exercise 21 | coass 6232 |
| [Enderton] p. 53 | Exercise 27 | dmco 6221 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6576 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6069 |
| [Enderton] p. 54 | Remark | ixpf 8870 ixpssmap 8882 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8848 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10405 ac9s 10415 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 38934 erref 8666 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 38937 erthi 8702 |
| [Enderton] p. 57 | Definition | df-ec 8647 |
| [Enderton] p. 58 | Definition | df-qs 8651 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8647 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5867 |
| [Enderton] p. 68 | Definition of successor | df-suc 6331 |
| [Enderton] p. 71 | Definition | df-tr 5208 dftr4 5213 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6406 unisucg 6405 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6406 unisucg 6405 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5222 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5224 trintALT 45225 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8542 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8544 onasuc 8465 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7371 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8543 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8545 onmsuc 8466 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8560 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8547 nnacom 8555 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8561 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8562 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8564 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8548 nnmsucr 8563 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8576 |
| [Enderton] p. 129 | Definition | df-en 8896 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7322 |
| [Enderton] p. 133 | Exercise 1 | xpomen 9937 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16150 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9143 |
| [Enderton] p. 135 | Corollary 6C | php3 9145 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9142 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9174 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9176 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9105 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9109 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9081 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10102 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10103 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10098 dju1en 10094 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9255 unifi 9256 unifi2 9257 |
| [Enderton] p. 144 | Corollary 6K | undif2 4431 unfi 9107 unfi2 9222 |
| [Enderton] p. 145 | Figure 38 | ffoss 7900 |
| [Enderton] p. 145 | Definition | df-dom 8897 |
| [Enderton] p. 146 | Example 1 | domen 8910 domeng 8911 |
| [Enderton] p. 146 | Example 3 | nndomo 9154 nnsdom 9575 nnsdomg 9211 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10106 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9082 xpdom1 9016 xpdom1g 9014 xpdom2g 9013 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9088 |
| [Enderton] p. 151 | Theorem 6M | zorn 10429 zorng 10426 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10414 dfac5 10051 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10498 |
| [Enderton] p. 164 | Example | infdif 10130 |
| [Enderton] p. 168 | Definition | df-po 5540 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6440 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6372 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6439 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6380 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7791 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7736 |
| [Enderton] p. 194 | Remark | onprc 7733 |
| [Enderton] p. 194 | Exercise 16 | suc11 6434 |
| [Enderton] p. 197 | Definition | df-card 9863 |
| [Enderton] p. 197 | Theorem 7P | carden 10473 |
| [Enderton] p. 200 | Exercise 25 | tfis 7807 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9700 |
| [Enderton] p. 202 | Definition | df-r1 9688 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9710 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9791 rankval4b 35275 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9527 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9781 rankprb 9775 rankpw 9767 rankpwi 9747 rankuniss 9790 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9539 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9540 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10032 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 9998 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10012 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8283 |
| [Enderton] p. 222 | Definition of kard | karden 9819 kardex 9818 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8535 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8537 |
| [Enderton] p. 240 | Exercise 25 | oarec 8499 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10172 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17577 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17519 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18488 mrieqv2d 17574 mrieqvd 17573 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17578 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17583 mreexexlem2d 17580 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18494 mreexfidimd 17585 |
| [Frege1879] p. 11 | Statement | df3or2 44113 |
| [Frege1879] p. 12 | Statement | df3an2 44114 dfxor4 44111 dfxor5 44112 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 44135 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 44136 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 44140 |
| [Frege1879] p. 31 | Proposition 4 | frege4 44144 |
| [Frege1879] p. 32 | Proposition 5 | frege5 44145 |
| [Frege1879] p. 33 | Proposition 6 | frege6 44151 |
| [Frege1879] p. 34 | Proposition 7 | frege7 44153 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 44154 axfrege8 44152 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 90 wl-luk-pm2.04 37689 |
| [Frege1879] p. 35 | Proposition 9 | frege9 44157 |
| [Frege1879] p. 36 | Proposition 10 | frege10 44165 |
| [Frege1879] p. 36 | Proposition 11 | frege11 44159 |
| [Frege1879] p. 37 | Proposition 12 | frege12 44158 |
| [Frege1879] p. 37 | Proposition 13 | frege13 44167 |
| [Frege1879] p. 37 | Proposition 14 | frege14 44168 |
| [Frege1879] p. 38 | Proposition 15 | frege15 44171 |
| [Frege1879] p. 38 | Proposition 16 | frege16 44161 |
| [Frege1879] p. 39 | Proposition 17 | frege17 44166 |
| [Frege1879] p. 39 | Proposition 18 | frege18 44163 |
| [Frege1879] p. 39 | Proposition 19 | frege19 44169 |
| [Frege1879] p. 40 | Proposition 20 | frege20 44173 |
| [Frege1879] p. 40 | Proposition 21 | frege21 44172 |
| [Frege1879] p. 41 | Proposition 22 | frege22 44164 |
| [Frege1879] p. 42 | Proposition 23 | frege23 44170 |
| [Frege1879] p. 42 | Proposition 24 | frege24 44160 |
| [Frege1879] p. 42 | Proposition 25 | frege25 44162 rp-frege25 44150 |
| [Frege1879] p. 42 | Proposition 26 | frege26 44155 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 44175 |
| [Frege1879] p. 43 | Proposition 27 | frege27 44156 |
| [Frege1879] p. 43 | Proposition 28 | con3 153 |
| [Frege1879] p. 43 | Proposition 29 | frege29 44176 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 44179 axfrege31 44178 |
| [Frege1879] p. 44 | Proposition 30 | frege30 44177 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 130 |
| [Frege1879] p. 44 | Proposition 32 | frege32 44180 |
| [Frege1879] p. 44 | Proposition 33 | frege33 44181 |
| [Frege1879] p. 45 | Proposition 34 | frege34 44182 |
| [Frege1879] p. 45 | Proposition 35 | frege35 44183 |
| [Frege1879] p. 45 | Proposition 36 | frege36 44184 |
| [Frege1879] p. 46 | Proposition 37 | frege37 44185 |
| [Frege1879] p. 46 | Proposition 38 | frege38 44186 |
| [Frege1879] p. 46 | Proposition 39 | frege39 44187 |
| [Frege1879] p. 46 | Proposition 40 | frege40 44188 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 44190 axfrege41 44189 |
| [Frege1879] p. 47 | Proposition 41 | notnot 142 |
| [Frege1879] p. 47 | Proposition 42 | frege42 44191 |
| [Frege1879] p. 47 | Proposition 43 | frege43 44192 |
| [Frege1879] p. 47 | Proposition 44 | frege44 44193 |
| [Frege1879] p. 47 | Proposition 45 | frege45 44194 |
| [Frege1879] p. 48 | Proposition 46 | frege46 44195 |
| [Frege1879] p. 48 | Proposition 47 | frege47 44196 |
| [Frege1879] p. 49 | Proposition 48 | frege48 44197 |
| [Frege1879] p. 49 | Proposition 49 | frege49 44198 |
| [Frege1879] p. 49 | Proposition 50 | frege50 44199 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 44202 ax-frege52c 44233 frege52aid 44203 frege52b 44234 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 44207 ax-frege54c 44237 frege54b 44238 |
| [Frege1879] p. 50 | Proposition 51 | frege51 44200 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3744 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 44205 frege53aid 44204 frege53b 44235 frege53c 44259 |
| [Frege1879] p. 50 | Proposition 54 | biid 261 eqid 2737 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 44213 frege55aid 44210 frege55b 44242 frege55c 44263 frege55cor1a 44214 frege55lem2a 44212 frege55lem2b 44241 frege55lem2c 44262 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 44216 frege56aid 44215 frege56b 44243 frege56c 44264 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 44220 ax-frege58b 44246 frege58bid 44247 frege58c 44266 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 44218 frege57aid 44217 frege57b 44244 frege57c 44265 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3755 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 44222 frege59b 44249 frege59c 44267 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 44223 frege60b 44250 frege60c 44268 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 44224 frege61b 44251 frege61c 44269 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 44225 frege62b 44252 frege62c 44270 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 44226 frege63b 44253 frege63c 44271 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 44227 frege64b 44254 frege64c 44272 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 44228 frege65b 44255 frege65c 44273 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 44229 frege66b 44256 frege66c 44274 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 44230 frege67b 44257 frege67c 44275 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 44231 frege68b 44258 frege68c 44276 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 44277 |
| [Frege1879] p. 58 | Proposition 70 | frege70 44278 |
| [Frege1879] p. 59 | Proposition 71 | frege71 44279 |
| [Frege1879] p. 59 | Proposition 72 | frege72 44280 |
| [Frege1879] p. 59 | Proposition 73 | frege73 44281 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 44284 |
| [Frege1879] p. 60 | Proposition 74 | frege74 44282 |
| [Frege1879] p. 60 | Proposition 75 | frege75 44283 |
| [Frege1879] p. 62 | Proposition 77 | frege77 44285 frege77d 44091 |
| [Frege1879] p. 63 | Proposition 78 | frege78 44286 |
| [Frege1879] p. 63 | Proposition 79 | frege79 44287 |
| [Frege1879] p. 63 | Proposition 80 | frege80 44288 |
| [Frege1879] p. 63 | Proposition 81 | frege81 44289 frege81d 44092 |
| [Frege1879] p. 64 | Proposition 82 | frege82 44290 |
| [Frege1879] p. 65 | Proposition 83 | frege83 44291 frege83d 44093 |
| [Frege1879] p. 65 | Proposition 84 | frege84 44292 |
| [Frege1879] p. 66 | Proposition 85 | frege85 44293 |
| [Frege1879] p. 66 | Proposition 86 | frege86 44294 |
| [Frege1879] p. 66 | Proposition 87 | frege87 44295 frege87d 44095 |
| [Frege1879] p. 67 | Proposition 88 | frege88 44296 |
| [Frege1879] p. 68 | Proposition 89 | frege89 44297 |
| [Frege1879] p. 68 | Proposition 90 | frege90 44298 |
| [Frege1879] p. 68 | Proposition 91 | frege91 44299 frege91d 44096 |
| [Frege1879] p. 69 | Proposition 92 | frege92 44300 |
| [Frege1879] p. 70 | Proposition 93 | frege93 44301 |
| [Frege1879] p. 70 | Proposition 94 | frege94 44302 |
| [Frege1879] p. 70 | Proposition 95 | frege95 44303 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 44307 |
| [Frege1879] p. 71 | Proposition 96 | frege96 44304 frege96d 44094 |
| [Frege1879] p. 71 | Proposition 97 | frege97 44305 frege97d 44097 |
| [Frege1879] p. 71 | Proposition 98 | frege98 44306 frege98d 44098 |
| [Frege1879] p. 72 | Proposition 100 | frege100 44308 |
| [Frege1879] p. 72 | Proposition 101 | frege101 44309 |
| [Frege1879] p. 72 | Proposition 102 | frege102 44310 frege102d 44099 |
| [Frege1879] p. 73 | Proposition 103 | frege103 44311 |
| [Frege1879] p. 73 | Proposition 104 | frege104 44312 |
| [Frege1879] p. 73 | Proposition 105 | frege105 44313 |
| [Frege1879] p. 73 | Proposition 106 | frege106 44314 frege106d 44100 |
| [Frege1879] p. 74 | Proposition 107 | frege107 44315 |
| [Frege1879] p. 74 | Proposition 108 | frege108 44316 frege108d 44101 |
| [Frege1879] p. 74 | Proposition 109 | frege109 44317 frege109d 44102 |
| [Frege1879] p. 75 | Proposition 110 | frege110 44318 |
| [Frege1879] p. 75 | Proposition 111 | frege111 44319 frege111d 44104 |
| [Frege1879] p. 76 | Proposition 112 | frege112 44320 |
| [Frege1879] p. 76 | Proposition 113 | frege113 44321 |
| [Frege1879] p. 76 | Proposition 114 | frege114 44322 frege114d 44103 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 44323 |
| [Frege1879] p. 77 | Proposition 116 | frege116 44324 |
| [Frege1879] p. 78 | Proposition 117 | frege117 44325 |
| [Frege1879] p. 78 | Proposition 118 | frege118 44326 |
| [Frege1879] p. 78 | Proposition 119 | frege119 44327 |
| [Frege1879] p. 78 | Proposition 120 | frege120 44328 |
| [Frege1879] p. 79 | Proposition 121 | frege121 44329 |
| [Frege1879] p. 79 | Proposition 122 | frege122 44330 frege122d 44105 |
| [Frege1879] p. 79 | Proposition 123 | frege123 44331 |
| [Frege1879] p. 80 | Proposition 124 | frege124 44332 frege124d 44106 |
| [Frege1879] p. 81 | Proposition 125 | frege125 44333 |
| [Frege1879] p. 81 | Proposition 126 | frege126 44334 frege126d 44107 |
| [Frege1879] p. 82 | Proposition 127 | frege127 44335 |
| [Frege1879] p. 83 | Proposition 128 | frege128 44336 |
| [Frege1879] p. 83 | Proposition 129 | frege129 44337 frege129d 44108 |
| [Frege1879] p. 84 | Proposition 130 | frege130 44338 |
| [Frege1879] p. 85 | Proposition 131 | frege131 44339 frege131d 44109 |
| [Frege1879] p. 86 | Proposition 132 | frege132 44340 |
| [Frege1879] p. 86 | Proposition 133 | frege133 44341 frege133d 44110 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 46660 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 46983 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 46683 |
| [Fremlin1] p. 14 | Definition 112A | ismea 46798 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 46818 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 46809 meadjunre 46823 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 46810 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 46811 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 46807 meaiunle 46816 meaiunlelem 46815 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 46828 meaiuninc2 46829 meaiuninc3 46832 meaiuninc3v 46831 meaiunincf 46830 meaiuninclem 46827 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 46834 meaiininc2 46835 meaiininclem 46833 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 46853 caragendifcl 46861 caratheodory 46875 omelesplit 46865 |
| [Fremlin1] p. 19 | Definition 113A | isome 46841 isomennd 46878 isomenndlem 46877 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 46863 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 46882 voncmpl 46968 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 46845 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 46870 carageniuncllem1 46868 carageniuncllem2 46869 caragenuncl 46860 caragenuncllem 46859 caragenunicl 46871 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 46879 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 46873 caratheodorylem2 46874 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 46882 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 46941 hoidmv1lelem1 46938 hoidmv1lelem2 46939 hoidmv1lelem3 46940 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 46985 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 46941 hoidmvle 46947 hoidmvlelem1 46942 hoidmvlelem2 46943 hoidmvlelem3 46944 hoidmvlelem4 46945 hoidmvlelem5 46946 hsphoidmvle2 46932 hsphoif 46923 hsphoival 46926 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 46895 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 46903 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 46930 hoidmvn0val 46931 hoidmvval 46924 hoidmvval0 46934 hoidmvval0b 46937 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 46935 hsphoidmvle 46933 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 46884 df-voln 46886 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 46951 ovn0 46913 ovn0lem 46912 ovnf 46910 ovnome 46920 ovnssle 46908 ovnsslelem 46907 ovnsupge0 46904 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 46950 ovnhoilem1 46948 ovnhoilem2 46949 vonhoi 47014 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 46967 hoidifhspf 46965 hoidifhspval 46955 hoidifhspval2 46962 hoidifhspval3 46966 hspmbl 46976 hspmbllem1 46973 hspmbllem2 46974 hspmbllem3 46975 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 46968 vonmea 46921 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 46919 ovnsubadd2 46993 ovnsubadd2lem 46992 ovnsubaddlem1 46917 ovnsubaddlem2 46918 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 46978 hoimbl2 47012 hoimbllem 46977 hspdifhsp 46963 opnvonmbl 46981 opnvonmbllem2 46980 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 46983 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 47026 iccvonmbllem 47025 ioovonmbl 47024 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 47032 vonicclem2 47031 vonioo 47029 vonioolem2 47028 vonn0icc 47035 vonn0icc2 47039 vonn0ioo 47034 vonn0ioo2 47037 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 47036 snvonmbl 47033 vonct 47040 vonsn 47038 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 46706 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 46705 subsaliuncllem 46704 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 47072 salpreimalegt 47056 salpreimaltle 47073 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 47075 issmff 47081 issmflem 47074 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 47092 issmflelem 47091 smfpreimale 47101 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 47103 issmfgtlem 47102 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 47043 issmf 47075 issmff 47081 issmfge 47117 issmfgelem 47116 issmfgt 47103 issmfgtlem 47102 issmfle 47092 issmflelem 47091 issmflem 47074 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 47054 salpreimagtlt 47077 salpreimalelt 47076 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 47117 issmfgelem 47116 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 47100 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 47098 cnfsmf 47087 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 47114 decsmflem 47113 incsmf 47089 incsmflem 47088 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 47048 pimconstlt1 47049 smfconst 47096 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 47112 smfaddlem1 47110 smfaddlem2 47111 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 47143 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 47142 smfmullem1 47138 smfmullem2 47139 smfmullem3 47140 smfmullem4 47141 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 47144 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 47147 smfpimbor1lem2 47146 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 47149 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 47137 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 47136 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 47145 smfresal 47135 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 47124 smflim2 47153 smflimlem1 47118 smflimlem2 47119 smflimlem3 47120 smflimlem4 47121 smflimlem5 47122 smflimlem6 47123 smflimmpt 47157 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 47161 smfsuplem1 47158 smfsuplem2 47159 smfsuplem3 47160 smfsupmpt 47162 smfsupxr 47163 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 47165 smfinflem 47164 smfinfmpt 47166 |
