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 17635 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17635 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18044 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17656 0funcg 49002 df-termc 49351 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 49428 prsthinc 49342 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 49456 df-mndtc 49456 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 49452 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17679 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 49444 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 49469 oppgoppchom 49468 oppgoppcid 49470 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17749 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17737 invisoinvl 17758 |
| [Adamek] p. 28 | Example 3.13 | idinv 17757 idiso 17756 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17742 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17716 df-iso 17717 dfiso2 17740 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17723 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17774 cicerALT 48963 |
| [Adamek] p. 29 | Definition 3.15 | cic 17767 df-cic 17764 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17826 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17738 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17739 isoco 17745 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17826 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17849 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 49199 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17842 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 49452 discthing 49339 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 49296 prsthinc 49342 thincciso 49331 thincciso2 49333 thincciso3 49334 thinccisod 49332 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 49456 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17856 cofucla 49013 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 49073 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18079 catcisoi 49292 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18134 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17875 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17874 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18134 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17899 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17905 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17904 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18119 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18119 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 49040 funcoppc 17843 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18067 elcatchom 49289 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17893 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17892 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18076 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 49002 df-catc 18067 |
| [Adamek] p. 45 | Exercise 3G | incat 49479 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 49482 nelsubc3 48988 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 49062 imasubc2 49063 imasubc3 49067 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17806 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17807 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 48988 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17818 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17780 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 49071 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 49070 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 49072 ressffth 17908 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 49480 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 17914 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 17935 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 17939 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 17915 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 17941 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 49002 df-inito 17952 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 49002 df-termc 49351 initc 49008 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21395 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 17953 oppctermo 49137 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 17980 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 17984 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 49138 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 17954 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21396 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 17987 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17715 |
| [Adamek] p. 185 | Section 10.67 | updjud 9905 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 49520 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 49520 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 49520 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 49521 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 49521 |
| [Adamek] p. 478 | Item Rng | df-ringc 20561 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 48470 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 48492 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14546 df-pfx 14646 df-substr 14616 df-word 14489 lencl 14508 wrd0 14514 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24602 df-nmoo 30681 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32089 hmopidmchi 32087 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32137 pjcmul2i 32138 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 31854 unoplin 31856 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 31855 unopadj2 31874 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 31949 lnopunii 31948 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32022 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 27842 |
| [Alling] p. 184 | Axiom B | bdayfo 27596 |
| [Alling] p. 184 | Axiom O | sltso 27595 |
| [Alling] p. 184 | Axiom SD | nodense 27611 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27697 |
| [Alling] p. 185 | Theorem | conway 27718 |
| [Alling] p. 185 | Axiom FE | noeta 27662 |
| [Alling] p. 186 | Theorem 4 | slerec 27738 |
| [Alling], p. 2 | Definition | rp-brsslt 43384 |
| [Alling], p. 3 | Note | nla0001 43387 nla0002 43385 nla0003 43386 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11376 addcan2d 11396 addcan2i 11386 addcand 11395 addcani 11385 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11429 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11488 negsubd 11557 negsubi 11518 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11490 negnegd 11542 negnegi 11510 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11627 subdid 11650 subdii 11643 subdir 11628 subdird 11651 subdiri 11644 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11371 mul01d 11391 mul01i 11382 mul02 11370 mul02d 11390 mul02i 11381 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11831 mulcan2d 11828 mulcand 11827 mulcani 11833 |
| [Apostol] p. 18 | Theorem I.8 | receu 11839 xreceu 32850 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11869 divrecd 11977 divreci 11943 divreczi 11936 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11895 recreci 11930 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11834 mul0ord 11844 mul0ori 11842 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11633 mul2negd 11649 mul2negi 11642 mulneg1 11630 mulneg1d 11647 mulneg1i 11640 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11913 divadddivd 12018 divadddivi 11960 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11898 divmuldivd 12015 divmuldivi 11958 rdivmuldivd 20328 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11899 divdivdivd 12021 divdivdivi 11961 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 12988 rpaddcld 13023 rpmulcl 12989 rpmulcld 13024 |
| [Apostol] p. 20 | Axiom 8 | rpneg 12998 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 13001 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11318 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11787 ltadd1dd 11805 ltadd1i 11748 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12048 ltmul1a 12047 ltmul1i 12117 ltmul1ii 12127 ltmul2 12049 ltmul2d 13050 ltmul2dd 13064 ltmul2i 12120 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11714 msqgt0d 11761 msqgt0i 11731 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11716 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11700 lt0neg1d 11763 ltneg 11694 ltnegd 11772 ltnegi 11738 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11679 lt2addd 11817 lt2addi 11756 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 12966 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12044 recgt0d 12133 recgt0i 12104 recgt0ii 12105 |
| [Apostol] p. 22 | Definition of integers | df-z 12546 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12211 |
| [Apostol] p. 22 | Definition of rationals | df-q 12922 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9423 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12454 |
| [Apostol] p. 26 | Theorem I.29 | arch 12455 archd 45128 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12653 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12456 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12920 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12919 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13172 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16315 zneo 12633 zneoALTV 47625 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26646 msqsqrtd 15416 resqrtth 15231 sqrtth 15340 sqrtthi 15346 sqsqrtd 15415 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12200 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12886 |
| [Apostol] p. 361 | Remark | crreczi 14203 |
| [Apostol] p. 363 | Remark | absgt0i 15375 |
| [Apostol] p. 363 | Example | abssubd 15429 abssubi 15379 |
| [ApostolNT] p. 7 | Remark | fmtno0 47496 fmtno1 47497 fmtno2 47506 fmtno3 47507 fmtno4 47508 fmtno5fac 47538 fmtnofz04prm 47533 |
| [ApostolNT] p. 7 | Definition | df-fmtno 47484 |
| [ApostolNT] p. 8 | Definition | df-ppi 27017 |
| [ApostolNT] p. 14 | Definition | df-dvds 16230 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16246 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16270 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16265 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16259 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16261 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16247 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16248 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16253 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16287 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16289 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16291 |
| [ApostolNT] p. 15 | Definition | df-gcd 16471 dfgcd2 16522 |
| [ApostolNT] p. 16 | Definition | isprm2 16658 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16629 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16892 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16489 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16523 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16525 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16504 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16496 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16687 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16689 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16905 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16899 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16379 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16563 |
| [ApostolNT] p. 24 | Definition | df-mu 27018 |
| [ApostolNT] p. 25 | Definition | df-phi 16742 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27108 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16767 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16752 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16756 |
| [ApostolNT] p. 32 | Definition | df-vma 27015 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27110 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27134 |
| [ApostolNT] p. 38 | Remark | df-sgm 27019 |
| [ApostolNT] p. 38 | Definition | df-sgm 27019 |
| [ApostolNT] p. 75 | Definition | df-chp 27016 df-cht 27014 |
| [ApostolNT] p. 104 | Definition | congr 16640 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16233 |
| [ApostolNT] p. 106 | Definition | moddvds 16240 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16322 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16323 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13862 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13900 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14213 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16264 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16643 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17051 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16645 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16759 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16778 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16760 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 26989 |
| [ApostolNT] p. 179 | Definition | df-lgs 27213 lgsprme0 27257 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27258 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27234 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27249 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27306 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27325 2lgsoddprm 27334 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27292 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27301 |
| [ApostolNT] p. 188 | Definition | df-lgs 27213 lgs1 27259 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27250 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27252 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27260 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27261 |
| [Baer] p. 40 | Property (b) | mapdord 41624 |
| [Baer] p. 40 | Property (c) | mapd11 41625 |
| [Baer] p. 40 | Property (e) | mapdin 41648 mapdlsm 41650 |
| [Baer] p. 40 | Property (f) | mapd0 41651 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 41611 mapd1o 41634 |
| [Baer] p. 41 | Property (g) | mapdat 41653 |
| [Baer] p. 44 | Part (1) | mapdpg 41692 |
| [Baer] p. 45 | Part (2) | hdmap1eq 41787 mapdheq 41714 mapdheq2 41715 mapdheq2biN 41716 |
| [Baer] p. 45 | Part (3) | baerlem3 41699 |
| [Baer] p. 46 | Part (4) | mapdheq4 41718 mapdheq4lem 41717 |
| [Baer] p. 46 | Part (5) | baerlem5a 41700 baerlem5abmN 41704 baerlem5amN 41702 baerlem5b 41701 baerlem5bmN 41703 |
| [Baer] p. 47 | Part (6) | hdmap1l6 41807 hdmap1l6a 41795 hdmap1l6e 41800 hdmap1l6f 41801 hdmap1l6g 41802 hdmap1l6lem1 41793 hdmap1l6lem2 41794 mapdh6N 41733 mapdh6aN 41721 mapdh6eN 41726 mapdh6fN 41727 mapdh6gN 41728 mapdh6lem1N 41719 mapdh6lem2N 41720 |
| [Baer] p. 48 | Part 9 | hdmapval 41814 |
| [Baer] p. 48 | Part 10 | hdmap10 41826 |
| [Baer] p. 48 | Part 11 | hdmapadd 41829 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 41803 mapdh6hN 41729 |
| [Baer] p. 48 | Part (7) | mapdh75cN 41739 mapdh75d 41740 mapdh75e 41738 mapdh75fN 41741 mapdh7cN 41735 mapdh7dN 41736 mapdh7eN 41734 mapdh7fN 41737 |
| [Baer] p. 48 | Part (8) | mapdh8 41774 mapdh8a 41761 mapdh8aa 41762 mapdh8ab 41763 mapdh8ac 41764 mapdh8ad 41765 mapdh8b 41766 mapdh8c 41767 mapdh8d 41769 mapdh8d0N 41768 mapdh8e 41770 mapdh8g 41771 mapdh8i 41772 mapdh8j 41773 |
| [Baer] p. 48 | Part (9) | mapdh9a 41775 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 41755 |
| [Baer] p. 49 | Part 12 | hdmap11 41834 hdmapeq0 41830 hdmapf1oN 41851 hdmapneg 41832 hdmaprnN 41850 hdmaprnlem1N 41835 hdmaprnlem3N 41836 hdmaprnlem3uN 41837 hdmaprnlem4N 41839 hdmaprnlem6N 41840 hdmaprnlem7N 41841 hdmaprnlem8N 41842 hdmaprnlem9N 41843 hdmapsub 41833 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 41854 hdmap14lem10 41863 hdmap14lem1a 41852 hdmap14lem2N 41855 hdmap14lem2a 41853 hdmap14lem3 41856 hdmap14lem8 41861 hdmap14lem9 41862 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 41864 hdmap14lem12 41865 hdmap14lem13 41866 hdmap14lem14 41867 hdmap14lem15 41868 hgmapval 41873 |
| [Baer] p. 50 | Part 15 | hgmapadd 41880 hgmapmul 41881 hgmaprnlem2N 41883 hgmapvs 41877 |
| [Baer] p. 50 | Part 16 | hgmaprnN 41887 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 41903 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 41904 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 41905 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 41906 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 41908 hgmapvv 41912 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 41907 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 41909 |
| [Baer] p. 111 | Line 15 | hdmapg 41916 hdmapglem7 41915 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26647 2irrexpqALT 26717 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 23 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2563 |
| [BellMachover] p. 460 | Notation | df-mo 2534 |
| [BellMachover] p. 460 | Definition | mo3 2558 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2702 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2706 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5250 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5259 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37049 sepex 5263 |
| [BellMachover] p. 466 | Problem | axpow2 5330 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5331 |
| [BellMachover] p. 466 | Axiom Union | axun2 7720 |
| [BellMachover] p. 468 | Definition | df-ord 6343 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6358 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6365 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6360 |
| [BellMachover] p. 471 | Definition of N | df-om 7851 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7784 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6345 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9613 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7866 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9735 |
| [BellMachover] p. 478 | Definition | rankval2 9789 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9753 r1ord3g 9750 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9566 |
| [BellMachover] p. 488 | Axiom AC | ac5 10448 dfac4 10093 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10081 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 39304 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32289 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32331 chirredi 32330 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32319 |
| [Beran] p. 3 | Definition of join | sshjval3 31290 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 31552 cmcm2i 31529 cmcm2ii 31534 cmt2N 39235 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 31553 lecmi 31538 lecmii 31539 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 31527 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 31556 cm2ji 31561 cm2mi 31562 |
| [Beran] p. 95 | Definition | df-sh 31143 issh2 31145 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31022 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31035 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31026 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 31764 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 31766 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 31765 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 31767 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31018 his1i 31036 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31019 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31020 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31021 |
| [Beran] p. 96 | Definition of norm | df-hnorm 30904 dfhnorm2 31058 normval 31060 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31120 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 30909 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31177 |
| [Beran] p. 96 | Definition of converge | df-hlim 30908 hlimi 31124 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31069 norm-i 31065 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31073 norm-ii 31074 normlem0 31045 normlem1 31046 normlem2 31047 normlem3 31048 normlem4 31049 normlem5 31050 normlem6 31051 normlem7 31052 normlem7tALT 31055 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31075 norm-iii 31076 |
| [Beran] p. 98 | Remark 3.4 | bcs 31117 bcsiALT 31115 bcsiHIL 31116 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31057 normpar 31091 normpari 31090 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31082 normpyth 31081 normpythi 31078 |
| [Beran] p. 99 | Remark | lnfn0 31983 lnfn0i 31978 lnop0 31902 lnop0i 31906 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 31962 nmcfnex 31989 nmcfnexi 31987 nmcopex 31965 nmcopexi 31963 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 31990 nmcfnlbi 31988 nmcoplb 31966 nmcoplbi 31964 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 31992 lnfnconi 31991 lnopcon 31971 lnopconi 31970 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31092 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31089 norm3adifii 31084 norm3dif 31086 norm3difi 31083 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31237 pjhth 31329 pjhtheu 31330 pjpjhth 31361 pjpjhthi 31362 pjth 25346 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31342 ococi 31341 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 31997 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 31998 riesz4 32000 riesz4i 31999 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32015 cnlnadjeu 32014 cnlnadjeui 32013 cnlnadji 32012 cnlnadjlem1 32003 nmopadjlei 32024 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32027 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32026 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32028 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 31872 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32038 nmopcoadji 32037 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32029 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32039 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32036 pjadj2coi 32140 pjadjcoi 32097 |
| [Beran] p. 107 | Definition | df-ch 31157 isch2 31159 |
| [Beran] p. 107 | Remark 3.12 | choccl 31242 isch3 31177 occl 31240 ocsh 31219 shoccl 31241 shocsh 31220 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31344 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31268 |
| [Beran] p. 109 | Property (i) | pjadj2 32123 pjadj3 32124 pjadji 31621 pjadjii 31610 |
| [Beran] p. 109 | Property (ii) | pjidmco 32117 pjidmcoi 32113 pjidmi 31609 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32109 |
| [Beran] p. 111 | Remark | ho0val 31686 pjch1 31606 |
| [Beran] p. 111 | Definition | df-hfmul 31670 df-hfsum 31669 df-hodif 31668 df-homul 31667 df-hosum 31666 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 31607 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 31630 pjchi 31368 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31375 pjoc2i 31374 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 31616 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32101 pjssmii 31617 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32100 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32099 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32104 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32102 pjssge0ii 31618 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32103 pjdifnormii 31619 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1776 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1774 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1777 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1772 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34291 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34299 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34297 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34301 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34321 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34352 df-sitm 34330 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34352 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34329 |