| [Fremlin1] p. 39 | Remark 121G | smflim 47124 smflim2 47153 smflimmpt 47157 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 47155 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 47185 smfdivdmmbl2 47188 smfinfdmmbl 47196 smfinfdmmbllem 47195 smfsupdmmbl 47192 smfsupdmmbllem 47191 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 47175 smflimsuplem2 47168 smflimsuplem6 47172 smflimsuplem7 47173 smflimsuplem8 47174 smflimsupmpt 47176 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 47178 smfliminflem 47177 smfliminfmpt 47179 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 47043 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 47189 fsupdm2 47190 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 47180 adddmmbl2 47181 finfdm 47193 finfdm2 47194 fsupdm 47189 fsupdm2 47190 muldmmbl 47182 muldmmbl2 47183 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 47193 finfdm2 47194 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25505 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25548 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25558 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 37938 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 37941 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9559 inf1 9543 inf2 9544 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10834 enqer 10844 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10839 df-nq 10835 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10831 df-plq 10837 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7605 df-mpq 10832 df-mq 10838 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10840 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10898 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10899 ltbtwnnq 10901 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10894 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10895 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10902 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10904 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 10916 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 10918 |
| [Gleason] p. 122 | Definition | df-1p 10905 |
| [Gleason] p. 122 | Remark (1) | prub 10917 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 10956 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10908 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 10955 psslinpr 10954 supexpr 10977 suplem1pr 10975 suplem2pr 10976 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 10941 addclprlem1 10939 addclprlem2 10940 df-plp 10906 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 10945 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 10944 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 10957 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 10966 ltexprlem1 10959 ltexprlem2 10960 ltexprlem3 10961 ltexprlem4 10962 ltexprlem5 10963 ltexprlem6 10964 ltexprlem7 10965 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 10968 ltaprlem 10967 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 10969 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 10970 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10907 mulclpr 10943 mulclprlem 10942 reclem2pr 10971 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 10952 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 10947 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 10946 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 10951 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 10974 reclem3pr 10972 reclem4pr 10973 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 10978 enrer 10986 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 10983 df-1r 10984 df-nr 10979 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 10981 df-plr 10980 negexsr 11025 recexsr 11030 recexsrlem 11026 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 10982 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12152 creur 12151 cru 12149 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11111 axcnre 11087 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15050 crimd 15167 crimi 15128 crre 15049 crred 15166 crrei 15127 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15052 remimd 15133 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15219 absval2d 15383 absval2i 15333 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15076 cjaddd 15155 cjaddi 15123 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15077 cjmuld 15156 cjmuli 15124 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15075 cjcjd 15134 cjcji 15106 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15074 cjreb 15058 cjrebd 15137 cjrebi 15109 cjred 15161 rere 15057 rereb 15055 rerebd 15136 rerebi 15108 rered 15159 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15083 addcjd 15147 addcji 15118 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15173 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15214 abscjd 15388 abscji 15337 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15224 abs00d 15384 abs00i 15334 absne0d 15385 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15257 releabsd 15389 releabsi 15338 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15229 absmuld 15392 absmuli 15340 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15217 sqabsaddi 15341 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15266 abstrid 15394 abstrii 15344 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 13997 exp0 14000 expp1 14003 expp1d 14082 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26656 cxpaddd 26694 expadd 14039 expaddd 14083 expaddz 14041 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26665 cxpmuld 26714 expmul 14042 expmuld 14084 expmulz 14043 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26662 mulcxpd 26705 mulexp 14036 mulexpd 14096 mulexpz 14037 |
| [Gleason] p. 140 | Exercise 1 | znnen 16149 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13437 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15567 rlimadd 15578 rlimdiv 15581 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15569 rlimsub 15579 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15568 rlimmul 15580 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15572 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15518 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15539 climcj 15540 climim 15542 climre 15541 rlimabs 15544 rlimcj 15545 rlimim 15547 rlimre 15546 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11183 df-xr 11182 ltxr 13041 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15406 limsupval 15409 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15605 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15614 caucvgb 15615 caucvgbf 45836 caucvgr 15611 climcau 15606 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15751 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15818 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15271 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13760 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21315 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24299 xmet0 24298 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24315 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24306 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24308 mstri 24425 xmettri 24307 xmstri 24424 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24338 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23604 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25278 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24496 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24822 addcn2 15529 mulcn 24824 mulcn2 15531 subcn 24823 subcn2 15530 |
| [Gleason] p. 295 | Remark | bcval3 14241 bcval4 14242 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14256 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14239 df-bc 14238 |
| [Gleason] p. 296 | Remark | bcn0 14245 bcnn 14247 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15765 |
| [Gleason] p. 308 | Equation 2 | ef0 16026 |
| [Gleason] p. 308 | Equation 3 | efcj 16027 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16033 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16038 |
| [Gleason] p. 310 | Equation 14 | sinadd 16101 |
| [Gleason] p. 310 | Equation 15 | cosadd 16102 |
| [Gleason] p. 311 | Equation 17 | sincossq 16113 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16118 sinbnd 16117 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14151 sqeqori 14149 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16007 |
| [Godowski] p. 730 | Equation SF | goeqi 32360 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 31755 |
| [Golan] p. 1 | Remark | srgisid 20156 |
| [Golan] p. 1 | Definition | df-srg 20134 |
| [Golan] p. 149 | Definition | df-slmd 33294 |
| [Gonshor] p. 7 | Definition | df-cuts 27768 |
| [Gonshor] p. 9 | Theorem 2.5 | lesrec 27807 lesrecd 27808 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 27928 cofcut1d 27929 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 27930 cofcut2d 27931 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 27932 cofcutr1d 27933 cofcutr2d 27934 |
| [Gonshor] p. 13 | Definition | df-adds 27968 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 27984 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 28010 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28138 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28158 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28466 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28468 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28467 |
| [Gonshor] p. 39 | Theorem 4.4(b) | elreno2 28503 |
| [Gonshor] p. 95 | Theorem 6.1 | addbday 28026 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36372 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17517 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17519 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 48537 df-cllaw 48535 df-comlaw 48536 |
| [Hall] p. 2 | Section 1.2 | df-clintop 48549 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 48570 |
| [Halmos] p. 28 | Partition ` ` | df-parts 39108 dfmembpart2 39113 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32152 riesz2 32153 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 32028 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32260 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32272 elpjidm 32271 pjnmopi 32235 |
| [Halmos] p. 44 | Remark | pjinormi 31774 pjinormii 31763 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32276 pjrn 31794 pjrni 31789 pjvec 31783 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 31814 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32241 hmopidmpji 32239 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32278 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32267 pjocvec 31784 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32256 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32259 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32262 pjssdif2i 32261 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 31942 |
| [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 1797 |
| [Hatcher] p. 25 | Definition | df-phtpc 24959 df-phtpy 24938 |
| [Hatcher] p. 26 | Definition | df-pco 24973 df-pi1 24976 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 24962 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 25018 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22446 df-dmatalt 48747 |
| [Helfgott] p. 2 | Theorem | tgoldbach 48166 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 48151 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 48163 bgoldbtbnd 48158 bgoldbtbnd 48158 tgblthelfgott 48164 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 34819 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 34820 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 34834 hgt750lemb 34833 hgt750leme 34835 hgt750lemf 34830 hgt750lemg 34831 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 48160 tgoldbachgt 34840 tgoldbachgtALTV 48161 tgoldbachgtd 34839 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 34821 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30580 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 18886 grpoideu 30596 mndideu 18682 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 18916 grpoinveu 30606 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 18947 grpo2inv 30618 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 18960 grpoinvop 30620 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 18982 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1770 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1771 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1773 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32507 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32520 cdj3i 32528 cdj3lem1 32521 cdjreui 32519 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32518 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 42326 |
| [Holland95] p. 14 | Line 15 | hgmapvs 42256 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 42278 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 42279 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 42276 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 42282 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 42201 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 42296 |
| [Holland95] p. 204 | Definition of involution | df-srng 20785 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 39868 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 41893 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 41846 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 40298 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 41742 poml4N 40318 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 41833 pexmidALTN 40343 pexmidN 40334 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 41898 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 39489 ldualset 39490 |
| [Holland95] p. 222 | Item 1 | df-lines 39866 df-pointsN 39867 |
| [Holland95] p. 222 | Item 2 | df-polarityN 40268 |
| [Holland95] p. 223 | Remark | ispsubcl2N 40312 omllaw4 39611 pol1N 40275 polcon3N 40282 |
| [Holland95] p. 223 | Definition | df-psubclN 40300 |
| [Holland95] p. 223 | Equation for polarity | polval2N 40271 |
| [Holmes] p. 40 | Definition | df-xrn 38620 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31171 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32269 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 32050 eigre 31922 eigrei 31921 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 32051 eigorth 31925 eigorthi 31924 |
| [Hughes] p. 137 | Remark (ii) | eigposi 31923 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30396 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30392 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30393 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30394 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30412 frgrregorufr0 30411 frgrregorufrg 30413 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30419 frrusgrord 30428 frrusgrord0 30427 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30175 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30402 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30405 frgrwopreg2 30406 frgrwopregasn 30403 frgrwopregbsn 30404 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30408 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30422 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30425 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30173 numclwlk1 30458 numclwlk1lem1 30456 numclwlk1lem2 30457 numclwwlk1 30448 numclwwlk8 30479 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30399 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 29856 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30434 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30460 numclwwlkovh0 30459 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30468 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 30065 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30472 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30475 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30478 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30490 natded 30490 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30490 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30490 natded 30490 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30490 |
| [Jech] p. 4 | Definition of class | cv 1541 cvjust 2731 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10502 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10500 alephmul 10501 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10499 infmap2 10139 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9738 |
| [Jech] p. 72 | Equation 9.3 | scott0 9810 scottex 9809 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9791 rankval4b 35275 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9815 |
| [Jech] p. 78 | Note | opthprc 5696 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 43261 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 43349 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 43350 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 43273 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 43277 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 43278 rmyp1 43279 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 43280 rmym1 43281 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 43271 rmx1 43272 rmxluc 43282 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 43275 rmy1 43276 rmyluc 43283 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 43285 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 43286 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 43306 jm2.17b 43307 jm2.17c 43308 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 43339 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 43343 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 43334 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 43309 jm2.24nn 43305 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 43348 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 43354 rmygeid 43310 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 43366 |
| [Juillerat] p. 11 | Section *5 | etransc 46630 etransclem47 46628 etransclem48 46629 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 46625 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 46627 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 46613 |
| [Juillerat] p. 13 | Proof | etransclem35 46616 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 46619 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 46605 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 46622 |
| [Juillerat] p. 14 | Proof | etransclem23 46604 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1969 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2014 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2019 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2009 cbvaliw 2008 wl-cbvmotv 37757 wl-motae 37759 wl-moteq 37758 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 1988 spimw 1972 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2035 spw 2036 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31603 chabs1i 31605 chabs2 31604 chabs2i 31606 chjass 31620 chjassi 31573 latabs1 18410 latabs2 18411 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32425 ela 32426 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32370 cvrval2 39639 |
| [Kalmbach] p. 16 | Definition | df-ol 39543 df-oml 39544 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 31671 cmbri 31677 cmtvalN 39576 df-cm 31670 df-cmtN 39542 |
| [Kalmbach] p. 22 | Remark | omllaw5N 39612 pjoml5 31700 pjoml5i 31675 |
| [Kalmbach] p. 22 | Definition | pjoml2 31698 pjoml2i 31672 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 31701 cmcmi 31679 cmcmii 31684 cmtcomN 39614 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 39610 omlsi 31491 pjoml 31523 pjomli 31522 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 39609 |
| [Kalmbach] p. 23 | Remark | cmbr2i 31683 cmcm3 31702 cmcm3i 31681 cmcm3ii 31686 cmcm4i 31682 cmt3N 39616 cmt4N 39617 cmtbr2N 39618 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 31695 cmbr3i 31687 cmtbr3N 39619 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 31705 fh1i 31708 fh2 31706 fh2i 31709 omlfh1N 39623 |
| [Kalmbach] p. 65 | Remark | chjatom 32444 chslej 31585 chsleji 31545 shslej 31467 shsleji 31457 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31582 chocini 31541 chsupcl 31427 chsupval2 31497 h0elch 31342 helch 31330 hsupval2 31496 ocin 31383 ococss 31380 shococss 31381 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31399 |
| [Kalmbach] p. 66 | Remark | df-pjh 31482 pjssmi 32252 pjssmii 31768 |
| [Kalmbach] p. 67 | Lemma 3 | osum 31732 osumi 31729 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32287 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32487 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32397 |
| [Kalmbach] p. 140 | Remark | hatomic 32447 hatomici 32446 hatomistici 32449 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 39684 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32468 lsatexch 39408 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32442 cvlcvr1 39704 cvr1 39775 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32461 cvexchi 32456 cvrexch 39785 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32451 hlrelat 39767 hlrelat5N 39766 lrelat 39379 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21108 lsmsatcv 39375 spansncv 31740 spansncvi 31739 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 39394 spansncv2 32380 |
| [Kalmbach] p. 266 | Definition | df-st 32298 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 31936 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10569 fpwwe2 10566 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10570 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10577 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10572 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10574 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10587 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10591 gchxpidm 10592 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10603 gchhar 10602 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10137 unxpwdom 9506 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10593 |
| [Kreyszig] p. 3 | Property M1 | metcl 24288 xmetcl 24287 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24295 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24528 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11870 muleqadd 11793 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24394 |
| [Kreyszig] p. 19 | Remark | mopntopon 24395 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24454 mopnm 24400 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24452 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24457 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24498 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23214 lmmbr 25226 lmmbr2 25227 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23336 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25281 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25244 iscmet2 25262 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25284 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23417 metelcls 25273 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25274 metcld2 25275 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25067 lmodvneg1 20868 nvinv 30726 vcm 30663 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25063 lmod0vs 20858 slmd0vs 33317 vc0 30661 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20859 slmdvs0 33318 vcz 30662 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 30778 ngpmet 24559 nrmmetd 24530 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 30773 imsdval2 30774 ncvspds 25129 ngpds 24560 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24545 nvnd 30775 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24574 nmge0 24573 nvge0 30760 nvz 30756 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24580 nvabs 30759 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 30888 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 30832 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 30894 blocni 30892 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 30893 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25172 ipeq0 21605 ipz 30806 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25184 pythi 30937 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 30941 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25206 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15791 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25404 minveco 30971 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 30837 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25297 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 30960 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32210 leopg 32209 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32228 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 31005 |
| [Kulpa] p. 547 | Theorem | poimir 37893 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 37892 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 37891 |
| [Kulpa] p. 548 | Theorem | broucube 37894 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 37886 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 37887 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2388 axnul 5252 |
| [Kunen] p. 11 | Axiom 3 | axnul 5252 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 7909 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8787 mapvalg 8785 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10444 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7893 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9688 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9730 r1elssi 9729 |
| [Kunen] p. 107 | Exercise 4 | rankop 9782 rankopb 9776 rankuni 9787 rankxplim 9803 rankxpsuc 9806 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 45299 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 45307 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 45306 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 45308 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 45313 rexabso 45314 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 45320 n0abso 45321 ssabso 45319 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 45322 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 45332 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 45327 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 45330 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 45331 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 45326 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 45338 wfaxpr 45343 wfaxreg 45345 wfaxrep 45339 wfaxsep 45340 wfaxun 45344 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 45329 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 45342 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 45338 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 45337 omelaxinf2 45334 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 45347 wfaxinf2 45346 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 45360 permaxext 45350 permaxinf2 45358 permaxnul 45353 permaxpow 45354 permaxpr 45355 permaxrep 45351 permaxsep 45352 permaxun 45356 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 45348 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 45359 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4961 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 33842 |
| [Lang] p. | Definition | df-rn 5643 |
| [Lang] p. 3 | Statement | lidrideqd 18606 mndbn0 18687 |
| [Lang] p. 3 | Definition | df-mnd 18672 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18624 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18778 |
| [Lang] p. 5 | Equation | gsumreidx 19858 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 48531 |
| [Lang] p. 6 | Example | nn0mnd 48528 |
| [Lang] p. 6 | Equation | gsumxp2 19921 |
| [Lang] p. 6 | Statement | cycsubm 19143 |
| [Lang] p. 6 | Definition | mulgnn0gsum 19022 |
| [Lang] p. 6 | Observation | mndlsmidm 19611 |
| [Lang] p. 7 | Definition | dfgrp2e 18905 |
| [Lang] p. 30 | Definition | df-tocyc 33200 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33245 |
| [Lang] p. 32 | Property (b) | cyc3conja 33250 cycpmconjv 33235 |
| [Lang] p. 53 | Definition | df-cat 17603 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18033 cat1lem 18032 |
| [Lang] p. 54 | Definition | df-iso 17685 |
| [Lang] p. 57 | Definition | df-inito 17920 df-termo 17921 |
| [Lang] p. 58 | Example | irinitoringc 21446 |
| [Lang] p. 58 | Statement | initoeu1 17947 termoeu1 17954 |
| [Lang] p. 62 | Definition | df-func 17794 |
| [Lang] p. 65 | Definition | df-nat 17882 |
| [Lang] p. 91 | Note | df-ringc 20591 |
| [Lang] p. 92 | Statement | mxidlprm 33562 |
| [Lang] p. 92 | Definition | isprmidlc 33539 |
| [Lang] p. 128 | Remark | dsmmlmod 21712 |
| [Lang] p. 129 | Proof | lincscm 48779 lincscmcl 48781 lincsum 48778 lincsumcl 48780 |
| [Lang] p. 129 | Statement | lincolss 48783 |
| [Lang] p. 129 | Observation | dsmmfi 21705 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 33804 qusdimsum 33805 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 33784 |
| [Lang] p. 147 | Definition | snlindsntor 48820 |
| [Lang] p. 504 | Statement | mat1 22403 matring 22399 |
| [Lang] p. 504 | Definition | df-mamu 22347 |
| [Lang] p. 505 | Statement | mamuass 22358 mamutpos 22414 matassa 22400 mattposvs 22411 tposmap 22413 |
| [Lang] p. 513 | Definition | mdet1 22557 mdetf 22551 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22647 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22543 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22567 |
| [Lang] p. 515 | Definition | df-minmar1 22591 smadiadetr 22631 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22566 mdetralt 22564 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22579 |
| [Lang] p. 518 | Definition | df-madu 22590 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22601 madurid 22600 matinv 22633 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 22846 |
| [Lang], p. 190 | Chapter 6 | vieta 33756 |
| [Lang], p. 224 | Proposition 1.1 | extdgfialg 33871 finextalg 33875 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 33840 fedgmul 33808 |
| [Lang], p. 225 | Proposition 1.4 | algextdeg 33902 |
| [Lang], p. 561 | Remark | chpmatply1 22788 |
| [Lang], p. 561 | Definition | df-chpmat 22783 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 44679 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 44674 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 44680 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5252 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2716 |
| [Levy] p. 59 | Definition | df-ttrcl 9629 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9675 |
| [Levy] p. 338 | Axiom | df-clel 2812 df-cleq 2729 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2812 df-cleq 2729 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2716 |
| [Levy] p. 358 | Axiom | df-clab 2716 |
| [Levy58] p. 2 | Definition I | isfin1-3 10308 |
| [Levy58] p. 2 | Definition II | df-fin2 10208 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10207 |
| [Levy58] p. 2 | Definition III | df-fin3 10210 |
| [Levy58] p. 3 | Definition V | df-fin5 10211 |
| [Levy58] p. 3 | Definition IV | df-fin4 10209 |
| [Levy58] p. 4 | Definition VI | df-fin6 10212 |
| [Levy58] p. 4 | Definition VII | df-fin7 10213 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10337 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27666 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27677 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27709 nosupbnd1 27694 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27711 nosupbnd2 27696 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27715 noetasuplem4 27716 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27712 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1770 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1771 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1773 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32495 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32499 mdsymi 32498 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32493 mdsymlem6 32495 mdsymlem7 32496 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32497 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32400 ssdmd2 32401 ssmd1 32398 ssmd2 32399 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32396 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32368 df-md 32367 mdbr 32381 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32418 mdslj1i 32406 mdslj2i 32407 mdslle1i 32404 mdslle2i 32405 mdslmd1i 32416 mdslmd2i 32417 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32408 mdsl2bi 32410 mdsl2i 32409 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32422 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32419 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32420 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32397 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32402 mdsl3 32403 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32421 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32516 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 39686 hlrelat1 39765 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 39404 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32423 cvmdi 32411 cvnbtwn4 32376 cvrnbtwn4 39644 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32424 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 39705 cvp 32462 cvrp 39781 lcvp 39405 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32486 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32485 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 39698 hlexch4N 39757 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32488 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 39808 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 40114 atpsubN 40118 df-pointsN 39867 pointpsubN 40116 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 39869 pmap11 40127 pmaple 40126 pmapsub 40133 pmapval 40122 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 40130 pmap1N 40132 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 40135 pmapglb2N 40136 pmapglb2xN 40137 pmapglbx 40134 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 40217 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 39842 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 40161 paddclN 40207 paddidm 40206 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 39843 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 40203 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 39842 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 39843 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19616 lsmmod2 19617 lssats 39377 shatomici 32445 shatomistici 32448 shmodi 31477 shmodsi 31476 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32387 mdsymlem7 32496 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 31676 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31580 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32502 |