| [Bollobas] p. 1 | Section I.1 | df-edg 28982 isuhgrop 29004 isusgrop 29096 isuspgrop 29095 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 47816 df-subgr 29202 uhgrspan1 29237 uhgrspansubgr 29225 |
| [Bollobas] p. 3 | Definition | df-gric 47836 gricuspgr 47873 isuspgrim 47851 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29389 df-clnbgr 47775 df-cusgr 29346 df-nbgr 29267 fusgrmaxsize 29399 |
| [Bollobas] p. 4 | Definition | df-upwlks 48051 df-wlks 29534 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 29485 finsumvtxdgeven 29487 fusgr1th 29486 fusgrvtxdgonume 29489 vtxdgoddnumeven 29488 |
| [Bollobas] p. 5 | Notation | df-pths 29651 |
| [Bollobas] p. 5 | Definition | df-crcts 29723 df-cycls 29724 df-trls 29627 df-wlkson 29535 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 28993 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 48117 df-cllaw 48103 df-mgm 18573 df-mgm2 48136 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 48118 df-asslaw 48105 df-sgrp 18652 df-sgrp2 48138 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 48137 df-comlaw 48104 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18668 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 32975 mndlactf1o 32979 mndractf1 32977 mndractf1o 32980 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20150 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20068 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 33637 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 33641 assarrginv 33640 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 33681 fldextrspunfld 33679 fldextrspunlem1 33678 fldextrspunlem2 33680 fldextrspunlsp 33677 fldextrspunlsplem 33676 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 33516 dfufd2 33529 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7269 fcofo 7270 |
| [BourbakiTop1] p. | Remark | xnegmnf 13183 xnegpnf 13182 |
| [BourbakiTop1] p. | Remark | rexneg 13184 |
| [BourbakiTop1] p. | Remark 3 | ust0 24113 ustfilxp 24106 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 23983 |
| [BourbakiTop1] p. | Criterion | ishmeo 23652 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24177 iducn 24176 snfil 23757 |
| [BourbakiTop1] p. | Example 2 | neifil 23773 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 23960 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24197 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 33955 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23756 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24169 df-ust 24094 filintn0 23754 filn0 23755 istgp 23970 ucnprima 24175 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24180 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24191 df-usp 24151 df-utop 24125 trust 24123 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 33854 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23009 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23162 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24099 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24102 |
| [BourbakiTop1] p. | Property V_ii | innei 23018 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23026 neissex 23020 |
| [BourbakiTop1] p. | Proposition 1 | neips 23006 neiss 23002 ucncn 24178 ustund 24115 ustuqtop 24140 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23160 neiptopreu 23026 utop2nei 24144 utop3cls 24145 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24185 uspreg 24167 utopreg 24146 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23584 imasncls 23585 imasnopn 23583 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 23893 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24101 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24103 |
| [BourbakiTop1] p. | Property V_iii | elnei 23004 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24196 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24100 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24104 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23280 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23739 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 22787 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 33851 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 46033 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 46035 stoweid 46034 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 45972 stoweidlem10 45981 stoweidlem14 45985 stoweidlem15 45986 stoweidlem35 46006 stoweidlem36 46007 stoweidlem37 46008 stoweidlem38 46009 stoweidlem40 46011 stoweidlem41 46012 stoweidlem43 46014 stoweidlem44 46015 stoweidlem46 46017 stoweidlem5 45976 stoweidlem50 46021 stoweidlem52 46023 stoweidlem53 46024 stoweidlem55 46026 stoweidlem56 46027 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 45994 stoweidlem24 45995 stoweidlem27 45998 stoweidlem28 45999 stoweidlem30 46001 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 46005 stoweidlem59 46030 stoweidlem60 46031 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 46016 stoweidlem49 46020 stoweidlem7 45978 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 46002 stoweidlem39 46010 stoweidlem42 46013 stoweidlem48 46019 stoweidlem51 46022 stoweidlem54 46025 stoweidlem57 46028 stoweidlem58 46029 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 45996 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 45988 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 45982 stoweidlem13 45984 stoweidlem26 45997 stoweidlem61 46032 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 45989 |
| [Bruck] p. 1 | Section I.1 | df-clintop 48117 df-mgm 18573 df-mgm2 48136 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18652 df-sgrp2 48138 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 18977 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5197 |
| [Church] p. 129 | Section II.24 | df-ifp 1063 dfifp2 1064 |
| [Clemente] p. 10 | Definition IT | natded 30339 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30339 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30339 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30339 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30339 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30339 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30339 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30339 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30339 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30339 |
| [Clemente] p. 14 | Proof 5.11 | natded 30339 |
| [Clemente] p. 14 | Definition E` `n | natded 30339 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30341 ex-natded5.2 30340 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30344 ex-natded5.3 30343 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30346 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30348 ex-natded5.7 30347 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30350 ex-natded5.8 30349 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30352 ex-natded5.13 30351 |
| [Clemente] p. 32 | Definition I` `n | natded 30339 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30339 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30339 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30339 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30353 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30354 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30356 ex-natded9.26 30355 |
| [Cohen] p. 301 | Remark | relogoprlem 26507 |
| [Cohen] p. 301 | Property 2 | relogmul 26508 relogmuld 26541 |
| [Cohen] p. 301 | Property 3 | relogdiv 26509 relogdivd 26542 |
| [Cohen] p. 301 | Property 4 | relogexp 26512 |
| [Cohen] p. 301 | Property 1a | log1 26501 |
| [Cohen] p. 301 | Property 1b | loge 26502 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26704 |
| [Cohen4] p. 349 | Property | relogbf 26708 |
| [Cohen4] p. 352 | Definition | elogb 26687 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26694 |
| [Cohen4] p. 361 | Property 3 | logbrec 26699 relogbdiv 26696 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26692 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26697 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26685 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26686 |
| [Cohen4] p. 367 | Property | logbchbase 26688 |
| [Cohen4] p. 377 | Property 2 | logblt 26701 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34284 sxbrsigalem4 34286 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18522 acsinfd 18521 acsinfdimd 18523 acsmap2d 18520 acsmapd 18519 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34289 |
| [Connell] p. 57 | Definition | df-scmat 22384 df-scmatalt 48317 |
| [Conway] p. 4 | Definition | slerec 27738 |
| [Conway] p. 5 | Definition | addsval 27876 addsval2 27877 df-adds 27874 df-muls 28017 df-negs 27934 |
| [Conway] p. 7 | Theorem | 0slt1s 27748 |
| [Conway] p. 16 | Theorem 0(i) | ssltright 27790 |
| [Conway] p. 16 | Theorem 0(ii) | ssltleft 27789 |
| [Conway] p. 16 | Theorem 0(iii) | slerflex 27682 |
| [Conway] p. 17 | Theorem 3 | addsass 27919 addsassd 27920 addscom 27880 addscomd 27881 addsrid 27878 addsridd 27879 |
| [Conway] p. 17 | Definition | df-0s 27743 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 27957 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 27954 negsidd 27955 |
| [Conway] p. 18 | Theorem 5 | sleadd1 27903 sleadd1d 27909 |
| [Conway] p. 18 | Definition | df-1s 27744 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 27949 negscld 27950 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 27894 |
| [Conway] p. 19 | Note | mulsunif2 28080 |
| [Conway] p. 19 | Theorem 7 | addsdi 28065 addsdid 28066 addsdird 28067 mulnegs1d 28070 mulnegs2d 28071 mulsass 28076 mulsassd 28077 mulscom 28049 mulscomd 28050 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28044 mulscld 28045 |
| [Conway] p. 19 | Theorem 8(iii) | slemuld 28048 sltmul 28046 sltmuld 28047 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28054 mulsgt0d 28055 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28127 |
| [Conway] p. 24 | Definition | df-reno 28352 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28357 remulscl 28360 renegscl 28356 |
| [Conway] p. 27 | Definition | df-ons 28160 elons2 28166 |
| [Conway] p. 27 | Theorem 14 | sltonex 28170 |
| [Conway] p. 28 | Theorem 15 | onscutlt 28172 onswe 28177 |
| [Conway] p. 29 | Remark | madebday 27818 newbday 27820 oldbday 27819 |
| [Conway] p. 29 | Definition | df-made 27762 df-new 27764 df-old 27763 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13835 |
| [Crawley] p. 1 | Definition of poset | df-poset 18280 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 39372 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 40176 dalaw 39872 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 41947 |
| [Crawley] p. 111 | Definition of set W | df-watsN 39976 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 40092 df-ldil 40090 isldil 40096 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 40091 df-trnN 40093 isltrn 40105 ltrnu 40107 |
| [Crawley] p. 112 | Lemma A | cdlema1N 39777 cdlema2N 39778 exatleN 39390 |
| [Crawley] p. 112 | Lemma B | 1cvrat 39462 cdlemb 39780 cdlemb2 40027 cdlemb3 40592 idltrn 40136 l1cvat 39040 lhpat 40029 lhpat2 40031 lshpat 39041 ltrnel 40125 ltrnmw 40137 |
| [Crawley] p. 112 | Lemma C | cdlemc1 40177 cdlemc2 40178 ltrnnidn 40160 trlat 40155 trljat1 40152 trljat2 40153 trljat3 40154 trlne 40171 trlnidat 40159 trlnle 40172 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 39977 |
| [Crawley] p. 113 | Lemma C | cdlemc 40183 cdlemc3 40179 cdlemc4 40180 |
| [Crawley] p. 113 | Lemma D | cdlemd 40193 cdlemd1 40184 cdlemd2 40185 cdlemd3 40186 cdlemd4 40187 cdlemd5 40188 cdlemd6 40189 cdlemd7 40190 cdlemd8 40191 cdlemd9 40192 cdleme31sde 40371 cdleme31se 40368 cdleme31se2 40369 cdleme31snd 40372 cdleme32a 40427 cdleme32b 40428 cdleme32c 40429 cdleme32d 40430 cdleme32e 40431 cdleme32f 40432 cdleme32fva 40423 cdleme32fva1 40424 cdleme32fvcl 40426 cdleme32le 40433 cdleme48fv 40485 cdleme4gfv 40493 cdleme50eq 40527 cdleme50f 40528 cdleme50f1 40529 cdleme50f1o 40532 cdleme50laut 40533 cdleme50ldil 40534 cdleme50lebi 40526 cdleme50rn 40531 cdleme50rnlem 40530 cdlemeg49le 40497 cdlemeg49lebilem 40525 |
| [Crawley] p. 113 | Lemma E | cdleme 40546 cdleme00a 40195 cdleme01N 40207 cdleme02N 40208 cdleme0a 40197 cdleme0aa 40196 cdleme0b 40198 cdleme0c 40199 cdleme0cp 40200 cdleme0cq 40201 cdleme0dN 40202 cdleme0e 40203 cdleme0ex1N 40209 cdleme0ex2N 40210 cdleme0fN 40204 cdleme0gN 40205 cdleme0moN 40211 cdleme1 40213 cdleme10 40240 cdleme10tN 40244 cdleme11 40256 cdleme11a 40246 cdleme11c 40247 cdleme11dN 40248 cdleme11e 40249 cdleme11fN 40250 cdleme11g 40251 cdleme11h 40252 cdleme11j 40253 cdleme11k 40254 cdleme11l 40255 cdleme12 40257 cdleme13 40258 cdleme14 40259 cdleme15 40264 cdleme15a 40260 cdleme15b 40261 cdleme15c 40262 cdleme15d 40263 cdleme16 40271 cdleme16aN 40245 cdleme16b 40265 cdleme16c 40266 cdleme16d 40267 cdleme16e 40268 cdleme16f 40269 cdleme16g 40270 cdleme19a 40289 cdleme19b 40290 cdleme19c 40291 cdleme19d 40292 cdleme19e 40293 cdleme19f 40294 cdleme1b 40212 cdleme2 40214 cdleme20aN 40295 cdleme20bN 40296 cdleme20c 40297 cdleme20d 40298 cdleme20e 40299 cdleme20f 40300 cdleme20g 40301 cdleme20h 40302 cdleme20i 40303 cdleme20j 40304 cdleme20k 40305 cdleme20l 40308 cdleme20l1 40306 cdleme20l2 40307 cdleme20m 40309 cdleme20y 40288 cdleme20zN 40287 cdleme21 40323 cdleme21d 40316 cdleme21e 40317 cdleme22a 40326 cdleme22aa 40325 cdleme22b 40327 cdleme22cN 40328 cdleme22d 40329 cdleme22e 40330 cdleme22eALTN 40331 cdleme22f 40332 cdleme22f2 40333 cdleme22g 40334 cdleme23a 40335 cdleme23b 40336 cdleme23c 40337 cdleme26e 40345 cdleme26eALTN 40347 cdleme26ee 40346 cdleme26f 40349 cdleme26f2 40351 cdleme26f2ALTN 40350 cdleme26fALTN 40348 cdleme27N 40355 cdleme27a 40353 cdleme27cl 40352 cdleme28c 40358 cdleme3 40223 cdleme30a 40364 cdleme31fv 40376 cdleme31fv1 40377 cdleme31fv1s 40378 cdleme31fv2 40379 cdleme31id 40380 cdleme31sc 40370 cdleme31sdnN 40373 cdleme31sn 40366 cdleme31sn1 40367 cdleme31sn1c 40374 cdleme31sn2 40375 cdleme31so 40365 cdleme35a 40434 cdleme35b 40436 cdleme35c 40437 cdleme35d 40438 cdleme35e 40439 cdleme35f 40440 cdleme35fnpq 40435 cdleme35g 40441 cdleme35h 40442 cdleme35h2 40443 cdleme35sn2aw 40444 cdleme35sn3a 40445 cdleme36a 40446 cdleme36m 40447 cdleme37m 40448 cdleme38m 40449 cdleme38n 40450 cdleme39a 40451 cdleme39n 40452 cdleme3b 40215 cdleme3c 40216 cdleme3d 40217 cdleme3e 40218 cdleme3fN 40219 cdleme3fa 40222 cdleme3g 40220 cdleme3h 40221 cdleme4 40224 cdleme40m 40453 cdleme40n 40454 cdleme40v 40455 cdleme40w 40456 cdleme41fva11 40463 cdleme41sn3aw 40460 cdleme41sn4aw 40461 cdleme41snaw 40462 cdleme42a 40457 cdleme42b 40464 cdleme42c 40458 cdleme42d 40459 cdleme42e 40465 cdleme42f 40466 cdleme42g 40467 cdleme42h 40468 cdleme42i 40469 cdleme42k 40470 cdleme42ke 40471 cdleme42keg 40472 cdleme42mN 40473 cdleme42mgN 40474 cdleme43aN 40475 cdleme43bN 40476 cdleme43cN 40477 cdleme43dN 40478 cdleme5 40226 cdleme50ex 40545 cdleme50ltrn 40543 cdleme51finvN 40542 cdleme51finvfvN 40541 cdleme51finvtrN 40544 cdleme6 40227 cdleme7 40235 cdleme7a 40229 cdleme7aa 40228 cdleme7b 40230 cdleme7c 40231 cdleme7d 40232 cdleme7e 40233 cdleme7ga 40234 cdleme8 40236 cdleme8tN 40241 cdleme9 40239 cdleme9a 40237 cdleme9b 40238 cdleme9tN 40243 cdleme9taN 40242 cdlemeda 40284 cdlemedb 40283 cdlemednpq 40285 cdlemednuN 40286 cdlemefr27cl 40389 cdlemefr32fva1 40396 cdlemefr32fvaN 40395 cdlemefrs32fva 40386 cdlemefrs32fva1 40387 cdlemefs27cl 40399 cdlemefs32fva1 40409 cdlemefs32fvaN 40408 cdlemesner 40282 cdlemeulpq 40206 |
| [Crawley] p. 114 | Lemma E | 4atex 40062 4atexlem7 40061 cdleme0nex 40276 cdleme17a 40272 cdleme17c 40274 cdleme17d 40484 cdleme17d1 40275 cdleme17d2 40481 cdleme18a 40277 cdleme18b 40278 cdleme18c 40279 cdleme18d 40281 cdleme4a 40225 |
| [Crawley] p. 115 | Lemma E | cdleme21a 40311 cdleme21at 40314 cdleme21b 40312 cdleme21c 40313 cdleme21ct 40315 cdleme21f 40318 cdleme21g 40319 cdleme21h 40320 cdleme21i 40321 cdleme22gb 40280 |
| [Crawley] p. 116 | Lemma F | cdlemf 40549 cdlemf1 40547 cdlemf2 40548 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 40553 cdlemg16 40643 cdlemg28 40690 cdlemg28a 40679 cdlemg28b 40689 cdlemg3a 40583 cdlemg42 40715 cdlemg43 40716 cdlemg44 40719 cdlemg44a 40717 cdlemg46 40721 cdlemg47 40722 cdlemg9 40620 ltrnco 40705 ltrncom 40724 tgrpabl 40737 trlco 40713 |
| [Crawley] p. 116 | Definition of G | df-tgrp 40729 |
| [Crawley] p. 117 | Lemma G | cdlemg17 40663 cdlemg17b 40648 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 40742 df-edring 40743 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 40746 |
| [Crawley] p. 118 | Remark | tendopltp 40766 |
| [Crawley] p. 118 | Lemma H | cdlemh 40803 cdlemh1 40801 cdlemh2 40802 |
| [Crawley] p. 118 | Lemma I | cdlemi 40806 cdlemi1 40804 cdlemi2 40805 |
| [Crawley] p. 118 | Lemma J | cdlemj1 40807 cdlemj2 40808 cdlemj3 40809 tendocan 40810 |
| [Crawley] p. 118 | Lemma K | cdlemk 40960 cdlemk1 40817 cdlemk10 40829 cdlemk11 40835 cdlemk11t 40932 cdlemk11ta 40915 cdlemk11tb 40917 cdlemk11tc 40931 cdlemk11u-2N 40875 cdlemk11u 40857 cdlemk12 40836 cdlemk12u-2N 40876 cdlemk12u 40858 cdlemk13-2N 40862 cdlemk13 40838 cdlemk14-2N 40864 cdlemk14 40840 cdlemk15-2N 40865 cdlemk15 40841 cdlemk16-2N 40866 cdlemk16 40843 cdlemk16a 40842 cdlemk17-2N 40867 cdlemk17 40844 cdlemk18-2N 40872 cdlemk18-3N 40886 cdlemk18 40854 cdlemk19-2N 40873 cdlemk19 40855 cdlemk19u 40956 cdlemk1u 40845 cdlemk2 40818 cdlemk20-2N 40878 cdlemk20 40860 cdlemk21-2N 40877 cdlemk21N 40859 cdlemk22-3 40887 cdlemk22 40879 cdlemk23-3 40888 cdlemk24-3 40889 cdlemk25-3 40890 cdlemk26-3 40892 cdlemk26b-3 40891 cdlemk27-3 40893 cdlemk28-3 40894 cdlemk29-3 40897 cdlemk3 40819 cdlemk30 40880 cdlemk31 40882 cdlemk32 40883 cdlemk33N 40895 cdlemk34 40896 cdlemk35 40898 cdlemk36 40899 cdlemk37 40900 cdlemk38 40901 cdlemk39 40902 cdlemk39u 40954 cdlemk4 40820 cdlemk41 40906 cdlemk42 40927 cdlemk42yN 40930 cdlemk43N 40949 cdlemk45 40933 cdlemk46 40934 cdlemk47 40935 cdlemk48 40936 cdlemk49 40937 cdlemk5 40822 cdlemk50 40938 cdlemk51 40939 cdlemk52 40940 cdlemk53 40943 cdlemk54 40944 cdlemk55 40947 cdlemk55u 40952 cdlemk56 40957 cdlemk5a 40821 cdlemk5auN 40846 cdlemk5u 40847 cdlemk6 40823 cdlemk6u 40848 cdlemk7 40834 cdlemk7u-2N 40874 cdlemk7u 40856 cdlemk8 40824 cdlemk9 40825 cdlemk9bN 40826 cdlemki 40827 cdlemkid 40922 cdlemkj-2N 40868 cdlemkj 40849 cdlemksat 40832 cdlemksel 40831 cdlemksv 40830 cdlemksv2 40833 cdlemkuat 40852 cdlemkuel-2N 40870 cdlemkuel-3 40884 cdlemkuel 40851 cdlemkuv-2N 40869 cdlemkuv2-2 40871 cdlemkuv2-3N 40885 cdlemkuv2 40853 cdlemkuvN 40850 cdlemkvcl 40828 cdlemky 40912 cdlemkyyN 40948 tendoex 40961 |
| [Crawley] p. 120 | Remark | dva1dim 40971 |
| [Crawley] p. 120 | Lemma L | cdleml1N 40962 cdleml2N 40963 cdleml3N 40964 cdleml4N 40965 cdleml5N 40966 cdleml6 40967 cdleml7 40968 cdleml8 40969 cdleml9 40970 dia1dim 41047 |
| [Crawley] p. 120 | Lemma M | dia11N 41034 diaf11N 41035 dialss 41032 diaord 41033 dibf11N 41147 djajN 41123 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 41018 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 41104 dia2dimlem1 41050 dia2dimlem2 41051 dia2dimlem3 41052 dia2dimlem4 41053 dia2dimlem5 41054 diaf1oN 41116 diarnN 41115 dvheveccl 41098 dvhopN 41102 |
| [Crawley] p. 121 | Lemma N | cdlemn 41198 cdlemn10 41192 cdlemn11 41197 cdlemn11a 41193 cdlemn11b 41194 cdlemn11c 41195 cdlemn11pre 41196 cdlemn2 41181 cdlemn2a 41182 cdlemn3 41183 cdlemn4 41184 cdlemn4a 41185 cdlemn5 41187 cdlemn5pre 41186 cdlemn6 41188 cdlemn7 41189 cdlemn8 41190 cdlemn9 41191 diclspsn 41180 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 41159 |
| [Crawley] p. 122 | Lemma N | dih11 41251 dihf11 41253 dihjust 41203 dihjustlem 41202 dihord 41250 dihord1 41204 dihord10 41209 dihord11b 41208 dihord11c 41210 dihord2 41213 dihord2a 41205 dihord2b 41206 dihord2cN 41207 dihord2pre 41211 dihord2pre2 41212 dihordlem6 41199 dihordlem7 41200 dihordlem7b 41201 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 41216 dihfval 41217 dihval 41218 |
| [Diestel] p. 3 | Definition | df-gric 47836 df-grim 47833 isuspgrim 47851 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29346 df-nbgr 29267 |
| [Diestel] p. 3 | Definition by | df-grisom 47832 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 47816 df-subgr 29202 uhgrspan1 29237 uhgrspansubgr 29225 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 29489 vtxdgoddnumeven 29488 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 28993 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 33862 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 33874 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 33866 zarcls1 33867 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 33877 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 33880 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 33883 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3925 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9618 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8805 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9626 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9951 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10526 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5268 |
| [Enderton] p. 19 | Definition | df-tp 4602 |
| [Enderton] p. 26 | Exercise 5 | unissb 4911 |
| [Enderton] p. 26 | Exercise 10 | pwel 5344 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5539 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5051 iinin2 5050 iinun2 5045 iunin1 5044 iunin1f 32493 iunin2 5043 uniin1 32487 uniin2 32488 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5049 iundif2 5046 |
| [Enderton] p. 32 | Exercise 20 | unineq 4259 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5070 |
| [Enderton] p. 33 | Exercise 25 | iununi 5071 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5078 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7754 iunpwss 5079 |
| [Enderton] p. 36 | Definition | opthwiener 5482 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5418 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4917 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5438 rnex 7895 rnexg 7887 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5886 rnuni 6129 |
| [Enderton] p. 42 | Definition of a function | dffun7 6551 dffun8 6552 |
| [Enderton] p. 43 | Definition of function value | funfv2 6956 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6593 |
| [Enderton] p. 44 | Definition (d) | dfima2 6041 dfima3 6042 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6965 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10444 ac7g 10445 df-ac 10087 dfac2 10103 dfac2a 10101 dfac2b 10102 dfac3 10092 dfac7 10104 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7227 |
| [Enderton] p. 52 | Definition | df-map 8805 |
| [Enderton] p. 53 | Exercise 21 | coass 6246 |
| [Enderton] p. 53 | Exercise 27 | dmco 6235 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6600 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6081 |
| [Enderton] p. 54 | Remark | ixpf 8897 ixpssmap 8909 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8875 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10454 ac9s 10464 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 38595 erref 8702 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 38598 erthi 8735 |
| [Enderton] p. 57 | Definition | df-ec 8684 |
| [Enderton] p. 58 | Definition | df-qs 8688 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8684 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5882 |