| [Margaris] p. 40 | Rule C | exlimiv 1932 |
| [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 396 df-ex 1782 df-or 849 dfbi2 474 |
| [Margaris] p. 51 | Theorem 1 | idALT 23 |
| [Margaris] p. 56 | Theorem 3 | conventions 30487 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 45259 |
| [Margaris] p. 60 | Theorem 8 | jcn 162 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 45260 |
| [Margaris] p. 79 | Rule C | exinst01 44970 exinst11 44971 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1978 19.2g 2196 r19.2z 4454 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2210 rr19.3v 3623 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2165 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1828 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1783 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2189 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2213 19.9h 2293 exlimd 2226 exlimdh 2297 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2168 excomim 2169 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2333 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30488 conventions-labels 30488 conventions-labels 30488 conventions-labels 30488 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1829 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 44723 albi 1820 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2233 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2234 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 44725 exbi 1849 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2237 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 44722 2alimdv 1920 alimd 2220 alimdh 1819 alimdv 1918 ax-4 1811 ralimdaa 3239 ralimdv 3152 ralimdva 3150 ralimdvva 3185 sbcimdv 3811 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2215 19.21h 2294 19.21t 2214 19.21vv 44721 alrimd 2223 alrimdd 2222 alrimdh 1865 alrimdv 1931 alrimi 2221 alrimih 1826 alrimiv 1929 alrimivv 1930 hbralrimi 3128 r19.21be 3231 r19.21bi 3230 ralrimd 3243 ralrimdv 3136 ralrimdva 3138 ralrimdvv 3182 ralrimdvva 3193 ralrimi 3236 ralrimia 3237 ralrimiv 3129 ralrimiva 3130 ralrimivv 3179 ralrimivva 3181 ralrimivvva 3184 ralrimivw 3134 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 44724 2eximdv 1921 bj-exim 36853 exim 1836 eximd 2224 eximdh 1866 eximdv 1919 rexim 3079 reximd2a 3248 reximdai 3240 reximdd 45496 reximddv 3154 reximddv2 3197 reximddv3 3155 reximdv 3153 reximdv2 3148 reximdva 3151 reximdvai 3149 reximdvva 3186 reximi2 3071 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2219 19.23bi 2199 19.23h 2295 19.23t 2218 exlimdv 1935 exlimdvv 1936 exlimexi 44869 exlimiv 1932 exlimivv 1934 rexlimd3 45492 rexlimdv 3137 rexlimdv3a 3143 rexlimdva 3139 rexlimdva2 3141 rexlimdvaa 3140 rexlimdvv 3194 rexlimdvva 3195 rexlimdvvva 3196 rexlimdvw 3144 rexlimiv 3132 rexlimiva 3131 rexlimivv 3180 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 1993 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1882 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1872 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2235 r19.27z 4465 r19.27zv 4466 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2236 19.28vv 44731 r19.28z 4457 r19.28zf 45507 r19.28zv 4461 rr19.28v 3624 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1875 r19.29d2r 3125 r19.29imd 3103 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1883 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2242 19.31vv 44729 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2241 r19.32 47447 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 44727 19.33 1886 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 1994 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1879 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2238 19.36vv 44728 r19.36zv 4467 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2240 19.37vv 44730 r19.37zv 4462 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1841 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 1992 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1889 19.40 1888 r19.40 3104 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2243 19.41rg 44895 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2244 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1884 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2245 r19.44zv 4464 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2246 r19.45zv 4463 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2611 |
| [Mayet] p. 370 | Remark | jpi 32357 largei 32354 stri 32344 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32299 ishst 32301 |
| [Mayet3] p. 10 | Theorem | hstrbi 32353 hstri 32352 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 31815 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 31816 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32365 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31419 chsupcl 31427 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32447 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32441 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32468 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 40348 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18422 latj32 18420 latjass 18418 |
| [Megill] p. 444 | Axiom C5 | ax-5 1912 ax5ALT 39272 |
| [Megill] p. 444 | Section 7 | conventions 30487 |
| [Megill] p. 445 | Lemma L12 | aecom-o 39266 ax-c11n 39253 axc11n 2431 |
| [Megill] p. 446 | Lemma L17 | equtrr 2024 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 39261 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 39293 hbnae 2437 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2486 sbid 2263 sbidd-misc 50067 sbidd 50066 |
| [Megill] p. 448 | Remark 9.6 | axc14 2468 |
| [Megill] p. 448 | Scheme C4' | ax-c4 39249 |
| [Megill] p. 448 | Scheme C5' | ax-c5 39248 sp 2191 |
| [Megill] p. 448 | Scheme C6' | ax-11 2163 |
| [Megill] p. 448 | Scheme C7' | ax-c7 39250 |
| [Megill] p. 448 | Scheme C8' | ax-7 2010 |
| [Megill] p. 448 | Scheme C9' | ax-c9 39255 |
| [Megill] p. 448 | Scheme C10' | ax-6 1969 ax-c10 39251 |
| [Megill] p. 448 | Scheme C11' | ax-c11 39252 |
| [Megill] p. 448 | Scheme C12' | ax-8 2116 |
| [Megill] p. 448 | Scheme C13' | ax-9 2124 |
| [Megill] p. 448 | Scheme C14' | ax-c14 39256 |
| [Megill] p. 448 | Scheme C15' | ax-c15 39254 |
| [Megill] p. 448 | Scheme C16' | ax-c16 39257 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 39269 dral1 2444 dral2-o 39295 dral2 2443 drex1 2446 drex2 2447 drsb1 2500 drsb2 2274 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2179 sbequ 2089 sbid2v 2514 |
| [Megill] p. 450 | Example in Appendix | hba1-o 39262 hba1 2300 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 47241 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 23 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3831 rspsbca 3832 stdpc4 2074 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 39249 ra4 3838 stdpc5 2216 |
| [Mendelson] p. 81 | Rule C | exlimiv 1932 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2030 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2258 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3740 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5470 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4352 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4353 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4231 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4288 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4232 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4095 |
| [Mendelson] p. 231 | Definition of union | dfun3 4230 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5406 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4862 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5523 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4574 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5524 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4889 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5783 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6235 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7730 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6331 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8533 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9080 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 9001 xpsneng 9002 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9008 xpcomeng 9009 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9011 |
| [Mendelson] p. 255 | Definition | brsdom 8923 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9004 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8779 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 8986 mapsnend 8985 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9086 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9085 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8832 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 8989 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9005 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10101 djucomen 10100 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10105 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10099 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8468 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8495 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10481 |
| [Mendelson] p. 281 | Definition | df-r1 9688 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9737 |
| [Mendelson] p. 287 | Axiom system MK | ru 3740 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30346 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30381 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30383 vdgn1frgrv3 30384 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30385 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30378 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30371 2pthfrgrrn 30369 2pthfrgrrn2 30370 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31339 |
| [Monk1] p. 22 | Remark | conventions 30487 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30487 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4193 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5740 ssrelf 32704 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5741 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5163 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6229 coi2 6230 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5877 rn0 5883 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 6107 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5650 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5886 rnxp 6136 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5731 xp0 5732 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6044 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6041 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7866 imaexg 7865 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6038 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7029 funfvop 7004 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6896 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6907 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6546 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7210 dff13f 7211 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7175 funrnex 7908 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7203 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6193 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4921 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 7960 df-1st 7943 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 7961 df-2nd 7944 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9778 ranksnb 9751 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9779 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9780 rankunb 9774 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9762 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9688 r1val2 9761 |
| [Monk1] p. 117 | Lemma | zorn2 10428 zorn2g 10425 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9910 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10483 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9905 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1811 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2010 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2185 ax-c15 39254 ax12v2 2187 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 39249 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2163 |
| [Monk2] p. 109 | Lemma 15 | equvini 2460 equvinv 2031 eqvinop 5443 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1912 ax5ALT 39272 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2147 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2163 |
| [Monk2] p. 114 | Lemma 21 | sp 2191 |
| [Monk2] p. 114 | Lemma 22 | axc4 2327 hba1-o 39262 hba1 2300 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2159 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2182 nfra2 3348 nfra2w 3274 |
| [Moore] p. 53 | Part I | df-mre 17517 |
| [Munkres] p. 77 | Example 2 | distop 22951 indistop 22958 indistopon 22957 |
| [Munkres] p. 77 | Example 3 | fctop 22960 fctop2 22961 |
| [Munkres] p. 77 | Example 4 | cctop 22962 |
| [Munkres] p. 78 | Definition of basis | df-bases 22902 isbasis3g 22905 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17375 tgval2 22912 |
| [Munkres] p. 79 | Remark | tgcl 22925 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 22919 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 22943 tgss3 22942 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 22944 basgen2 22945 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 37593 topdifinfeq 37594 topdifinffin 37592 topdifinfindis 37590 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23116 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 22994 topcld 22991 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 22995 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 22997 |
| [Munkres] p. 94 | Definition of closure | clsval 22993 |
| [Munkres] p. 94 | Definition of interior | ntrval 22992 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 23031 elcls 23029 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 23039 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23104 neindisj 23073 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23106 |
| [Munkres] p. 97 | Definition of limit point | islp2 23101 lpval 23095 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23271 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23183 iscn 23191 iscn2 23194 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23236 cncnp2 23237 cncnpi 23234 df-cnp 23184 iscnp 23193 iscnp2 23195 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24499 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25279 |
| [Nathanson] p. 123 | Remark | reprgt 34798 reprinfz1 34799 reprlt 34796 |
| [Nathanson] p. 123 | Definition | df-repr 34786 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 34818 |
| [Nathanson] p. 123 | Proposition | breprexp 34810 breprexpnat 34811 itgexpif 34783 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32191 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 48159 |
| [Pfenning] p. 17 | Definition XM | natded 30490 |
| [Pfenning] p. 17 | Definition NNC | natded 30490 notnotrd 133 |
| [Pfenning] p. 17 | Definition ` `C | natded 30490 |
| [Pfenning] p. 18 | Rule" | natded 30490 |
| [Pfenning] p. 18 | Definition /\I | natded 30490 |
| [Pfenning] p. 18 | Definition ` `E | natded 30490 natded 30490 natded 30490 natded 30490 natded 30490 |
| [Pfenning] p. 18 | Definition ` `I | natded 30490 natded 30490 natded 30490 natded 30490 natded 30490 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30490 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30490 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30490 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30490 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30490 |
| [Pfenning] p. 127 | Definition =E | natded 30490 |
| [Pfenning] p. 127 | Definition =I | natded 30490 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25170 df-dip 30788 dip0l 30805 ip0l 21603 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25211 ipval 30790 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 30801 ipcj 21601 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25173 dipdir 30929 ipdir 21606 ipdiri 30917 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 30797 nmsq 25162 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 30912 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 30914 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 30915 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25179 dipass 30932 ipass 21612 ipassi 30928 |
| [Prugovecki] p. 186 | Definition of bra | braval 32031 df-bra 31937 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 31938 kbval 32041 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32469 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 40253 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32483 atcvat4i 32484 cvrat3 39807 cvrat4 39808 lsatcvat3 39417 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32369 cvrval 39634 df-cv 32366 df-lcv 39384 lspsncv0 21113 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 40265 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 40266 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2716 rabid 3422 rabidd 45503 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2286 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2729 |
| [Quine] p. 19 | Definition 2.9 | conventions 30487 df-v 3444 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2876 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2873 abid2f 2930 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2283 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2091 sbalex 2250 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2812 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2737 eqid1 30554 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2744 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3743 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3744 dfsbcq2 3745 |
| [Quine] p. 43 | Theorem 6.8 | vex 3446 |
| [Quine] p. 43 | Theorem 6.9 | isset 3456 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3547 spcgv 3552 spcimgf 3509 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3755 spsbcd 3756 |
| [Quine] p. 44 | Theorem 6.12 | elex 3463 |
| [Quine] p. 44 | Theorem 6.13 | elab 3636 elabg 3633 elabgf 3631 |
| [Quine] p. 44 | Theorem 6.14 | noel 4292 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4676 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4585 df-sn 4583 |
| [Quine] p. 49 | Theorem 7.4 | snss 4743 snssg 4742 |
| [Quine] p. 49 | Theorem 7.5 | prss 4778 prssg 4777 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4721 prid1g 4719 prid2 4722 prid2g 4720 snid 4621 snidg 4619 |
| [Quine] p. 51 | Theorem 7.12 | snex 5385 |
| [Quine] p. 51 | Theorem 7.13 | prex 5384 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4884 unisnALT 45270 unisng 4883 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4888 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4896 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4893 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6470 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 47435 dfiota2 6457 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 47444 iotaval 6474 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6480 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6476 |
| [Quine] p. 58 | Definition 9.1 | df-op 4589 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5481 opabidw 5480 opelopab 5498 opelopaba 5492 opelopabaf 5500 opelopabf 5501 opelopabg 5494 opelopabga 5489 opelopabgf 5496 oprabid 7400 oprabidw 7399 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5638 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5640 |
| [Quine] p. 64 | Definition 9.15 | df-id 5527 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6565 |
| [Quine] p. 65 | Theorem 10.4 | funi 6532 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6553 funsng 6551 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6502 |
| [Quine] p. 65 | Definition 10.2 | args 6059 dffv4 6839 |
| [Quine] p. 68 | Definition 10.11 | conventions 30487 df-fv 6508 fv2 6837 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14207 nn0opth2i 14206 nn0opthi 14205 omopthi 8599 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8351 |
| [Quine] p. 232 | Equation i | carddom 10476 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6588 funimaexg 6587 |
| [Quine] p. 331 | Axiom system NF | ru 3740 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31171 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 30788 polid 31246 polid2i 31244 polidi 31245 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 30900 |
| [ReedSimon] p. 195 | Remark | lnophm 32106 lnophmi 32105 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32219 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32221 leopmuli 32220 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32224 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 31939 leoppos 32213 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32223 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32212 |
| [Roman] p. 4 | Definition | df-dmat 22446 df-dmatalt 48747 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20100 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20182 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 48834 |
| [Roman] p. 112 | Note | isldepslvec2 48834 ldepsnlinc 48857 zlmodzxznm 48846 |
| [Roman] p. 112 | Example | zlmodzxzequa 48845 zlmodzxzequap 48848 zlmodzxzldep 48853 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 22846 |
| [Rosenlicht] p. 80 | Theorem | heicant 37895 |
| [Rosser] p. 281 | Definition | df-op 4589 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 34822 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 34823 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 48715 pmtr3ncom 19416 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19412 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19355 cayleyth 19356 |
| [Rudin] p. 164 | Equation 27 | efcan 16031 |
| [Rudin] p. 164 | Equation 30 | efzval 16039 |
| [Rudin] p. 167 | Equation 48 | absefi 16133 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 197 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1773 |
| [Sanford] p. 39 | Rule 4 | mptxor 1771 |
| [Sanford] p. 40 | Rule 1 | mptnan 1770 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6080 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6083 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6079 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6077 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17517 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17518 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17518 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17520 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10059 |
| [Schechter] p. 141 | Definition (MC) | dfac11 43408 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10368 axdc3 10376 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20184 isrngo 38137 |
| [Schechter] p. 276 | Remark 11.6.e | span0 31629 |
| [Schechter] p. 276 | Definition of span | df-span 31396 spanval 31420 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 22949 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6350 onelord 43597 ordelon 6349 ordelord 6347 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 43598 sucidg 6408 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6380 onsuc 7765 ord0 6379 ordsuci 7763 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 43599 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5211 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 43374 elon2 6336 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6331 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5535 epelg 5533 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9516 epirron 43600 ordirr 6343 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 43602 oneptr 43601 ontr1 6372 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6368 oneptri 43603 ordtri3or 6357 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8438 ord0eln0 6381 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6394 onsucss 43612 trsucss 6415 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7770 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6421 ordnbtwn 6420 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 43614 ordnexbtwnsuc 43613 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10323 onsucf1lem 43615 onsucf1o 43618 onsucf1olem 43616 onsucrn 43617 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 43619 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7797 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 43608 ordne0gt0 43607 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 43610 limnsuc 43611 onsucelab 43609 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9564 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7812 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9567 ordom 7828 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9568 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8578 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7735 ssorduni 7734 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8468 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9571 limom 7834 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8407 df1o2 8414 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8453 oa0suclim 43621 oalim 8469 oasuc 8461 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8454 om0suclim 43622 omlim 8470 omsuc 8463 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8459 oe0m1 8458 oe0suclim 43623 oelim 8471 oesuc 8464 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 43575 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 43625 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 43626 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 43627 limexissupab 43629 limiun 43628 limuni 6387 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8475 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8479 om1om1r 43630 om1r 8480 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8472 oaomoecl 43624 oecl 8474 omcl 8473 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 43577 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8481 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8482 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 43631 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 43632 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8549 nnamecl 43633 nnecl 8551 nnmcl 8550 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 43634 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8489 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8490 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8497 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 43636 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 43637 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 43639 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8496 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 43643 omword1 8510 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 43642 oaordnrex 43641 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 43638 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 43644 omword2 8511 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 43645 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 43646 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 43647 omordi 8503 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8505 omord2com 43648 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 43649 df-2o 8408 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 43652 oewordi 8529 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 43653 oeworde 8531 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 43654 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 43655 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 43651 omnord1ex 43650 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 43656 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 43658 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 43662 oenord1ex 43661 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 43663 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8498 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 43657 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8516 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8517 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 43665 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8535 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 43666 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 43667 cantnfub2 43668 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 43671 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 28999 axtgcgrrflx 28546 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 29000 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 29001 axtgcgrid 28547 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28532 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 29012 axtgsegcon 28548 df-trkgcb 28534 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 29023 axtg5seg 28549 df-trkgcb 28534 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 29024 axtgbtwnid 28550 df-trkgb 28533 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 29026 axtgpasch 28551 df-trkgb 28533 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 29045 df-trkg2d 34842 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28554 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28555 df-trkg2d 34842 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 29048 axtgeucl 28556 df-trkge 28535 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 29061 axtgcont 28553 axtgcont1 28552 df-trkgb 28533 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 36200 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 36202 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 36205 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 36209 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 36210 tgcgrcomimp 28561 tgcgrcoml 28563 tgcgrcomr 28562 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 36215 tgcgrtriv 28568 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 36219 tg5segofs 34850 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 34847 df-ofs 36196 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 36221 tgcgrextend 28569 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 36223 tgsegconeq 28570 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36235 btwntriv2 36225 tgbtwntriv2 28571 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 36226 tgbtwncom 28572 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36229 tgbtwntriv1 28575 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36230 tgbtwnswapid 28576 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36236 btwnintr 36232 tgbtwnexch2 28580 tgbtwnintr 28577 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36238 btwnexch3 36233 tgbtwnexch 28582 tgbtwnexch3 28578 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36237 tgbtwnouttr 28581 tgbtwnouttr2 28579 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 29044 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36240 tgbtwndiff 28590 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28583 trisegint 36241 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36257 tgifscgr 28592 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28642 colrot1 28643 colrot2 28644 lncom 28706 lnrot1 28707 lnrot2 28708 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36253 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36258 tgcgrsub 28593 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36268 tgcgrxfr 28602 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28601 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36254 df-cgrg 28595 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28595 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36269 tgbtwnxfr 28614 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36275 colinearperm2 36277 colinearperm3 36276 colinearperm4 36278 colinearperm5 36279 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28617 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36252 tgellng 28637 tglng 28630 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36280 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36288 lnxfr 28650 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36289 lnext 28651 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36293 tgfscgr 28652 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36294 lncgr 28653 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36255 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36296 lnid 28654 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36297 tgidinside 28655 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36314 tgbtwnconn1 28659 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36315 tgbtwnconn2 28660 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36316 tgbtwnconn3 28661 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36322 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36320 legov 28669 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28670 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28683 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36323 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36325 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36327 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36328 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36329 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36326 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36331 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28671 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28673 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28674 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28675 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28676 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36338 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36339 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36334 df-outsideof 36333 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36335 ishlg 28686 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28691 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28693 outsideofrflx 36340 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28687 hlcomd 28688 outsideofcom 36341 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28694 outsideoftr 36342 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 28702 outsideofeu 36344 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36351 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36352 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36345 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36360 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36361 tglineelsb2 28716 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36363 linerflx1 36362 linerflx2 36364 tglinecom 28719 tglinerflx1 28717 tglinerflx2 28718 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36366 tglinethru 28720 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36350 tglng 28630 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28678 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36369 tglinethrueu 28723 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36370 tglineineq 28727 tglineinteq 28729 tglineintmo 28726 