| [Enderton] p. 68 | Definition of successor | df-suc 6346 |
| [Enderton] p. 71 | Definition | df-tr 5223 dftr4 5229 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6421 unisucg 6420 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6421 unisucg 6420 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5238 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5240 trintALT 44842 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8579 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8581 onasuc 8503 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7397 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8580 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8582 onmsuc 8504 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8597 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8584 nnacom 8592 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8598 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8599 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8601 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8585 nnmsucr 8600 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8613 |
| [Enderton] p. 129 | Definition | df-en 8923 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7348 |
| [Enderton] p. 133 | Exercise 1 | xpomen 9986 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16188 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9184 |
| [Enderton] p. 135 | Corollary 6C | php3 9186 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9183 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9221 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9223 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9145 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9150 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9118 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10151 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10152 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10147 dju1en 10143 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9312 unifi 9313 unifi2 9314 |
| [Enderton] p. 144 | Corollary 6K | undif2 4448 unfi 9148 unfi2 9277 |
| [Enderton] p. 145 | Figure 38 | ffoss 7933 |
| [Enderton] p. 145 | Definition | df-dom 8924 |
| [Enderton] p. 146 | Example 1 | domen 8939 domeng 8940 |
| [Enderton] p. 146 | Example 3 | nndomo 9198 nnsdom 9625 nnsdomg 9264 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10155 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9119 xpdom1 9048 xpdom1g 9046 xpdom2g 9045 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9125 |
| [Enderton] p. 151 | Theorem 6M | zorn 10478 zorng 10475 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10463 dfac5 10100 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10546 |
| [Enderton] p. 164 | Example | infdif 10179 |
| [Enderton] p. 168 | Definition | df-po 5554 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6456 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6387 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6455 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6395 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7822 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7764 |
| [Enderton] p. 194 | Remark | onprc 7761 |
| [Enderton] p. 194 | Exercise 16 | suc11 6449 |
| [Enderton] p. 197 | Definition | df-card 9910 |
| [Enderton] p. 197 | Theorem 7P | carden 10522 |
| [Enderton] p. 200 | Exercise 25 | tfis 7839 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9747 |
| [Enderton] p. 202 | Definition | df-r1 9735 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9757 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9838 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9577 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9828 rankprb 9822 rankpw 9814 rankpwi 9794 rankuniss 9837 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9589 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9590 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10081 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 10047 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10061 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8319 |
| [Enderton] p. 222 | Definition of kard | karden 9866 kardex 9865 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8572 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8574 |
| [Enderton] p. 240 | Exercise 25 | oarec 8537 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10221 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17609 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17555 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18518 mrieqv2d 17606 mrieqvd 17605 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17610 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17615 mreexexlem2d 17612 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18524 mreexfidimd 17617 |
| [Frege1879] p. 11 | Statement | df3or2 43729 |
| [Frege1879] p. 12 | Statement | df3an2 43730 dfxor4 43727 dfxor5 43728 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 43751 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 43752 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 43756 |
| [Frege1879] p. 31 | Proposition 4 | frege4 43760 |
| [Frege1879] p. 32 | Proposition 5 | frege5 43761 |
| [Frege1879] p. 33 | Proposition 6 | frege6 43767 |
| [Frege1879] p. 34 | Proposition 7 | frege7 43769 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 43770 axfrege8 43768 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 90 wl-luk-pm2.04 37430 |
| [Frege1879] p. 35 | Proposition 9 | frege9 43773 |
| [Frege1879] p. 36 | Proposition 10 | frege10 43781 |
| [Frege1879] p. 36 | Proposition 11 | frege11 43775 |
| [Frege1879] p. 37 | Proposition 12 | frege12 43774 |
| [Frege1879] p. 37 | Proposition 13 | frege13 43783 |
| [Frege1879] p. 37 | Proposition 14 | frege14 43784 |
| [Frege1879] p. 38 | Proposition 15 | frege15 43787 |
| [Frege1879] p. 38 | Proposition 16 | frege16 43777 |
| [Frege1879] p. 39 | Proposition 17 | frege17 43782 |
| [Frege1879] p. 39 | Proposition 18 | frege18 43779 |
| [Frege1879] p. 39 | Proposition 19 | frege19 43785 |
| [Frege1879] p. 40 | Proposition 20 | frege20 43789 |
| [Frege1879] p. 40 | Proposition 21 | frege21 43788 |
| [Frege1879] p. 41 | Proposition 22 | frege22 43780 |
| [Frege1879] p. 42 | Proposition 23 | frege23 43786 |
| [Frege1879] p. 42 | Proposition 24 | frege24 43776 |
| [Frege1879] p. 42 | Proposition 25 | frege25 43778 rp-frege25 43766 |
| [Frege1879] p. 42 | Proposition 26 | frege26 43771 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 43791 |
| [Frege1879] p. 43 | Proposition 27 | frege27 43772 |
| [Frege1879] p. 43 | Proposition 28 | con3 153 |
| [Frege1879] p. 43 | Proposition 29 | frege29 43792 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 43795 axfrege31 43794 |
| [Frege1879] p. 44 | Proposition 30 | frege30 43793 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 130 |
| [Frege1879] p. 44 | Proposition 32 | frege32 43796 |
| [Frege1879] p. 44 | Proposition 33 | frege33 43797 |
| [Frege1879] p. 45 | Proposition 34 | frege34 43798 |
| [Frege1879] p. 45 | Proposition 35 | frege35 43799 |
| [Frege1879] p. 45 | Proposition 36 | frege36 43800 |
| [Frege1879] p. 46 | Proposition 37 | frege37 43801 |
| [Frege1879] p. 46 | Proposition 38 | frege38 43802 |
| [Frege1879] p. 46 | Proposition 39 | frege39 43803 |
| [Frege1879] p. 46 | Proposition 40 | frege40 43804 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 43806 axfrege41 43805 |
| [Frege1879] p. 47 | Proposition 41 | notnot 142 |
| [Frege1879] p. 47 | Proposition 42 | frege42 43807 |
| [Frege1879] p. 47 | Proposition 43 | frege43 43808 |
| [Frege1879] p. 47 | Proposition 44 | frege44 43809 |
| [Frege1879] p. 47 | Proposition 45 | frege45 43810 |
| [Frege1879] p. 48 | Proposition 46 | frege46 43811 |
| [Frege1879] p. 48 | Proposition 47 | frege47 43812 |
| [Frege1879] p. 49 | Proposition 48 | frege48 43813 |
| [Frege1879] p. 49 | Proposition 49 | frege49 43814 |
| [Frege1879] p. 49 | Proposition 50 | frege50 43815 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 43818 ax-frege52c 43849 frege52aid 43819 frege52b 43850 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 43823 ax-frege54c 43853 frege54b 43854 |
| [Frege1879] p. 50 | Proposition 51 | frege51 43816 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3763 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 43821 frege53aid 43820 frege53b 43851 frege53c 43875 |
| [Frege1879] p. 50 | Proposition 54 | biid 261 eqid 2730 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 43829 frege55aid 43826 frege55b 43858 frege55c 43879 frege55cor1a 43830 frege55lem2a 43828 frege55lem2b 43857 frege55lem2c 43878 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 43832 frege56aid 43831 frege56b 43859 frege56c 43880 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 43836 ax-frege58b 43862 frege58bid 43863 frege58c 43882 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 43834 frege57aid 43833 frege57b 43860 frege57c 43881 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3774 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 43838 frege59b 43865 frege59c 43883 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 43839 frege60b 43866 frege60c 43884 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 43840 frege61b 43867 frege61c 43885 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 43841 frege62b 43868 frege62c 43886 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 43842 frege63b 43869 frege63c 43887 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 43843 frege64b 43870 frege64c 43888 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 43844 frege65b 43871 frege65c 43889 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 43845 frege66b 43872 frege66c 43890 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 43846 frege67b 43873 frege67c 43891 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 43847 frege68b 43874 frege68c 43892 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 43893 |
| [Frege1879] p. 58 | Proposition 70 | frege70 43894 |
| [Frege1879] p. 59 | Proposition 71 | frege71 43895 |
| [Frege1879] p. 59 | Proposition 72 | frege72 43896 |
| [Frege1879] p. 59 | Proposition 73 | frege73 43897 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 43900 |
| [Frege1879] p. 60 | Proposition 74 | frege74 43898 |
| [Frege1879] p. 60 | Proposition 75 | frege75 43899 |
| [Frege1879] p. 62 | Proposition 77 | frege77 43901 frege77d 43707 |
| [Frege1879] p. 63 | Proposition 78 | frege78 43902 |
| [Frege1879] p. 63 | Proposition 79 | frege79 43903 |
| [Frege1879] p. 63 | Proposition 80 | frege80 43904 |
| [Frege1879] p. 63 | Proposition 81 | frege81 43905 frege81d 43708 |
| [Frege1879] p. 64 | Proposition 82 | frege82 43906 |
| [Frege1879] p. 65 | Proposition 83 | frege83 43907 frege83d 43709 |
| [Frege1879] p. 65 | Proposition 84 | frege84 43908 |
| [Frege1879] p. 66 | Proposition 85 | frege85 43909 |
| [Frege1879] p. 66 | Proposition 86 | frege86 43910 |
| [Frege1879] p. 66 | Proposition 87 | frege87 43911 frege87d 43711 |
| [Frege1879] p. 67 | Proposition 88 | frege88 43912 |
| [Frege1879] p. 68 | Proposition 89 | frege89 43913 |
| [Frege1879] p. 68 | Proposition 90 | frege90 43914 |
| [Frege1879] p. 68 | Proposition 91 | frege91 43915 frege91d 43712 |
| [Frege1879] p. 69 | Proposition 92 | frege92 43916 |
| [Frege1879] p. 70 | Proposition 93 | frege93 43917 |
| [Frege1879] p. 70 | Proposition 94 | frege94 43918 |
| [Frege1879] p. 70 | Proposition 95 | frege95 43919 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 43923 |
| [Frege1879] p. 71 | Proposition 96 | frege96 43920 frege96d 43710 |
| [Frege1879] p. 71 | Proposition 97 | frege97 43921 frege97d 43713 |
| [Frege1879] p. 71 | Proposition 98 | frege98 43922 frege98d 43714 |
| [Frege1879] p. 72 | Proposition 100 | frege100 43924 |
| [Frege1879] p. 72 | Proposition 101 | frege101 43925 |
| [Frege1879] p. 72 | Proposition 102 | frege102 43926 frege102d 43715 |
| [Frege1879] p. 73 | Proposition 103 | frege103 43927 |
| [Frege1879] p. 73 | Proposition 104 | frege104 43928 |
| [Frege1879] p. 73 | Proposition 105 | frege105 43929 |
| [Frege1879] p. 73 | Proposition 106 | frege106 43930 frege106d 43716 |
| [Frege1879] p. 74 | Proposition 107 | frege107 43931 |
| [Frege1879] p. 74 | Proposition 108 | frege108 43932 frege108d 43717 |
| [Frege1879] p. 74 | Proposition 109 | frege109 43933 frege109d 43718 |
| [Frege1879] p. 75 | Proposition 110 | frege110 43934 |
| [Frege1879] p. 75 | Proposition 111 | frege111 43935 frege111d 43720 |
| [Frege1879] p. 76 | Proposition 112 | frege112 43936 |
| [Frege1879] p. 76 | Proposition 113 | frege113 43937 |
| [Frege1879] p. 76 | Proposition 114 | frege114 43938 frege114d 43719 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 43939 |
| [Frege1879] p. 77 | Proposition 116 | frege116 43940 |
| [Frege1879] p. 78 | Proposition 117 | frege117 43941 |
| [Frege1879] p. 78 | Proposition 118 | frege118 43942 |
| [Frege1879] p. 78 | Proposition 119 | frege119 43943 |
| [Frege1879] p. 78 | Proposition 120 | frege120 43944 |
| [Frege1879] p. 79 | Proposition 121 | frege121 43945 |
| [Frege1879] p. 79 | Proposition 122 | frege122 43946 frege122d 43721 |
| [Frege1879] p. 79 | Proposition 123 | frege123 43947 |
| [Frege1879] p. 80 | Proposition 124 | frege124 43948 frege124d 43722 |
| [Frege1879] p. 81 | Proposition 125 | frege125 43949 |
| [Frege1879] p. 81 | Proposition 126 | frege126 43950 frege126d 43723 |
| [Frege1879] p. 82 | Proposition 127 | frege127 43951 |
| [Frege1879] p. 83 | Proposition 128 | frege128 43952 |
| [Frege1879] p. 83 | Proposition 129 | frege129 43953 frege129d 43724 |
| [Frege1879] p. 84 | Proposition 130 | frege130 43954 |
| [Frege1879] p. 85 | Proposition 131 | frege131 43955 frege131d 43725 |
| [Frege1879] p. 86 | Proposition 132 | frege132 43956 |
| [Frege1879] p. 86 | Proposition 133 | frege133 43957 frege133d 43726 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 46284 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 46607 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 46307 |
| [Fremlin1] p. 14 | Definition 112A | ismea 46422 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 46442 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 46433 meadjunre 46447 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 46434 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 46435 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 46431 meaiunle 46440 meaiunlelem 46439 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 46452 meaiuninc2 46453 meaiuninc3 46456 meaiuninc3v 46455 meaiunincf 46454 meaiuninclem 46451 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 46458 meaiininc2 46459 meaiininclem 46457 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 46477 caragendifcl 46485 caratheodory 46499 omelesplit 46489 |
| [Fremlin1] p. 19 | Definition 113A | isome 46465 isomennd 46502 isomenndlem 46501 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 46487 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 46506 voncmpl 46592 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 46469 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 46494 carageniuncllem1 46492 carageniuncllem2 46493 caragenuncl 46484 caragenuncllem 46483 caragenunicl 46495 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 46503 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 46497 caratheodorylem2 46498 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 46506 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 46565 hoidmv1lelem1 46562 hoidmv1lelem2 46563 hoidmv1lelem3 46564 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 46609 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 46565 hoidmvle 46571 hoidmvlelem1 46566 hoidmvlelem2 46567 hoidmvlelem3 46568 hoidmvlelem4 46569 hoidmvlelem5 46570 hsphoidmvle2 46556 hsphoif 46547 hsphoival 46550 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 46519 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 46527 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 46554 hoidmvn0val 46555 hoidmvval 46548 hoidmvval0 46558 hoidmvval0b 46561 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 46559 hsphoidmvle 46557 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 46508 df-voln 46510 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 46575 ovn0 46537 ovn0lem 46536 ovnf 46534 ovnome 46544 ovnssle 46532 ovnsslelem 46531 ovnsupge0 46528 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 46574 ovnhoilem1 46572 ovnhoilem2 46573 vonhoi 46638 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 46591 hoidifhspf 46589 hoidifhspval 46579 hoidifhspval2 46586 hoidifhspval3 46590 hspmbl 46600 hspmbllem1 46597 hspmbllem2 46598 hspmbllem3 46599 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 46592 vonmea 46545 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 46543 ovnsubadd2 46617 ovnsubadd2lem 46616 ovnsubaddlem1 46541 ovnsubaddlem2 46542 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 46602 hoimbl2 46636 hoimbllem 46601 hspdifhsp 46587 opnvonmbl 46605 opnvonmbllem2 46604 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 46607 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 46650 iccvonmbllem 46649 ioovonmbl 46648 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 46656 vonicclem2 46655 vonioo 46653 vonioolem2 46652 vonn0icc 46659 vonn0icc2 46663 vonn0ioo 46658 vonn0ioo2 46661 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 46660 snvonmbl 46657 vonct 46664 vonsn 46662 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 46330 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 46329 subsaliuncllem 46328 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 46696 salpreimalegt 46680 salpreimaltle 46697 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 46699 issmff 46705 issmflem 46698 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 46716 issmflelem 46715 smfpreimale 46725 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 46727 issmfgtlem 46726 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 46667 issmf 46699 issmff 46705 issmfge 46741 issmfgelem 46740 issmfgt 46727 issmfgtlem 46726 issmfle 46716 issmflelem 46715 issmflem 46698 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 46678 salpreimagtlt 46701 salpreimalelt 46700 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 46741 issmfgelem 46740 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 46724 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 46722 cnfsmf 46711 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 46738 decsmflem 46737 incsmf 46713 incsmflem 46712 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 46672 pimconstlt1 46673 smfconst 46720 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 46736 smfaddlem1 46734 smfaddlem2 46735 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 46767 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 46766 smfmullem1 46762 smfmullem2 46763 smfmullem3 46764 smfmullem4 46765 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 46768 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 46771 smfpimbor1lem2 46770 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 46773 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 46761 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 46760 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 46769 smfresal 46759 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 46748 smflim2 46777 smflimlem1 46742 smflimlem2 46743 smflimlem3 46744 smflimlem4 46745 smflimlem5 46746 smflimlem6 46747 smflimmpt 46781 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 46785 smfsuplem1 46782 smfsuplem2 46783 smfsuplem3 46784 smfsupmpt 46786 smfsupxr 46787 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 46789 smfinflem 46788 smfinfmpt 46790 |
| [Fremlin1] p. 39 | Remark 121G | smflim 46748 smflim2 46777 smflimmpt 46781 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 46779 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 46809 smfdivdmmbl2 46812 smfinfdmmbl 46820 smfinfdmmbllem 46819 smfsupdmmbl 46816 smfsupdmmbllem 46815 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 46799 smflimsuplem2 46792 smflimsuplem6 46796 smflimsuplem7 46797 smflimsuplem8 46798 smflimsupmpt 46800 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 46802 smfliminflem 46801 smfliminfmpt 46803 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 46667 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 46813 fsupdm2 46814 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 46804 adddmmbl2 46805 finfdm 46817 finfdm2 46818 fsupdm 46813 fsupdm2 46814 muldmmbl 46806 muldmmbl2 46807 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 46817 finfdm2 46818 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25444 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25487 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25497 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 37689 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 37692 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9609 inf1 9593 inf2 9594 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10882 enqer 10892 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10887 df-nq 10883 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10879 df-plq 10885 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7633 df-mpq 10880 df-mq 10886 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10888 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10946 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10947 ltbtwnnq 10949 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10942 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10943 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10950 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10952 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 10964 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 10966 |
| [Gleason] p. 122 | Definition | df-1p 10953 |
| [Gleason] p. 122 | Remark (1) | prub 10965 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 11004 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10956 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 11003 psslinpr 11002 supexpr 11025 suplem1pr 11023 suplem2pr 11024 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 10989 addclprlem1 10987 addclprlem2 10988 df-plp 10954 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 10993 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 10992 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 11005 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 11014 ltexprlem1 11007 ltexprlem2 11008 ltexprlem3 11009 ltexprlem4 11010 ltexprlem5 11011 ltexprlem6 11012 ltexprlem7 11013 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 11016 ltaprlem 11015 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 11017 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 11018 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10955 mulclpr 10991 mulclprlem 10990 reclem2pr 11019 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 11000 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 10995 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 10994 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 10999 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 11022 reclem3pr 11020 reclem4pr 11021 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 11026 enrer 11034 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 11031 df-1r 11032 df-nr 11027 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 11029 df-plr 11028 negexsr 11073 recexsr 11078 recexsrlem 11074 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 11030 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12192 creur 12191 cru 12189 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11159 axcnre 11135 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15091 crimd 15208 crimi 15169 crre 15090 crred 15207 crrei 15168 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15093 remimd 15174 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15260 absval2d 15421 absval2i 15373 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15117 cjaddd 15196 cjaddi 15164 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15118 cjmuld 15197 cjmuli 15165 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15116 cjcjd 15175 cjcji 15147 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15115 cjreb 15099 cjrebd 15178 cjrebi 15150 cjred 15202 rere 15098 rereb 15096 rerebd 15177 rerebi 15149 rered 15200 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15124 addcjd 15188 addcji 15159 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15214 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15255 abscjd 15426 abscji 15377 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15265 abs00d 15422 abs00i 15374 absne0d 15423 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15297 releabsd 15427 releabsi 15378 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15270 absmuld 15430 absmuli 15380 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15258 sqabsaddi 15381 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15306 abstrid 15432 abstrii 15384 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14037 exp0 14040 expp1 14043 expp1d 14122 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26595 cxpaddd 26633 expadd 14079 expaddd 14123 expaddz 14081 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26604 cxpmuld 26653 expmul 14082 expmuld 14124 expmulz 14083 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26601 mulcxpd 26644 mulexp 14076 mulexpd 14136 mulexpz 14077 |
| [Gleason] p. 140 | Exercise 1 | znnen 16187 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13483 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15605 rlimadd 15616 rlimdiv 15619 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15607 rlimsub 15617 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15606 rlimmul 15618 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15610 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15556 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15577 climcj 15578 climim 15580 climre 15579 rlimabs 15582 rlimcj 15583 rlimim 15585 rlimre 15584 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11231 df-xr 11230 ltxr 13088 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15444 limsupval 15447 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15643 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15652 caucvgb 15653 caucvgbf 45458 caucvgr 15649 climcau 15644 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15789 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15856 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15311 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13802 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21264 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24237 xmet0 24236 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24253 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24244 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24246 mstri 24363 xmettri 24245 xmstri 24362 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24276 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23541 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25217 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24434 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24760 addcn2 15567 mulcn 24762 mulcn2 15569 subcn 24761 subcn2 15568 |
| [Gleason] p. 295 | Remark | bcval3 14281 bcval4 14282 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14296 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14279 df-bc 14278 |
| [Gleason] p. 296 | Remark | bcn0 14285 bcnn 14287 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15803 |
| [Gleason] p. 308 | Equation 2 | ef0 16064 |
| [Gleason] p. 308 | Equation 3 | efcj 16065 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16071 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16076 |
| [Gleason] p. 310 | Equation 14 | sinadd 16139 |
| [Gleason] p. 310 | Equation 15 | cosadd 16140 |
| [Gleason] p. 311 | Equation 17 | sincossq 16151 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16156 sinbnd 16155 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14191 sqeqori 14189 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16045 |
| [Godowski] p. 730 | Equation SF | goeqi 32209 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 31604 |
| [Golan] p. 1 | Remark | srgisid 20124 |
| [Golan] p. 1 | Definition | df-srg 20102 |
| [Golan] p. 149 | Definition | df-slmd 33162 |
| [Gonshor] p. 7 | Definition | df-scut 27702 |
| [Gonshor] p. 9 | Theorem 2.5 | slerec 27738 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 27835 cofcut1d 27836 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 27837 cofcut2d 27838 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 27839 cofcutr1d 27840 cofcutr2d 27841 |
| [Gonshor] p. 13 | Definition | df-adds 27874 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 27890 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 27916 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28040 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28060 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28340 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28342 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28341 |
| [Gonshor] p. 95 | Theorem 6.1 | addsbday 27931 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36144 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17553 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17555 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 48105 df-cllaw 48103 df-comlaw 48104 |
| [Hall] p. 2 | Section 1.2 | df-clintop 48117 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 48138 |
| [Halmos] p. 28 | Partition ` ` | df-parts 38750 dfmembpart2 38755 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32001 riesz2 32002 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 31877 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32109 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32121 elpjidm 32120 pjnmopi 32084 |
| [Halmos] p. 44 | Remark | pjinormi 31623 pjinormii 31612 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32125 pjrn 31643 pjrni 31638 pjvec 31632 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 31663 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32090 hmopidmpji 32088 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32127 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32116 pjocvec 31633 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32105 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32108 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32111 pjssdif2i 32110 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 31791 |
| [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 1795 |
| [Hatcher] p. 25 | Definition | df-phtpc 24897 df-phtpy 24876 |
| [Hatcher] p. 26 | Definition | df-pco 24911 df-pi1 24914 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 24900 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 24956 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22383 df-dmatalt 48316 |
| [Helfgott] p. 2 | Theorem | tgoldbach 47773 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 47758 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 47770 bgoldbtbnd 47765 bgoldbtbnd 47765 tgblthelfgott 47771 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 34641 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 34642 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 34656 hgt750lemb 34655 hgt750leme 34657 hgt750lemf 34652 hgt750lemg 34653 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 47767 tgoldbachgt 34662 tgoldbachgtALTV 47768 tgoldbachgtd 34661 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 34643 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30429 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 18882 grpoideu 30445 mndideu 18678 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 18912 grpoinveu 30455 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 18943 grpo2inv 30467 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 18956 grpoinvop 30469 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 18978 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1768 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1769 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1771 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32356 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32369 cdj3i 32377 cdj3lem1 32370 cdjreui 32368 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32367 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 41947 |
| [Holland95] p. 14 | Line 15 | hgmapvs 41877 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 41899 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 41900 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 41897 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 41903 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 41822 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 41917 |
| [Holland95] p. 204 | Definition of involution | df-srng 20755 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 39489 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 41514 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 41467 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 39919 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 41363 poml4N 39939 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 41454 pexmidALTN 39964 pexmidN 39955 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 41519 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 39109 ldualset 39110 |
| [Holland95] p. 222 | Item 1 | df-lines 39487 df-pointsN 39488 |
| [Holland95] p. 222 | Item 2 | df-polarityN 39889 |
| [Holland95] p. 223 | Remark | ispsubcl2N 39933 omllaw4 39231 pol1N 39896 polcon3N 39903 |
| [Holland95] p. 223 | Definition | df-psubclN 39921 |
| [Holland95] p. 223 | Equation for polarity | polval2N 39892 |
| [Holmes] p. 40 | Definition | df-xrn 38356 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31020 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32118 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 31899 eigre 31771 eigrei 31770 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 31900 eigorth 31774 eigorthi 31773 |
| [Hughes] p. 137 | Remark (ii) | eigposi 31772 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30245 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30241 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30242 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30243 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30261 frgrregorufr0 30260 frgrregorufrg 30262 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30268 frrusgrord 30277 frrusgrord0 30276 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30024 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30251 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30254 frgrwopreg2 30255 frgrwopregasn 30252 frgrwopregbsn 30253 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30257 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30271 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30274 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30022 numclwlk1 30307 numclwlk1lem1 30305 numclwlk1lem2 30306 numclwwlk1 30297 numclwwlk8 30328 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30248 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 29708 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30283 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30309 numclwwlkovh0 30308 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30317 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 29914 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30321 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30324 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30327 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30339 natded 30339 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30339 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30339 natded 30339 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30339 |
| [Jech] p. 4 | Definition of class | cv 1539 cvjust 2724 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10550 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10548 alephmul 10549 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10547 infmap2 10188 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9785 |
| [Jech] p. 72 | Equation 9.3 | scott0 9857 scottex 9856 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9838 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9862 |
| [Jech] p. 78 | Note | opthprc 5710 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 42876 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 42964 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 42965 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 42888 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 42892 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 42893 rmyp1 42894 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 42895 rmym1 42896 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 42886 rmx1 42887 rmxluc 42897 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 42890 rmy1 42891 rmyluc 42898 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 42900 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 42901 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 42921 jm2.17b 42922 jm2.17c 42923 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 42954 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 42958 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 42949 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 42924 jm2.24nn 42920 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 42963 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 42969 rmygeid 42925 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 42981 |
| [Juillerat] p. 11 | Section *5 | etransc 46254 etransclem47 46252 etransclem48 46253 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 46249 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 46251 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 46237 |
| [Juillerat] p. 13 | Proof | etransclem35 46240 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 46243 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 46229 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 46246 |
| [Juillerat] p. 14 | Proof | etransclem23 46228 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1967 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2012 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2017 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2007 cbvaliw 2006 wl-cbvmotv 37498 wl-motae 37500 wl-moteq 37499 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 1986 spimw 1970 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2033 spw 2034 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31452 chabs1i 31454 chabs2 31453 chabs2i 31455 chjass 31469 chjassi 31422 latabs1 18440 latabs2 18441 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32274 ela 32275 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32219 cvrval2 39259 |
| [Kalmbach] p. 16 | Definition | df-ol 39163 df-oml 39164 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 31520 cmbri 31526 cmtvalN 39196 df-cm 31519 df-cmtN 39162 |
| [Kalmbach] p. 22 | Remark | omllaw5N 39232 pjoml5 31549 pjoml5i 31524 |
| [Kalmbach] p. 22 | Definition | pjoml2 31547 pjoml2i 31521 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 31550 cmcmi 31528 cmcmii 31533 cmtcomN 39234 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 39230 omlsi 31340 pjoml 31372 pjomli 31371 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 39229 |
| [Kalmbach] p. 23 | Remark | cmbr2i 31532 cmcm3 31551 cmcm3i 31530 cmcm3ii 31535 cmcm4i 31531 cmt3N 39236 cmt4N 39237 cmtbr2N 39238 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 31544 cmbr3i 31536 cmtbr3N 39239 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 31554 fh1i 31557 fh2 31555 fh2i 31558 omlfh1N 39243 |
| [Kalmbach] p. 65 | Remark | chjatom 32293 chslej 31434 chsleji 31394 shslej 31316 shsleji 31306 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31431 chocini 31390 chsupcl 31276 chsupval2 31346 h0elch 31191 helch 31179 hsupval2 31345 ocin 31232 ococss 31229 shococss 31230 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31248 |
| [Kalmbach] p. 66 | Remark | df-pjh 31331 pjssmi 32101 pjssmii 31617 |
| [Kalmbach] p. 67 | Lemma 3 | osum 31581 osumi 31578 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32136 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32336 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32246 |
| [Kalmbach] p. 140 | Remark | hatomic 32296 hatomici 32295 hatomistici 32298 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 39304 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32317 lsatexch 39028 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32291 cvlcvr1 39324 cvr1 39396 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32310 cvexchi 32305 cvrexch 39406 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32300 hlrelat 39388 hlrelat5N 39387 lrelat 38999 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21057 lsmsatcv 38995 spansncv 31589 spansncvi 31588 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 39014 spansncv2 32229 |
| [Kalmbach] p. 266 | Definition | df-st 32147 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 31785 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10617 fpwwe2 10614 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10618 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10625 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10620 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10622 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10635 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10639 gchxpidm 10640 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10651 gchhar 10650 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10186 unxpwdom 9560 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10641 |
| [Kreyszig] p. 3 | Property M1 | metcl 24226 xmetcl 24225 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24233 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24466 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11915 muleqadd 11838 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24332 |
| [Kreyszig] p. 19 | Remark | mopntopon 24333 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24392 mopnm 24338 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24390 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24395 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24436 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23151 lmmbr 25165 lmmbr2 25166 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23273 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25220 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25183 iscmet2 25201 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25223 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23354 metelcls 25212 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25213 metcld2 25214 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25005 lmodvneg1 20817 nvinv 30575 vcm 30512 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25001 lmod0vs 20807 slmd0vs 33185 vc0 30510 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20808 slmdvs0 33186 vcz 30511 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 30627 ngpmet 24497 nrmmetd 24468 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 30622 imsdval2 30623 ncvspds 25068 ngpds 24498 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24483 nvnd 30624 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24512 nmge0 24511 nvge0 30609 nvz 30605 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24518 nvabs 30608 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 30737 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 30681 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 30743 blocni 30741 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 30742 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25111 ipeq0 21553 ipz 30655 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25123 pythi 30786 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 30790 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25145 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15829 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25343 minveco 30820 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 30686 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25236 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 30809 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32059 leopg 32058 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32077 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 30854 |
| [Kulpa] p. 547 | Theorem | poimir 37644 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 37643 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 37642 |
| [Kulpa] p. 548 | Theorem | broucube 37645 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 37637 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 37638 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2382 axnul 5268 |
| [Kunen] p. 11 | Axiom 3 | axnul 5268 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 7942 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8815 mapvalg 8813 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10493 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7926 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9735 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9777 r1elssi 9776 |
| [Kunen] p. 107 | Exercise 4 | rankop 9829 rankopb 9823 rankuni 9834 rankxplim 9850 rankxpsuc 9853 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 44916 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 44924 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 44923 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 44925 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 44930 rexabso 44931 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 44937 n0abso 44938 ssabso 44936 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 44939 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 44949 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 44944 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 44947 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 44948 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 44943 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 44955 wfaxpr 44960 wfaxreg 44962 wfaxrep 44956 wfaxsep 44957 wfaxun 44961 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 44946 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 44959 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 44955 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 44954 omelaxinf2 44951 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 44964 wfaxinf2 44963 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 44977 permaxext 44967 permaxinf2 44975 permaxnul 44970 permaxpow 44971 permaxpr 44972 permaxrep 44968 permaxsep 44969 permaxun 44973 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 44965 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 44976 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4976 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 33668 |
| [Lang] p. | Definition | df-rn 5657 |
| [Lang] p. 3 | Statement | lidrideqd 18602 mndbn0 18683 |
| [Lang] p. 3 | Definition | df-mnd 18668 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18620 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18774 |
| [Lang] p. 5 | Equation | gsumreidx 19853 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 48099 |
| [Lang] p. 6 | Example | nn0mnd 48096 |
| [Lang] p. 6 | Equation | gsumxp2 19916 |