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28733 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28734 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 28735 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 28750 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 28746 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 28738 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 28737 ismir 28743 mirbtwn 28742 mircgr 28741 mirfv 28740 mirval 28739 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 28748 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 28749 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 28750 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 28753 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 28754 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 28759 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 28756 mirbtwni 28755 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 28757 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 28769 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 28773 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 28770 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 28771 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 28772 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 28775 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 28776 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 28782 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 28778 israg 28781 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 28783 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 28784 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 28786 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 28787 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 28788 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 28789 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 28790 ragncol 28793 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 28791 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 28797 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 28801 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 28798 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 28780 isperp 28796 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 28799 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 28806 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 28814 colperpexlem2 28815 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 28817 colperpexlem3 28816 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 28822 midex 28821 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 28819 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 28828 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 28823 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 28832 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 28835 opphllem6 28836 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 28838 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28551 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 28839 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 28847 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 28842 hpgbr 28844 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 28849 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 28848 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 28850 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 28851 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 28852 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 28853 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 28854 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 28868 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 28858 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 28872 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 28873 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 28874 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 28875 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 28876 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 28879 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 28881 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 28859 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 28882 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 28885 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 28886 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 28887 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 28888 trgcopyeu 28890 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 28914 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 28893 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 28902 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 28900 cgrahl2 28901 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 28903 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 28904 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 28906 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 28907 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 28910 cgrahl 28911 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 28915 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 28916 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 28917 acopyeu 28918 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 28925 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 28929 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 28922 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 28937 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 28930 isleag 28931 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 28939 tgsas1 28938 tgsas2 28940 tgsas3 28941 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 28943 tgasa1 28942 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 28944 tgsss2 28945 tgsss3 28946 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27250 dchrsum 27248 dchrsum2 27247 sumdchr 27251 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27252 sum2dchr 27253 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 20009 ablfacrp2 20010 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27195 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27196 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27203 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27461 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27464 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27518 vmalogdivsum2 27517 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27508 dirith2 27507 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27506 rpvmasum 27505 rpvmasum2 27491 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27466 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27504 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27471 dchrisumlem1 27468 dchrisumlem2 27469 dchrisumlem3 27470 dchrisumlema 27467 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27474 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27503 dchrmusumlem 27501 dchrvmasumlem 27502 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27473 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27475 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27499 dchrisum0re 27492 dchrisumn0 27500 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27485 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27489 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27490 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27545 pntrsumbnd2 27546 pntrsumo1 27544 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27509 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27511 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27513 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27516 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27521 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27522 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27527 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27529 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27530 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27538 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27539 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27536 selberg3lem2 27537 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27540 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27534 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27547 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27548 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27549 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27563 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27575 pntlemb 27576 pntlemc 27574 pntlemd 27573 pntlemg 27577 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27575 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27567 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27572 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27575 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27588 pntleml 27590 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 33920 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 33907 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 33939 constrinvcl 33950 constrmulcl 33948 constrnegcl 33940 constrsqrtcl 33956 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 33926 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 33936 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 33958 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 33968 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4260 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4359 dif0 4332 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4446 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4429 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4251 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4252 |
| [Stoll] p. 20 | Remark | invdif 4233 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4591 |
| [Stoll] p. 43 | Definition | uniiun 5016 |
| [Stoll] p. 44 | Definition | intiin 5017 |
| [Stoll] p. 45 | Definition | df-iin 4951 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4950 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 401 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4260 |
| [Strang] p. 242 | Section 6.3 | expgrowth 44680 |
| [Suppes] p. 22 | Theorem 2 | eq0 4304 eq0f 4301 |
| [Suppes] p. 22 | Theorem 4 | eqss 3951 eqssd 3953 eqssi 3952 |
| [Suppes] p. 23 | Theorem 5 | ss0 4356 ss0b 4355 |
| [Suppes] p. 23 | Theorem 6 | sstr 3944 sstrALT2 45179 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4057 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4058 |
| [Suppes] p. 23 | Theorem 9 | psstr 4061 |
| [Suppes] p. 23 | Theorem 10 | pssss 4052 |
| [Suppes] p. 25 | Theorem 12 | elin 3919 elun 4107 |
| [Suppes] p. 26 | Theorem 15 | inidm 4181 |
| [Suppes] p. 26 | Theorem 16 | in0 4349 |
| [Suppes] p. 27 | Theorem 23 | unidm 4111 |
| [Suppes] p. 27 | Theorem 24 | un0 4348 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4132 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4140 |
| [Suppes] p. 27 | Theorem 27 | unss 4144 |
| [Suppes] p. 27 | Theorem 28 | indir 4240 |
| [Suppes] p. 27 | Theorem 29 | undir 4241 |
| [Suppes] p. 28 | Theorem 32 | difid 4330 |
| [Suppes] p. 29 | Theorem 33 | difin 4226 |
| [Suppes] p. 29 | Theorem 34 | indif 4234 |
| [Suppes] p. 29 | Theorem 35 | undif1 4430 |
| [Suppes] p. 29 | Theorem 36 | difun2 4435 |
| [Suppes] p. 29 | Theorem 37 | difin0 4428 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4426 |
| [Suppes] p. 29 | Theorem 39 | difundi 4244 |
| [Suppes] p. 29 | Theorem 40 | difindi 4246 |
| [Suppes] p. 30 | Theorem 41 | nalset 5260 |
| [Suppes] p. 39 | Theorem 61 | uniss 4873 |
| [Suppes] p. 39 | Theorem 65 | uniop 5471 |
| [Suppes] p. 41 | Theorem 70 | intsn 4941 |
| [Suppes] p. 42 | Theorem 71 | intpr 4939 intprg 4938 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5427 |
| [Suppes] p. 42 | Theorem 78 | intun 4937 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4989 dfiun2g 4987 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4990 |
| [Suppes] p. 47 | Theorem 86 | elpw 4560 elpw2 5281 elpw2g 5280 elpwg 4559 elpwgdedVD 45261 |
| [Suppes] p. 47 | Theorem 87 | pwid 4578 |
| [Suppes] p. 47 | Theorem 89 | pw0 4770 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4771 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5647 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5790 xpindir 5791 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5701 xpundir 5702 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9514 |
| [Suppes] p. 58 | Theorem 2 | relss 5739 |
| [Suppes] p. 59 | Theorem 4 | eldm 5857 eldm2 5858 eldm2g 5856 eldmg 5855 |
| [Suppes] p. 59 | Definition 3 | df-dm 5642 |
| [Suppes] p. 60 | Theorem 6 | dmin 5868 |
| [Suppes] p. 60 | Theorem 8 | rnun 6111 |
| [Suppes] p. 60 | Theorem 9 | rnin 6112 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5845 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5839 brcnvg 5836 |
| [Suppes] p. 62 | Equation 5 | elcnv 5833 elcnv2 5834 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6071 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6110 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6108 |
| [Suppes] p. 63 | Definition | dftrrels2 38899 |
| [Suppes] p. 63 | Theorem 20 | co02 6227 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5932 |
| [Suppes] p. 63 | Definition 7 | df-co 5641 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5842 |
| [Suppes] p. 64 | Theorem 27 | coass 6232 |
| [Suppes] p. 65 | Theorem 31 | resundi 5960 |
| [Suppes] p. 65 | Theorem 34 | elima 6032 elima2 6033 elima3 6034 elimag 6031 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6115 |
| [Suppes] p. 66 | Theorem 40 | dminss 6119 |
| [Suppes] p. 66 | Theorem 41 | imainss 6120 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6123 |
| [Suppes] p. 81 | Definition 34 | dfec2 8648 |
| [Suppes] p. 82 | Theorem 72 | elec 8692 elecALTV 38511 elecg 8690 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 38935 erth 8700 erth2 8701 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 38938 erdisj 8703 |
| [Suppes] p. 83 | Definition 35, | df-parts 39108 dfmembpart2 39113 |
| [Suppes] p. 89 | Theorem 96 | map0b 8833 |
| [Suppes] p. 89 | Theorem 97 | map0 8837 map0g 8834 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8838 mapsnd 8836 |
| [Suppes] p. 89 | Theorem 99 | mapss 8839 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 9990 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 9989 |
| [Suppes] p. 92 | Theorem 1 | enref 8934 enrefg 8933 |
| [Suppes] p. 92 | Theorem 2 | ensym 8952 ensymb 8951 ensymi 8953 |
| [Suppes] p. 92 | Theorem 3 | entr 8955 |
| [Suppes] p. 92 | Theorem 4 | unen 8994 |
| [Suppes] p. 94 | Theorem 15 | endom 8928 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 8949 |
| [Suppes] p. 94 | Theorem 17 | domtr 8956 |
| [Suppes] p. 95 | Theorem 18 | sbth 9037 |
| [Suppes] p. 97 | Theorem 23 | canth2 9070 canth2g 9071 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9041 df-sdom 8898 dfsdom2 9040 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9054 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9043 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9042 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9052 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8931 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9055 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9050 |
| [Suppes] p. 98 | Exercise 4 | fundmen 8980 fundmeng 8981 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9015 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9051 |
| [Suppes] p. 104 | Theorem 37 | fofi 9225 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9231 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9231 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10473 |
| [Suppes] p. 130 | Definition 3 | df-tr 5208 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7735 |
| [Suppes] p. 134 | Definition 6 | df-suc 6331 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7852 finds 7848 finds1 7851 finds2 7850 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9573 isfinite2 9210 isfiniteg 9212 unbnn 9208 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10841 df-ltpq 10833 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7815 tfinds 7812 tfinds2 7816 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8488 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8490 |
| [Suppes] p. 211 | Theorem 25 | oaass 8498 |
| [Suppes] p. 225 | Definition 8 | iscard2 9900 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10485 |
| [Suppes] p. 228 | Theorem 59 | harcard 9902 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 9988 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6377 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7748 onminsb 7749 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10495 |
| [Suppes] p. 229 | Theorem 65 | alephcard 9992 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 9999 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 9993 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9864 |
| [Suppes] p. 242 | Theorem 6 | weth 10417 |
| [Suppes] p. 242 | Theorem 8 | entric 10479 |
| [Suppes] p. 242 | Theorem 9 | carden 10473 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 35909 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 35913 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2709 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2729 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2812 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2731 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2757 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7372 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3740 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5368 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4607 elpr2 4609 elpr2g 4608 elprg 4605 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4597 elsn2 4624 elsn2g 4623 elsng 4596 velsn 4598 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5423 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4592 sneqr 4798 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4603 dfsn2 4595 dfsn2ALT 4604 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7696 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5432 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5419 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5403 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7699 unexg 7698 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4650 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4866 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3910 df-un 3908 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4882 uniprg 4881 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5324 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4648 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6397 elsucg 6395 sstr2 3942 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4112 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4163 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4126 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4182 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4238 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4239 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3923 df-ss 3920 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4558 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4141 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3921 sseqin2 4177 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3958 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4191 inss2 4192 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 4000 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4876 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5404 sspwimp 45262 sspwimpALT 45269 sspwimpALT2 45272 sspwimpcf 45264 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5411 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5226 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3402 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5254 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3906 |
| [TakeutiZaring] p. 20 | Definition 5.14 | dfnul2 4290 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4330 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4307 n0f 4303 neq0 4306 neq0f 4302 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9513 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9653 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9668 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3444 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5262 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4354 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5268 ssexg 5270 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5264 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9522 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9516 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4320 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4089 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4254 undif3VD 45226 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4090 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4097 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3053 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3063 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7708 xpexg 7705 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5639 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6571 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6747 fun11 6574 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6513 svrelfun 6572 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5844 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5846 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5644 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5645 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5641 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6160 dfrel2 6155 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5648 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5768 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5775 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5788 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 5972 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5952 opelresi 5954 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 5979 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5968 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 5973 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6542 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6075 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6540 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6749 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2610 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30487 df-fv 6508 fv3 6860 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7877 cnvexg 7876 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7861 dmexg 7853 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7862 rnexg 7854 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 44798 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7872 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6855 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 47523 tz6.12-1-afv2 47590 tz6.12-1 6865 tz6.12-afv 47522 tz6.12-afv2 47589 tz6.12 6866 tz6.12c-afv2 47591 tz6.12c 6864 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 47586 tz6.12-2 6829 tz6.12i-afv2 47592 tz6.12i 6868 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6503 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6504 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6506 wfo 6498 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6505 wf1 6497 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6507 wf1o 6499 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 6985 eqfnfv2 6986 eqfnfv2f 6989 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6940 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7173 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7171 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6588 funimaexg 6587 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5101 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5541 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5593 dffr3 6066 eliniseg 6061 iniseg 6064 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5532 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5609 fr3nr 7727 frirr 5608 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5585 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7729 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5596 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5618 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6313 tz6.26i 6314 wefrc 5626 wereu2 5629 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6315 wfii 6316 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6509 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7285 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7286 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7292 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7293 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7294 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7298 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7305 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7307 |
| [TakeutiZaring] p. 35 | Notation | wtr 5207 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 44799 tz7.2 5615 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5212 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6338 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6346 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6347 ordelordALT 44882 ordelordALTVD 45211 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6353 ordelssne 6352 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6351 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6355 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7737 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7738 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6329 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6357 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 44894 ordon 7732 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7733 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7805 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6373 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5209 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7747 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7783 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6431 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6430 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7734 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4896 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6331 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6407 sucidg 6408 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7765 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6421 ordnbtwn 6420 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7780 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6330 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7833 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7838 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7793 ordelsuc 7772 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7774 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7803 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7820 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7841 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7842 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7843 |
| [TakeutiZaring] p. 43 | Remark | omon 7830 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9556 omex 9564 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7828 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7847 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7844 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7845 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7823 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4919 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5225 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4920 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5291 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7750 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6376 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4905 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9581 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7745 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8317 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8338 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8339 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8340 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8347 tz7.44-2 8348 tz7.44-3 8349 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8309 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8304 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8288 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8386 tz7.49c 8387 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8384 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8383 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8385 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2657 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 9933 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 9934 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8469 oasuc 8461 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7813 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8472 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8453 oa0r 8475 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8473 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8485 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8557 nnaordi 8556 oaord 8484 oaordi 8483 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5007 uniss2 4899 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8487 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8492 oawordex 8494 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8549 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8586 |
| [TakeutiZaring] p. 60 | Remark | oancom 9572 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8497 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8554 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8489 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8456 omlim 8470 omsuc 8463 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8454 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8551 nnmcl 8550 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8570 nnmordi 8569 omord 8505 omordi 8503 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8506 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8574 omwordri 8509 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8476 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8479 om1r 8480 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8512 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8514 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8515 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8516 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8517 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8546 oe0 8459 oelim 8471 oesuc 8464 onesuc 8467 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8457 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8524 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8525 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8458 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8482 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8526 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8532 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8530 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8531 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8535 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8537 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9649 tz9.1 9650 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9688 r10 9692 r1lim 9696 r1limg 9695 r1suc 9694 r1sucg 9693 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9704 r1ord2 9705 r1ordg 9702 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9714 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9739 tz9.13 9715 tz9.13g 9716 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9689 rankval 9740 rankvalb 9721 rankvalg 9741 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9763 rankelb 9748 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9777 rankval3 9764 rankval3b 9750 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9753 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9719 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9758 rankr1c 9745 rankr1g 9756 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9759 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9773 rankssb 9772 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9766 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9765 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10397 dfac3 10043 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 9952 numth 10394 numth2 10393 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10468 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10469 cardid2 9877 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9884 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10473 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9883 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9868 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9889 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9881 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9090 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 8967 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9095 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9019 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9887 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10020 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9142 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9150 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10021 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9147 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10010 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 9988 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9896 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10138 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9235 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8899 isfi 8924 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9151 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10456 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9012 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10448 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10108 unxpdom 9171 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9898 cardsdomelir 9897 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9173 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 9936 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8777 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10484 infxpidm2 9939 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10129 infxp 10136 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9024 pw2f1o 9022 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9083 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10409 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10404 ac6s5 10413 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10465 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10466 uniimadomf 10467 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10196 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10191 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10176 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10173 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10179 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10186 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10195 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10505 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10174 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10198 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10019 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10018 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10030 alephfp2 10031 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10622 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10034 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10492 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10506 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10507 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 39248 |