| [Lang] p. 6 | Statement | cycsubm 19140 |
| [Lang] p. 6 | Definition | mulgnn0gsum 19018 |
| [Lang] p. 6 | Observation | mndlsmidm 19606 |
| [Lang] p. 7 | Definition | dfgrp2e 18901 |
| [Lang] p. 30 | Definition | df-tocyc 33072 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33117 |
| [Lang] p. 32 | Property (b) | cyc3conja 33122 cycpmconjv 33107 |
| [Lang] p. 53 | Definition | df-cat 17635 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18065 cat1lem 18064 |
| [Lang] p. 54 | Definition | df-iso 17717 |
| [Lang] p. 57 | Definition | df-inito 17952 df-termo 17953 |
| [Lang] p. 58 | Example | irinitoringc 21395 |
| [Lang] p. 58 | Statement | initoeu1 17979 termoeu1 17986 |
| [Lang] p. 62 | Definition | df-func 17826 |
| [Lang] p. 65 | Definition | df-nat 17914 |
| [Lang] p. 91 | Note | df-ringc 20561 |
| [Lang] p. 92 | Statement | mxidlprm 33449 |
| [Lang] p. 92 | Definition | isprmidlc 33426 |
| [Lang] p. 128 | Remark | dsmmlmod 21660 |
| [Lang] p. 129 | Proof | lincscm 48348 lincscmcl 48350 lincsum 48347 lincsumcl 48349 |
| [Lang] p. 129 | Statement | lincolss 48352 |
| [Lang] p. 129 | Observation | dsmmfi 21653 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 33631 qusdimsum 33632 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 33611 |
| [Lang] p. 147 | Definition | snlindsntor 48389 |
| [Lang] p. 504 | Statement | mat1 22340 matring 22336 |
| [Lang] p. 504 | Definition | df-mamu 22284 |
| [Lang] p. 505 | Statement | mamuass 22295 mamutpos 22351 matassa 22337 mattposvs 22348 tposmap 22350 |
| [Lang] p. 513 | Definition | mdet1 22494 mdetf 22488 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22584 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22480 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22504 |
| [Lang] p. 515 | Definition | df-minmar1 22528 smadiadetr 22568 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22503 mdetralt 22501 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22516 |
| [Lang] p. 518 | Definition | df-madu 22527 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22538 madurid 22537 matinv 22570 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 22783 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 33667 fedgmul 33635 |
| [Lang], p. 561 | Remark | chpmatply1 22725 |
| [Lang], p. 561 | Definition | df-chpmat 22720 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 44295 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 44290 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 44296 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5268 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2709 |
| [Levy] p. 59 | Definition | df-ttrcl 9679 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9722 |
| [Levy] p. 338 | Axiom | df-clel 2804 df-cleq 2722 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2804 df-cleq 2722 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2709 |
| [Levy] p. 358 | Axiom | df-clab 2709 |
| [Levy58] p. 2 | Definition I | isfin1-3 10357 |
| [Levy58] p. 2 | Definition II | df-fin2 10257 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10256 |
| [Levy58] p. 2 | Definition III | df-fin3 10259 |
| [Levy58] p. 3 | Definition V | df-fin5 10260 |
| [Levy58] p. 3 | Definition IV | df-fin4 10258 |
| [Levy58] p. 4 | Definition VI | df-fin6 10261 |
| [Levy58] p. 4 | Definition VII | df-fin7 10262 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10386 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27605 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27616 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27648 nosupbnd1 27633 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27650 nosupbnd2 27635 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27654 noetasuplem4 27655 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27651 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1768 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1769 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1771 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32344 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32348 mdsymi 32347 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32342 mdsymlem6 32344 mdsymlem7 32345 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32346 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32249 ssdmd2 32250 ssmd1 32247 ssmd2 32248 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32245 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32217 df-md 32216 mdbr 32230 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32267 mdslj1i 32255 mdslj2i 32256 mdslle1i 32253 mdslle2i 32254 mdslmd1i 32265 mdslmd2i 32266 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32257 mdsl2bi 32259 mdsl2i 32258 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32271 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32268 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32269 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32246 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32251 mdsl3 32252 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32270 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32365 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 39306 hlrelat1 39386 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 39024 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32272 cvmdi 32260 cvnbtwn4 32225 cvrnbtwn4 39264 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32273 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 39325 cvp 32311 cvrp 39402 lcvp 39025 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32335 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32334 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 39318 hlexch4N 39378 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32337 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 39429 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 39735 atpsubN 39739 df-pointsN 39488 pointpsubN 39737 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 39490 pmap11 39748 pmaple 39747 pmapsub 39754 pmapval 39743 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 39751 pmap1N 39753 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 39756 pmapglb2N 39757 pmapglb2xN 39758 pmapglbx 39755 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 39838 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 39463 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 39782 paddclN 39828 paddidm 39827 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 39464 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 39824 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 39463 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 39464 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19611 lsmmod2 19612 lssats 38997 shatomici 32294 shatomistici 32297 shmodi 31326 shmodsi 31325 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32236 mdsymlem7 32345 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 31525 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31429 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32351 |
| [Margaris] p. 40 | Rule C | exlimiv 1930 |
| [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 1780 df-or 848 dfbi2 474 |
| [Margaris] p. 51 | Theorem 1 | idALT 23 |
| [Margaris] p. 56 | Theorem 3 | conventions 30336 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 44876 |
| [Margaris] p. 60 | Theorem 8 | jcn 162 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 44877 |
| [Margaris] p. 79 | Rule C | exinst01 44587 exinst11 44588 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1976 19.2g 2189 r19.2z 4466 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2203 rr19.3v 3642 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2160 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1826 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1781 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2182 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2206 19.9h 2286 exlimd 2219 exlimdh 2290 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2163 excomim 2164 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2326 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30337 conventions-labels 30337 conventions-labels 30337 conventions-labels 30337 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1827 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 44339 albi 1818 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2226 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2227 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 44341 exbi 1847 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2230 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 44338 2alimdv 1918 alimd 2213 alimdh 1817 alimdv 1916 ax-4 1809 ralimdaa 3240 ralimdv 3149 ralimdva 3147 ralimdvva 3186 sbcimdv 3830 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2208 19.21h 2287 19.21t 2207 19.21vv 44337 alrimd 2216 alrimdd 2215 alrimdh 1863 alrimdv 1929 alrimi 2214 alrimih 1824 alrimiv 1927 alrimivv 1928 hbralrimi 3125 r19.21be 3232 r19.21bi 3231 ralrimd 3244 ralrimdv 3133 ralrimdva 3135 ralrimdvv 3183 ralrimdvva 3194 ralrimi 3237 ralrimia 3238 ralrimiv 3126 ralrimiva 3127 ralrimivv 3180 ralrimivva 3182 ralrimivvva 3185 ralrimivw 3131 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 44340 2eximdv 1919 exim 1834 eximd 2217 eximdh 1864 eximdv 1917 rexim 3072 reximd2a 3249 reximdai 3241 reximdd 45114 reximddv 3151 reximddv2 3198 reximddv3 3152 reximdv 3150 reximdv2 3145 reximdva 3148 reximdvai 3146 reximdvva 3187 reximi2 3064 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2212 19.23bi 2192 19.23h 2288 19.23t 2211 exlimdv 1933 exlimdvv 1934 exlimexi 44486 exlimiv 1930 exlimivv 1932 rexlimd3 45110 rexlimdv 3134 rexlimdv3a 3140 rexlimdva 3136 rexlimdva2 3138 rexlimdvaa 3137 rexlimdvv 3195 rexlimdvva 3196 rexlimdvvva 3197 rexlimdvw 3141 rexlimiv 3129 rexlimiva 3128 rexlimivv 3181 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 1991 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1880 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1870 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2228 r19.27z 4476 r19.27zv 4477 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2229 19.28vv 44347 r19.28z 4469 r19.28zf 45125 r19.28zv 4472 rr19.28v 3643 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1873 r19.29d2r 3122 r19.29imd 3100 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1881 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2235 19.31vv 44345 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2234 r19.32 47069 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 44343 19.33 1884 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 1992 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1877 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2231 19.36vv 44344 r19.36zv 4478 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2233 19.37vv 44346 r19.37zv 4473 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1839 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 1990 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1887 19.40 1886 r19.40 3101 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2236 19.41rg 44512 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2237 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1882 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2238 r19.44zv 4475 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2239 r19.45zv 4474 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2604 |
| [Mayet] p. 370 | Remark | jpi 32206 largei 32203 stri 32193 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32148 ishst 32150 |
| [Mayet3] p. 10 | Theorem | hstrbi 32202 hstri 32201 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 31664 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 31665 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32214 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31268 chsupcl 31276 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32296 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32290 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32317 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 39969 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18452 latj32 18450 latjass 18448 |
| [Megill] p. 444 | Axiom C5 | ax-5 1910 ax5ALT 38892 |
| [Megill] p. 444 | Section 7 | conventions 30336 |
| [Megill] p. 445 | Lemma L12 | aecom-o 38886 ax-c11n 38873 axc11n 2425 |
| [Megill] p. 446 | Lemma L17 | equtrr 2022 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 38881 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 38913 hbnae 2431 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2480 sbid 2256 sbidd-misc 49585 sbidd 49584 |
| [Megill] p. 448 | Remark 9.6 | axc14 2462 |
| [Megill] p. 448 | Scheme C4' | ax-c4 38869 |
| [Megill] p. 448 | Scheme C5' | ax-c5 38868 sp 2184 |
| [Megill] p. 448 | Scheme C6' | ax-11 2158 |
| [Megill] p. 448 | Scheme C7' | ax-c7 38870 |
| [Megill] p. 448 | Scheme C8' | ax-7 2008 |
| [Megill] p. 448 | Scheme C9' | ax-c9 38875 |
| [Megill] p. 448 | Scheme C10' | ax-6 1967 ax-c10 38871 |
| [Megill] p. 448 | Scheme C11' | ax-c11 38872 |
| [Megill] p. 448 | Scheme C12' | ax-8 2111 |
| [Megill] p. 448 | Scheme C13' | ax-9 2119 |
| [Megill] p. 448 | Scheme C14' | ax-c14 38876 |
| [Megill] p. 448 | Scheme C15' | ax-c15 38874 |
| [Megill] p. 448 | Scheme C16' | ax-c16 38877 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 38889 dral1 2438 dral2-o 38915 dral2 2437 drex1 2440 drex2 2441 drsb1 2494 drsb2 2267 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2174 sbequ 2084 sbid2v 2508 |
| [Megill] p. 450 | Example in Appendix | hba1-o 38882 hba1 2293 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 46863 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 23 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3850 rspsbca 3851 stdpc4 2069 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 38869 ra4 3857 stdpc5 2209 |
| [Mendelson] p. 81 | Rule C | exlimiv 1930 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2028 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2251 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3759 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5482 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4369 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4370 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4248 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4305 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4249 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4112 |
| [Mendelson] p. 231 | Definition of union | dfun3 4247 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5419 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4876 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5537 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4589 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5538 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4903 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5797 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6249 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7758 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6346 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8570 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9117 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 9032 xpsneng 9033 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9040 xpcomeng 9041 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9043 |
| [Mendelson] p. 255 | Definition | brsdom 8952 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9035 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8807 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 9014 mapsnend 9013 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9123 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9122 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8859 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 9017 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9036 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10150 djucomen 10149 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10154 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10148 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8506 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8533 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10530 |
| [Mendelson] p. 281 | Definition | df-r1 9735 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9784 |
| [Mendelson] p. 287 | Axiom system MK | ru 3759 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30195 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30230 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30232 vdgn1frgrv3 30233 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30234 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30227 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30220 2pthfrgrrn 30218 2pthfrgrrn2 30219 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31188 |
| [Monk1] p. 22 | Remark | conventions 30336 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30336 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4210 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5753 ssrelf 32550 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5755 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5178 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6243 coi2 6244 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5892 rn0 5897 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 6122 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5664 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5900 rnxp 6151 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5745 xp0 6139 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6056 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6053 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7899 imaexALTV 38315 imaexg 7898 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6050 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7054 funfvop 7029 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6922 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6933 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6570 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7236 dff13f 7237 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7200 funrnex 7941 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7228 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6208 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4936 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 7994 df-1st 7977 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 7995 df-2nd 7978 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9825 ranksnb 9798 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9826 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9827 rankunb 9821 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9809 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9735 r1val2 9808 |
| [Monk1] p. 117 | Lemma | zorn2 10477 zorn2g 10474 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9957 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10532 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9952 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1809 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2008 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2178 ax-c15 38874 ax12v2 2180 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 38869 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2158 |
| [Monk2] p. 109 | Lemma 15 | equvini 2454 equvinv 2029 eqvinop 5455 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1910 ax5ALT 38892 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2142 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2158 |
| [Monk2] p. 114 | Lemma 21 | sp 2184 |
| [Monk2] p. 114 | Lemma 22 | axc4 2320 hba1-o 38882 hba1 2293 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2154 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2177 nfra2 3353 nfra2w 3277 |
| [Moore] p. 53 | Part I | df-mre 17553 |
| [Munkres] p. 77 | Example 2 | distop 22888 indistop 22895 indistopon 22894 |
| [Munkres] p. 77 | Example 3 | fctop 22897 fctop2 22898 |
| [Munkres] p. 77 | Example 4 | cctop 22899 |
| [Munkres] p. 78 | Definition of basis | df-bases 22839 isbasis3g 22842 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17412 tgval2 22849 |
| [Munkres] p. 79 | Remark | tgcl 22862 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 22856 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 22880 tgss3 22879 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 22881 basgen2 22882 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 37334 topdifinfeq 37335 topdifinffin 37333 topdifinfindis 37331 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23053 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 22931 topcld 22928 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 22932 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 22934 |
| [Munkres] p. 94 | Definition of closure | clsval 22930 |
| [Munkres] p. 94 | Definition of interior | ntrval 22929 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 22968 elcls 22966 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 22976 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23041 neindisj 23010 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23043 |
| [Munkres] p. 97 | Definition of limit point | islp2 23038 lpval 23032 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23208 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23120 iscn 23128 iscn2 23131 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23173 cncnp2 23174 cncnpi 23171 df-cnp 23121 iscnp 23130 iscnp2 23132 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24437 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25218 |
| [Nathanson] p. 123 | Remark | reprgt 34620 reprinfz1 34621 reprlt 34618 |
| [Nathanson] p. 123 | Definition | df-repr 34608 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 34640 |
| [Nathanson] p. 123 | Proposition | breprexp 34632 breprexpnat 34633 itgexpif 34605 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32040 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 47766 |
| [Pfenning] p. 17 | Definition XM | natded 30339 |
| [Pfenning] p. 17 | Definition NNC | natded 30339 notnotrd 133 |
| [Pfenning] p. 17 | Definition ` `C | natded 30339 |
| [Pfenning] p. 18 | Rule" | natded 30339 |
| [Pfenning] p. 18 | Definition /\I | natded 30339 |
| [Pfenning] p. 18 | Definition ` `E | natded 30339 natded 30339 natded 30339 natded 30339 natded 30339 |
| [Pfenning] p. 18 | Definition ` `I | natded 30339 natded 30339 natded 30339 natded 30339 natded 30339 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30339 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30339 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30339 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30339 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30339 |
| [Pfenning] p. 127 | Definition =E | natded 30339 |
| [Pfenning] p. 127 | Definition =I | natded 30339 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25109 df-dip 30637 dip0l 30654 ip0l 21551 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25150 ipval 30639 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 30650 ipcj 21549 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25112 dipdir 30778 ipdir 21554 ipdiri 30766 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 30646 nmsq 25101 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 30761 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 30763 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 30764 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25118 dipass 30781 ipass 21560 ipassi 30777 |