| [Tarski] p. 67 | Scheme B5 | sp 2191 |
| [Tarski] p. 68 | Lemma 6 | avril1 30550 equid 2014 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2019 |
| [Tarski] p. 70 | Lemma 14 | spim 2392 spime 2394 spimew 1973 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2185 ax-c15 39254 ax12i 1968 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2091 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1970 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1912 ax5ALT 39272 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2010 ax-8 2116 ax-9 2124 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28548 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28549 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28551 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28551 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28552 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16180 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 37899 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 37901 |
| [Weierstrass] p. 272 | Definition | df-mdet 22541 mdetuni 22578 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 904 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 869 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 870 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 920 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 970 |
| [WhiteheadRussell] p. 100 | Theorem *2.01 | pm2.01 188 |
| [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 37689 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 44145 imim2 58 wl-luk-imim2 37684 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 47368 imim1 83 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 897 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2664 syl 17 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 903 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 22 wl-luk-id 37687 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 895 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 142 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 898 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 130 notnotrALT2 45271 wl-luk-notnotr 37688 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 146 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 44175 axfrege28 44174 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 868 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 925 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 123 wl-luk-pm2.21 37681 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 124 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 890 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 942 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 30488 pm2.27 42 wl-luk-pm2.27 37679 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 923 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 38611 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 924 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 972 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 973 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 971 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1088 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 907 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 908 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 945 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 56 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 882 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 883 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5 169 pm2.5g 168 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6 191 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 884 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 885 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 886 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 172 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 852 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 853 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 889 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 891 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 192 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 900 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 943 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 944 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 193 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 892 pm2.67 893 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 176 pm2.521g 174 pm2.521g2 175 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 899 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 975 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 901 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 203 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 976 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 977 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 934 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 932 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 974 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 978 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 84 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 933 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 109 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 994 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 469 pm3.2im 160 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 995 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 996 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 997 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 998 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 471 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 459 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 402 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 803 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 448 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 449 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 482 simplim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 484 simprim 166 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 765 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 766 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 808 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 623 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 810 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 492 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 493 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 963 pm3.44 962 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 809 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 473 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 966 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34b 316 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 261 |
| [WhiteheadRussell] p. 117 | Theorem *4.11 | notbi 319 |
| [WhiteheadRussell] p. 117 | Theorem *4.12 | con2bi 353 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotb 315 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14 807 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 833 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 222 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 806 bitr 805 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 563 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 905 pm4.25 906 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 460 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1010 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 871 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 468 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 922 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 634 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 918 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 638 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 979 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1089 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1008 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1054 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1025 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 999 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 1001 pm4.45 1000 pm4.45im 828 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 985 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 854 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 545 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 984 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 987 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 988 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 989 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 990 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 986 pm4.56 991 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 992 pm4.57 993 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 404 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 857 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 397 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 850 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 405 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 851 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67 398 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 557 pm4.71d 561 pm4.71i 559 pm4.71r 558 pm4.71rd 562 pm4.71ri 560 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 952 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 527 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 937 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 517 pm4.76 518 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 964 pm4.77 965 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 935 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1006 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 392 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81 393 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 1026 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1027 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 347 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 348 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 351 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 387 impexp 450 pm4.87 844 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 824 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 947 pm5.11g 946 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 948 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 950 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 949 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1015 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1016 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1014 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbn 383 pm5.18 381 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 386 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 825 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1017 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1050 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1051 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 902 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 572 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 388 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 361 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6 1004 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 956 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 831 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 573 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 836 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 826 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 834 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 389 pm5.41 390 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 543 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 542 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 1007 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1020 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 951 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1003 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1021 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1022 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1030 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 366 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 270 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 1031 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 44703 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 44704 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1872 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 44705 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 44706 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 44707 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1895 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 44708 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 44709 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 44710 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 44711 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 44712 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 44714 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 44715 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 44716 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 44713 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2096 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 44719 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 44720 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2076 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2166 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1831 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1832 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 44721 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 44722 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 44723 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 44724 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 44726 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 44725 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1889 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 44728 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 44729 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 44727 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1830 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 44730 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 44731 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1848 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 44732 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2351 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1862 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 44737 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 44733 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 44734 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 44735 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 44736 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 44741 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 44738 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 44739 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 44740 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 44742 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2570 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 44752 pm13.13b 44753 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 44754 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3014 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3015 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3622 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 44760 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 44761 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 44755 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 44897 pm13.193 44756 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 44757 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 44758 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 44759 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 44766 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 44765 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 44764 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3805 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 44767 pm14.122b 44768 pm14.122c 44769 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 44770 pm14.123b 44771 pm14.123c 44772 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 44774 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 44773 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 44775 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6481 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 44776 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6482 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 44777 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 44779 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2634 eupickbi 2637 sbaniota 44780 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 44778 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2585 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 44781 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30487 df-fv 6508 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 9925 pm54.43lem 9924 |
| [Young] p. 141 | Definition of operator ordering | leop2 32211 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32217 idleop 32218 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 43174 |
| [vandenDries] p. 43 | Theorem 62 | pellex 43181 pellexlem1 43175 |