| [Prugovecki] p. 186 | Definition of bra | braval 31880 df-bra 31786 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 31787 kbval 31890 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32318 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 39874 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32332 atcvat4i 32333 cvrat3 39428 cvrat4 39429 lsatcvat3 39037 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32218 cvrval 39254 df-cv 32215 df-lcv 39004 lspsncv0 21062 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 39886 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 39887 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2709 rabid 3433 rabidd 45121 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2279 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2722 |
| [Quine] p. 19 | Definition 2.9 | conventions 30336 df-v 3457 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2869 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2866 abid2f 2924 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2276 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2086 sbalex 2243 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2804 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2730 eqid1 30403 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2737 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3762 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3763 dfsbcq2 3764 |
| [Quine] p. 43 | Theorem 6.8 | vex 3459 |
| [Quine] p. 43 | Theorem 6.9 | isset 3469 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3566 spcgv 3571 spcimgf 3525 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3774 spsbcd 3775 |
| [Quine] p. 44 | Theorem 6.12 | elex 3476 |
| [Quine] p. 44 | Theorem 6.13 | elab 3654 elabg 3651 elabgf 3649 |
| [Quine] p. 44 | Theorem 6.14 | noel 4309 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4689 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4600 df-sn 4598 |
| [Quine] p. 49 | Theorem 7.4 | snss 4757 snssg 4755 |
| [Quine] p. 49 | Theorem 7.5 | prss 4792 prssg 4791 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4734 prid1g 4732 prid2 4735 prid2g 4733 snid 4634 snidg 4632 |
| [Quine] p. 51 | Theorem 7.12 | snex 5399 |
| [Quine] p. 51 | Theorem 7.13 | prex 5400 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4898 unisnALT 44887 unisng 4897 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4902 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4909 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4907 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6486 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 47057 dfiota2 6473 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 47066 iotaval 6490 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6497 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6492 |
| [Quine] p. 58 | Definition 9.1 | df-op 4604 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5493 opabidw 5492 opelopab 5510 opelopaba 5504 opelopabaf 5512 opelopabf 5513 opelopabg 5506 opelopabga 5501 opelopabgf 5508 oprabid 7426 oprabidw 7425 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5652 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5654 |
| [Quine] p. 64 | Definition 9.15 | df-id 5541 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6589 |
| [Quine] p. 65 | Theorem 10.4 | funi 6556 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6577 funsng 6575 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6521 |
| [Quine] p. 65 | Definition 10.2 | args 6071 dffv4 6862 |
| [Quine] p. 68 | Definition 10.11 | conventions 30336 df-fv 6527 fv2 6860 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14247 nn0opth2i 14246 nn0opthi 14245 omopthi 8636 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8387 |
| [Quine] p. 232 | Equation i | carddom 10525 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6613 funimaexg 6611 |
| [Quine] p. 331 | Axiom system NF | ru 3759 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31020 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 30637 polid 31095 polid2i 31093 polidi 31094 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 30749 |
| [ReedSimon] p. 195 | Remark | lnophm 31955 lnophmi 31954 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32068 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32070 leopmuli 32069 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32073 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 31788 leoppos 32062 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32072 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32061 |
| [Roman] p. 4 | Definition | df-dmat 22383 df-dmatalt 48316 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20068 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20150 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 48403 |
| [Roman] p. 112 | Note | isldepslvec2 48403 ldepsnlinc 48426 zlmodzxznm 48415 |
| [Roman] p. 112 | Example | zlmodzxzequa 48414 zlmodzxzequap 48417 zlmodzxzldep 48422 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 22783 |
| [Rosenlicht] p. 80 | Theorem | heicant 37646 |
| [Rosser] p. 281 | Definition | df-op 4604 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 34644 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 34645 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 48283 pmtr3ncom 19411 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19407 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19350 cayleyth 19351 |
| [Rudin] p. 164 | Equation 27 | efcan 16069 |
| [Rudin] p. 164 | Equation 30 | efzval 16077 |
| [Rudin] p. 167 | Equation 48 | absefi 16171 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 197 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1771 |
| [Sanford] p. 39 | Rule 4 | mptxor 1769 |
| [Sanford] p. 40 | Rule 1 | mptnan 1768 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6096 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6099 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6093 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6091 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17553 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17554 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17554 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17556 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10108 |
| [Schechter] p. 141 | Definition (MC) | dfac11 43023 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10417 axdc3 10425 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20152 isrngo 37888 |
| [Schechter] p. 276 | Remark 11.6.e | span0 31478 |
| [Schechter] p. 276 | Definition of span | df-span 31245 spanval 31269 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 22886 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6365 onelord 43212 ordelon 6364 ordelord 6362 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 43213 sucidg 6423 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6395 onsuc 7794 ord0 6394 ordsuci 7791 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 43214 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5226 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 42989 elon2 6351 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6346 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5549 epelg 5547 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9568 epirron 43215 ordirr 6358 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 43217 oneptr 43216 ontr1 6387 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6383 oneptri 43218 ordtri3or 6372 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8476 ord0eln0 6396 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6409 onsucss 43227 trsucss 6430 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7801 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6436 ordnbtwn 6435 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 43229 ordnexbtwnsuc 43228 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10372 onsucf1lem 43230 onsucf1o 43233 onsucf1olem 43231 onsucrn 43232 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 43234 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7829 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 43223 ordne0gt0 43222 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 43225 limnsuc 43226 onsucelab 43224 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9614 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7844 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9617 ordom 7860 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9618 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8615 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7763 ssorduni 7762 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8506 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9621 limom 7866 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8443 df1o2 8450 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8491 oa0suclim 43236 oalim 8507 oasuc 8499 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8492 om0suclim 43237 omlim 8508 omsuc 8501 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8497 oe0m1 8496 oe0suclim 43238 oelim 8509 oesuc 8502 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 43190 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 43240 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 43241 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 43242 limexissupab 43244 limiun 43243 limuni 6402 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8513 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8517 om1om1r 43245 om1r 8518 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8510 oaomoecl 43239 oecl 8512 omcl 8511 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 43192 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8519 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8520 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 43246 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 43247 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8586 nnamecl 43248 nnecl 8588 nnmcl 8587 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 43249 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8527 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8528 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8535 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 43251 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 43252 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 43254 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8534 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 43258 omword1 8548 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 43257 oaordnrex 43256 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 43253 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 43259 omword2 8549 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 43260 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 43261 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 43262 omordi 8541 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8543 omord2com 43263 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 43264 df-2o 8444 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 43267 oewordi 8566 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 43268 oeworde 8568 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 43269 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 43270 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 43266 omnord1ex 43265 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 43271 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 43273 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 43277 oenord1ex 43276 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 43278 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8536 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 43272 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8554 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8555 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 43280 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8572 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 43281 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 43282 cantnfub2 43283 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 43286 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 28848 axtgcgrrflx 28396 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 28849 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 28850 axtgcgrid 28397 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28382 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 28861 axtgsegcon 28398 df-trkgcb 28384 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 28872 axtg5seg 28399 df-trkgcb 28384 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 28873 axtgbtwnid 28400 df-trkgb 28383 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 28875 axtgpasch 28401 df-trkgb 28383 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 28894 df-trkg2d 34664 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28404 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28405 df-trkg2d 34664 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 28897 axtgeucl 28406 df-trkge 28385 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 28910 axtgcont 28403 axtgcont1 28402 df-trkgb 28383 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 35972 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 35974 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 35977 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 35981 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 35982 tgcgrcomimp 28411 tgcgrcoml 28413 tgcgrcomr 28412 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 35987 tgcgrtriv 28418 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 35991 tg5segofs 34672 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 34669 df-ofs 35968 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 35993 tgcgrextend 28419 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 35995 tgsegconeq 28420 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36007 btwntriv2 35997 tgbtwntriv2 28421 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 35998 tgbtwncom 28422 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36001 tgbtwntriv1 28425 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36002 tgbtwnswapid 28426 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36008 btwnintr 36004 tgbtwnexch2 28430 tgbtwnintr 28427 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36010 btwnexch3 36005 tgbtwnexch 28432 tgbtwnexch3 28428 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36009 tgbtwnouttr 28431 tgbtwnouttr2 28429 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 28893 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36012 tgbtwndiff 28440 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28433 trisegint 36013 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36029 tgifscgr 28442 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28492 colrot1 28493 colrot2 28494 lncom 28556 lnrot1 28557 lnrot2 28558 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36025 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36030 tgcgrsub 28443 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36040 tgcgrxfr 28452 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28451 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36026 df-cgrg 28445 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28445 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36041 tgbtwnxfr 28464 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36047 colinearperm2 36049 colinearperm3 36048 colinearperm4 36050 colinearperm5 36051 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28467 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36024 tgellng 28487 tglng 28480 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36052 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36060 lnxfr 28500 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36061 lnext 28501 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36065 tgfscgr 28502 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36066 lncgr 28503 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36027 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36068 lnid 28504 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36069 tgidinside 28505 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36086 tgbtwnconn1 28509 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36087 tgbtwnconn2 28510 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36088 tgbtwnconn3 28511 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36094 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36092 legov 28519 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28520 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28533 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36095 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36097 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36099 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36100 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36101 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36098 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36103 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28521 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28523 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28524 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28525 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28526 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36110 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36111 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36106 df-outsideof 36105 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36107 ishlg 28536 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28541 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28543 outsideofrflx 36112 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28537 hlcomd 28538 outsideofcom 36113 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28544 outsideoftr 36114 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 28552 outsideofeu 36116 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36123 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36124 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36117 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36132 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36133 tglineelsb2 28566 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36135 linerflx1 36134 linerflx2 36136 tglinecom 28569 tglinerflx1 28567 tglinerflx2 28568 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36138 tglinethru 28570 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36122 tglng 28480 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28528 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36141 tglinethrueu 28573 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36142 tglineineq 28577 tglineinteq 28579 tglineintmo 28576 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28583 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28584 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 28585 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 28600 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 28596 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 28588 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 28587 ismir 28593 mirbtwn 28592 mircgr 28591 mirfv 28590 mirval 28589 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 28598 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 28599 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 28600 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 28603 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 28604 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 28609 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 28606 mirbtwni 28605 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 28607 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 28619 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 28623 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 28620 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 28621 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 28622 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 28625 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 28626 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 28632 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 28628 israg 28631 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 28633 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 28634 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 28636 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 28637 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 28638 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 28639 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 28640 ragncol 28643 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 28641 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 28647 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 28651 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 28648 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 28630 isperp 28646 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 28649 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 28656 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 28664 colperpexlem2 28665 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 28667 colperpexlem3 28666 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 28672 midex 28671 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 28669 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 28678 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 28673 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 28682 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 28685 opphllem6 28686 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 28688 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28401 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 28689 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 28697 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 28692 hpgbr 28694 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 28699 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 28698 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 28700 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 28701 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 28702 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 28703 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 28704 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 28718 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 28708 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 28722 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 28723 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 28724 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 28725 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 28726 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 28729 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 28731 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 28709 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 28732 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 28735 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 28736 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 28737 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 28738 trgcopyeu 28740 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 28764 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 28743 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 28752 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 28750 cgrahl2 28751 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 28753 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 28754 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 28756 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 28757 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 28760 cgrahl 28761 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 28765 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 28766 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 28767 acopyeu 28768 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 28775 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 28779 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 28772 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 28787 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 28780 isleag 28781 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 28789 tgsas1 28788 tgsas2 28790 tgsas3 28791 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 28793 tgasa1 28792 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 28794 tgsss2 28795 tgsss3 28796 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27189 dchrsum 27187 dchrsum2 27186 sumdchr 27190 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27191 sum2dchr 27192 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 20004 ablfacrp2 20005 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27134 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27135 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27142 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27400 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27403 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27457 vmalogdivsum2 27456 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27447 dirith2 27446 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27445 rpvmasum 27444 rpvmasum2 27430 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27405 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27443 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27410 dchrisumlem1 27407 dchrisumlem2 27408 dchrisumlem3 27409 dchrisumlema 27406 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27413 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27442 dchrmusumlem 27440 dchrvmasumlem 27441 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27412 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27414 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27438 dchrisum0re 27431 dchrisumn0 27439 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27424 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27428 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27429 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27484 pntrsumbnd2 27485 pntrsumo1 27483 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27448 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27450 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27452 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27455 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27460 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27461 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27466 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27468 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27469 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27477 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27478 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27475 selberg3lem2 27476 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27479 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27473 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27486 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27487 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27488 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27502 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27514 pntlemb 27515 pntlemc 27513 pntlemd 27512 pntlemg 27516 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27514 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27506 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27511 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27514 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27527 pntleml 27529 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 33741 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 33728 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 33760 constrinvcl 33771 constrmulcl 33769 constrnegcl 33761 constrsqrtcl 33777 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 33747 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 33757 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 33779 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 33789 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4277 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4376 dif0 4349 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4463 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4446 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4268 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4269 |
| [Stoll] p. 20 | Remark | invdif 4250 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4606 |
| [Stoll] p. 43 | Definition | uniiun 5030 |
| [Stoll] p. 44 | Definition | intiin 5031 |
| [Stoll] p. 45 | Definition | df-iin 4966 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4965 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 401 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4277 |
| [Strang] p. 242 | Section 6.3 | expgrowth 44296 |
| [Suppes] p. 22 | Theorem 2 | eq0 4321 eq0f 4318 |
| [Suppes] p. 22 | Theorem 4 | eqss 3970 eqssd 3972 eqssi 3971 |
| [Suppes] p. 23 | Theorem 5 | ss0 4373 ss0b 4372 |
| [Suppes] p. 23 | Theorem 6 | sstr 3963 sstrALT2 44796 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4074 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4075 |
| [Suppes] p. 23 | Theorem 9 | psstr 4078 |
| [Suppes] p. 23 | Theorem 10 | pssss 4069 |
| [Suppes] p. 25 | Theorem 12 | elin 3938 elun 4124 |
| [Suppes] p. 26 | Theorem 15 | inidm 4198 |
| [Suppes] p. 26 | Theorem 16 | in0 4366 |
| [Suppes] p. 27 | Theorem 23 | unidm 4128 |
| [Suppes] p. 27 | Theorem 24 | un0 4365 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4149 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4157 |
| [Suppes] p. 27 | Theorem 27 | unss 4161 |
| [Suppes] p. 27 | Theorem 28 | indir 4257 |
| [Suppes] p. 27 | Theorem 29 | undir 4258 |
| [Suppes] p. 28 | Theorem 32 | difid 4347 |
| [Suppes] p. 29 | Theorem 33 | difin 4243 |
| [Suppes] p. 29 | Theorem 34 | indif 4251 |
| [Suppes] p. 29 | Theorem 35 | undif1 4447 |
| [Suppes] p. 29 | Theorem 36 | difun2 4452 |
| [Suppes] p. 29 | Theorem 37 | difin0 4445 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4443 |
| [Suppes] p. 29 | Theorem 39 | difundi 4261 |
| [Suppes] p. 29 | Theorem 40 | difindi 4263 |
| [Suppes] p. 30 | Theorem 41 | nalset 5276 |
| [Suppes] p. 39 | Theorem 61 | uniss 4887 |
| [Suppes] p. 39 | Theorem 65 | uniop 5483 |
| [Suppes] p. 41 | Theorem 70 | intsn 4956 |
| [Suppes] p. 42 | Theorem 71 | intpr 4954 intprg 4953 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5439 |
| [Suppes] p. 42 | Theorem 78 | intun 4952 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 5005 dfiun2g 5002 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 5006 |
| [Suppes] p. 47 | Theorem 86 | elpw 4575 elpw2 5297 elpw2g 5296 elpwg 4574 elpwgdedVD 44878 |
| [Suppes] p. 47 | Theorem 87 | pwid 4593 |
| [Suppes] p. 47 | Theorem 89 | pw0 4784 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4785 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5661 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5805 xpindir 5806 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5715 xpundir 5716 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9567 |
| [Suppes] p. 58 | Theorem 2 | relss 5752 |
| [Suppes] p. 59 | Theorem 4 | eldm 5872 eldm2 5873 eldm2g 5871 eldmg 5870 |
| [Suppes] p. 59 | Definition 3 | df-dm 5656 |
| [Suppes] p. 60 | Theorem 6 | dmin 5883 |
| [Suppes] p. 60 | Theorem 8 | rnun 6126 |
| [Suppes] p. 60 | Theorem 9 | rnin 6127 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5860 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5854 brcnvg 5851 |
| [Suppes] p. 62 | Equation 5 | elcnv 5848 elcnv2 5849 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6083 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6125 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6123 |
| [Suppes] p. 63 | Definition | dftrrels2 38560 |
| [Suppes] p. 63 | Theorem 20 | co02 6241 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5946 |
| [Suppes] p. 63 | Definition 7 | df-co 5655 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5857 |
| [Suppes] p. 64 | Theorem 27 | coass 6246 |
| [Suppes] p. 65 | Theorem 31 | resundi 5972 |
| [Suppes] p. 65 | Theorem 34 | elima 6044 elima2 6045 elima3 6046 elimag 6043 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6130 |
| [Suppes] p. 66 | Theorem 40 | dminss 6134 |
| [Suppes] p. 66 | Theorem 41 | imainss 6135 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6138 |
| [Suppes] p. 81 | Definition 34 | dfec2 8685 |
| [Suppes] p. 82 | Theorem 72 | elec 8728 elecALTV 38251 elecg 8726 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 38596 erth 8733 erth2 8734 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 38599 erdisj 8736 |
| [Suppes] p. 83 | Definition 35, | df-parts 38750 dfmembpart2 38755 |
| [Suppes] p. 89 | Theorem 96 | map0b 8860 |
| [Suppes] p. 89 | Theorem 97 | map0 8864 map0g 8861 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8865 mapsnd 8863 |
| [Suppes] p. 89 | Theorem 99 | mapss 8866 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 10039 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 10038 |
| [Suppes] p. 92 | Theorem 1 | enref 8962 enrefg 8961 |
| [Suppes] p. 92 | Theorem 2 | ensym 8980 ensymb 8979 ensymi 8981 |
| [Suppes] p. 92 | Theorem 3 | entr 8983 |
| [Suppes] p. 92 | Theorem 4 | unen 9023 |
| [Suppes] p. 94 | Theorem 15 | endom 8956 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 8977 |
| [Suppes] p. 94 | Theorem 17 | domtr 8984 |
| [Suppes] p. 95 | Theorem 18 | sbth 9070 |
| [Suppes] p. 97 | Theorem 23 | canth2 9107 canth2g 9108 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9074 df-sdom 8925 dfsdom2 9073 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9091 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9076 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9075 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9089 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8959 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9092 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9087 |
| [Suppes] p. 98 | Exercise 4 | fundmen 9008 fundmeng 9009 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9047 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9088 |
| [Suppes] p. 104 | Theorem 37 | fofi 9280 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9286 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9286 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10522 |
| [Suppes] p. 130 | Definition 3 | df-tr 5223 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7763 |
| [Suppes] p. 134 | Definition 6 | df-suc 6346 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7885 finds 7881 finds1 7884 finds2 7883 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9623 isfinite2 9263 isfiniteg 9266 unbnn 9261 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10889 df-ltpq 10881 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7847 tfinds 7844 tfinds2 7848 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8526 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8528 |
| [Suppes] p. 211 | Theorem 25 | oaass 8536 |
| [Suppes] p. 225 | Definition 8 | iscard2 9947 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10534 |
| [Suppes] p. 228 | Theorem 59 | harcard 9949 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 10037 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6392 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7776 onminsb 7777 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10543 |
| [Suppes] p. 229 | Theorem 65 | alephcard 10041 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 10048 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 10042 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9911 |
| [Suppes] p. 242 | Theorem 6 | weth 10466 |
| [Suppes] p. 242 | Theorem 8 | entric 10528 |
| [Suppes] p. 242 | Theorem 9 | carden 10522 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 35680 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 35684 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2702 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2722 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2804 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2724 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2750 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7398 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3759 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5384 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4622 elpr2 4624 elpr2g 4623 elprg 4620 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4612 elsn2 4637 elsn2g 4636 elsng 4611 velsn 4613 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5435 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4607 sneqr 4812 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4618 dfsn2 4610 dfsn2ALT 4619 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7724 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5444 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5432 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5416 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7727 unexg 7726 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4663 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4880 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3929 df-un 3927 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4896 uniprg 4895 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5340 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4661 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6412 elsucg 6410 sstr2 3961 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4129 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4180 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4143 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4199 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4255 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4256 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3942 df-ss 3939 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4573 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4158 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3940 sseqin2 4194 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3977 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4208 inss2 4209 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 4019 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4890 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5417 sspwimp 44879 sspwimpALT 44886 sspwimpALT2 44889 sspwimpcf 44881 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5424 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5242 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3412 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5270 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3925 |
| [TakeutiZaring] p. 20 | Definition 5.14 | dfnul2 4307 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4347 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4324 n0f 4320 neq0 4323 neq0f 4319 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9566 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9703 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9705 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3457 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5278 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4371 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5284 ssexg 5286 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5280 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9573 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9568 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4337 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4106 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4271 undif3VD 44843 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4107 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4114 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3047 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3056 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7736 xpexg 7733 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5653 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6595 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6772 fun11 6598 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6535 svrelfun 6596 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5859 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5861 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5658 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5659 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5655 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6175 dfrel2 6170 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5662 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5782 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5789 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5803 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 5984 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5964 opelresi 5966 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 5991 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5980 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 5985 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6566 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6087 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6564 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6774 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2603 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30336 df-fv 6527 fv3 6883 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7910 cnvexg 7909 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7894 dmexg 7886 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7895 rnexg 7887 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 44415 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7905 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6878 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 47145 tz6.12-1-afv2 47212 tz6.12-1 6888 tz6.12-afv 47144 tz6.12-afv2 47211 tz6.12 6890 tz6.12c-afv2 47213 tz6.12c 6887 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 47208 tz6.12-2 6853 tz6.12i-afv2 47214 tz6.12i 6893 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6522 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6523 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6525 wfo 6517 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6524 wf1 6516 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6526 wf1o 6518 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 7010 eqfnfv2 7011 eqfnfv2f 7014 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6966 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7198 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7196 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6613 funimaexg 6611 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5116 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5555 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5607 dffr3 6078 eliniseg 6073 iniseg 6076 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5546 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5623 fr3nr 7755 frirr 5622 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5599 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7757 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5610 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5632 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6328 tz6.26i 6329 wefrc 5640 wereu2 5643 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6330 wfii 6331 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6528 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7311 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7312 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7318 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7319 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7320 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7324 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7331 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7333 |
| [TakeutiZaring] p. 35 | Notation | wtr 5222 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 44416 tz7.2 5629 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5228 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6353 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6361 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6362 ordelordALT 44499 ordelordALTVD 44828 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6368 ordelssne 6367 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6366 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6370 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7765 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7766 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6344 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6372 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 44511 ordon 7760 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7761 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7837 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6388 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5224 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7775 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7814 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6446 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6445 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7762 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4909 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6346 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6422 sucidg 6423 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7794 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6436 ordnbtwn 6435 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7811 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6345 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7865 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7870 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7825 ordelsuc 7803 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7805 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7835 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7852 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7873 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7875 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7876 |
| [TakeutiZaring] p. 43 | Remark | omon 7862 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9606 omex 9614 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7860 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7880 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7877 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7878 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7855 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4934 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5241 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4935 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5307 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7778 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6391 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4919 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9631 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7773 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8353 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8374 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8375 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8376 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8383 tz7.44-2 8384 tz7.44-3 8385 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8345 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8340 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8324 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8422 tz7.49c 8423 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8420 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8419 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8421 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2650 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 9982 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 9983 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8507 oasuc 8499 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7845 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8510 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8491 oa0r 8513 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8511 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8523 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8594 nnaordi 8593 oaord 8522 oaordi 8521 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5021 uniss2 4913 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8525 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8530 oawordex 8532 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8586 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8623 |
| [TakeutiZaring] p. 60 | Remark | oancom 9622 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8535 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8591 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8527 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8494 omlim 8508 omsuc 8501 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8492 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8588 nnmcl 8587 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8607 nnmordi 8606 omord 8543 omordi 8541 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8544 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8611 omwordri 8547 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8514 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8517 om1r 8518 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8550 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8552 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8553 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8554 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8555 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8583 oe0 8497 oelim 8509 oesuc 8502 onesuc 8505 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8495 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8561 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8562 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8496 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8520 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8563 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8569 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8567 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8568 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8572 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8574 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9699 tz9.1 9700 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9735 r10 9739 r1lim 9743 r1limg 9742 r1suc 9741 r1sucg 9740 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9751 r1ord2 9752 r1ordg 9749 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9761 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9786 tz9.13 9762 tz9.13g 9763 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9736 rankval 9787 rankvalb 9768 rankvalg 9788 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9810 rankelb 9795 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9824 rankval3 9811 rankval3b 9797 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9800 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9766 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9805 rankr1c 9792 rankr1g 9803 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9806 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9820 rankssb 9819 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9813 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9812 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10446 dfac3 10092 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 10001 numth 10443 numth2 10442 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10517 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10518 cardid2 9924 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9931 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10522 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9930 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9915 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9936 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9928 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9127 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 8995 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9132 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9051 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9934 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10069 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9183 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9194 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10070 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9188 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10059 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 10037 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9943 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10187 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9291 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8926 isfi 8953 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9196 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10505 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9044 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10497 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10157 unxpdom 9218 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9945 cardsdomelir 9944 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9220 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 9985 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8805 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10533 infxpidm2 9988 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10178 infxp 10185 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9056 pw2f1o 9054 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9120 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10458 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10453 ac6s5 10462 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10514 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10515 uniimadomf 10516 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10245 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10240 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10225 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10222 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10228 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10235 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10244 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10553 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10223 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10247 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10068 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10067 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10079 alephfp2 10080 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10670 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10083 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10540 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10554 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10555 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 38868 |
| [Tarski] p. 67 | Scheme B5 | sp 2184 |
| [Tarski] p. 68 | Lemma 6 | avril1 30399 equid 2012 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2017 |
| [Tarski] p. 70 | Lemma 14 | spim 2386 spime 2388 spimew 1971 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2178 ax-c15 38874 ax12i 1966 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2086 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1968 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1910 ax5ALT 38892 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2008 ax-8 2111 ax-9 2119 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28398 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28399 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28401 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28401 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28402 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16218 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 37650 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 37652 |
| [Weierstrass] p. 272 | Definition | df-mdet 22478 mdetuni 22515 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 903 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 868 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 869 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 919 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 969 |
| [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 37430 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 43761 imim2 58 wl-luk-imim2 37425 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 46990 imim1 83 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 896 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2657 syl 17 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 902 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 22 wl-luk-id 37428 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 894 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 142 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 897 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 130 notnotrALT2 44888 wl-luk-notnotr 37429 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 146 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 43791 axfrege28 43790 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 867 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 924 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 123 wl-luk-pm2.21 37422 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 124 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 889 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 941 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 30337 pm2.27 42 wl-luk-pm2.27 37420 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 922 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 38348 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 923 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 971 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 972 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 970 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1087 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 906 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 907 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 944 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 56 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 881 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 882 |
| [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 | pm2.47 883 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 884 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 885 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 172 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 851 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 852 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 888 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 890 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 192 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 899 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 942 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 943 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 193 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 891 pm2.67 892 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 176 pm2.521g 174 pm2.521g2 175 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 898 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 974 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 900 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 203 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 975 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 976 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 933 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 931 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 973 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 977 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 84 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 932 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 109 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 993 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 469 pm3.2im 160 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 994 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 995 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 996 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 997 |
| [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 | pm3.35 802 |
| [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) | pm3.33 764 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 765 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 807 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 622 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 809 |
| [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 962 pm3.44 961 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 808 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 473 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 965 |
| [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 | pm4.14 806 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 832 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 222 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 805 bitr 804 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 563 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 904 pm4.25 905 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 460 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1009 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 870 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 468 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 921 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 633 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 917 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 637 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 978 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1088 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1007 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1053 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1024 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 998 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 1000 pm4.45 999 pm4.45im 827 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 984 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 853 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 545 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 983 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 986 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 987 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 988 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 989 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 985 pm4.56 990 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 991 pm4.57 992 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 404 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 856 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 397 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 849 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 405 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 850 |
| [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 | pm4.72 951 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 527 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 936 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 517 pm4.76 518 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 963 pm4.77 964 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 934 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1005 |
| [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 1025 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1026 |
| [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 pm4.87 843 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 823 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 946 pm5.11g 945 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 947 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 949 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 948 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1014 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1015 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1013 |
| [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 | pm5.21 824 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1016 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1049 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1050 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 901 |
| [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 1003 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 955 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 830 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 573 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 835 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 825 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 833 |
| [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 1006 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1019 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 950 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1002 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1020 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1021 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1029 |
| [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 1030 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 44319 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 44320 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1870 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 44321 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 44322 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 44323 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1893 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 44324 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 44325 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 44326 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 44327 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 44328 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 44330 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 44331 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 44332 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 44329 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2091 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 44335 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 44336 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2071 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2161 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1829 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1830 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 44337 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 44338 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 44339 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 44340 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 44342 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 44341 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1887 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 44344 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 44345 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 44343 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1828 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 44346 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 44347 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1846 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 44348 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2344 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1860 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 44353 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 44349 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 44350 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 44351 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 44352 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 44357 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 44354 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 44355 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 44356 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 44358 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2563 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 44368 pm13.13b 44369 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 44370 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3008 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3009 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3641 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 44376 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 44377 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 44371 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 44514 pm13.193 44372 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 44373 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 44374 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 44375 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 44382 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 44381 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 44380 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3824 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 44383 pm14.122b 44384 pm14.122c 44385 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 44386 pm14.123b 44387 pm14.123c 44388 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 44390 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 44389 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 44391 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6500 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 44392 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6501 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 44393 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 44395 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2627 eupickbi 2630 sbaniota 44396 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 44394 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2578 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 44398 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30336 df-fv 6527 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 9972 pm54.43lem 9971 |
| [Young] p. 141 | Definition of operator ordering | leop2 32060 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32066 idleop 32067 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 42788 |
| [vandenDries] p. 43 | Theorem 62 | pellex 42795 pellexlem1 42789 |