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 17566 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17566 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 17975 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17587 0funcg 49096 df-termc 49484 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 49561 prsthinc 49475 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 49589 df-mndtc 49589 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 49585 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17610 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 49577 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 49602 oppgoppchom 49601 oppgoppcid 49603 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17680 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17668 invisoinvl 17689 |
| [Adamek] p. 28 | Example 3.13 | idinv 17688 idiso 17687 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17673 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17647 df-iso 17648 dfiso2 17671 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17654 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17705 cicerALT 49057 |
| [Adamek] p. 29 | Definition 3.15 | cic 17698 df-cic 17695 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17757 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17669 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17670 isoco 17676 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17757 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17780 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 49315 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17773 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 49585 discthing 49472 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 49429 prsthinc 49475 thincciso 49464 thincciso2 49466 thincciso3 49467 thinccisod 49465 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 49589 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17787 cofucla 49107 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 49173 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18010 catcisoi 49411 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18065 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17806 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17805 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18065 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17830 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17836 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17835 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18050 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18050 |
| [Adamek] p. 39 | Remark 3.42 | 2oppf 49143 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 49134 funcoppc 17774 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 17998 elcatchom 49408 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17824 fthoppf 49175 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17823 fulloppf 49174 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18007 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 49096 df-catc 17998 |
| [Adamek] p. 45 | Exercise 3G | incat 49612 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 49615 nelsubc3 49082 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 49162 imasubc2 49163 imasubc3 49167 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17737 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17738 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 49082 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17749 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17711 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 49171 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 49170 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 49172 ressffth 17839 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 49613 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 17845 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 17866 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 17870 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 17846 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 17872 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 49096 df-inito 17883 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 49096 df-termc 49484 initc 49102 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21409 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 17884 oppctermo 49247 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 17911 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 17915 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 49248 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 17885 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21410 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 17918 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17646 |
| [Adamek] p. 107 | Example 7.20(7) | thincinv 49480 |
| [Adamek] p. 108 | Example 7.25(4) | thincsect2 49479 |
| [Adamek] p. 110 | Example 7.33(9) | thincmon 49444 |
| [Adamek] p. 110 | Proposition 7.35 | sectmon 17681 |
| [Adamek] p. 112 | Proposition 7.42 | sectepi 17683 |
| [Adamek] p. 185 | Section 10.67 | updjud 9819 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 49656 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 49656 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 49656 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 49657 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 49657 |
| [Adamek] p. 478 | Item Rng | df-ringc 20554 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 48559 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 48581 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14470 df-pfx 14571 df-substr 14541 df-word 14413 lencl 14432 wrd0 14438 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24616 df-nmoo 30715 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32123 hmopidmchi 32121 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32171 pjcmul2i 32172 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 31888 unoplin 31890 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 31889 unopadj2 31908 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 31983 lnopunii 31982 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32056 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 27864 |
| [Alling] p. 184 | Axiom B | bdayfo 27609 |
| [Alling] p. 184 | Axiom O | sltso 27608 |
| [Alling] p. 184 | Axiom SD | nodense 27624 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27711 |
| [Alling] p. 185 | Theorem | conway 27733 |
| [Alling] p. 185 | Axiom FE | noeta 27675 |
| [Alling] p. 186 | Theorem 4 | slerec 27753 slerecd 27754 |
| [Alling], p. 2 | Definition | rp-brsslt 43435 |
| [Alling], p. 3 | Note | nla0001 43438 nla0002 43436 nla0003 43437 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11289 addcan2d 11309 addcan2i 11299 addcand 11308 addcani 11298 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11342 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11401 negsubd 11470 negsubi 11431 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11403 negnegd 11455 negnegi 11423 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11542 subdid 11565 subdii 11558 subdir 11543 subdird 11566 subdiri 11559 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11284 mul01d 11304 mul01i 11295 mul02 11283 mul02d 11303 mul02i 11294 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11746 mulcan2d 11743 mulcand 11742 mulcani 11748 |
| [Apostol] p. 18 | Theorem I.8 | receu 11754 xreceu 32892 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11784 divrecd 11892 divreci 11858 divreczi 11851 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11810 recreci 11845 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11749 mul0ord 11757 mul0ori 11756 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11548 mul2negd 11564 mul2negi 11557 mulneg1 11545 mulneg1d 11562 mulneg1i 11555 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11828 divadddivd 11933 divadddivi 11875 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11813 divmuldivd 11930 divmuldivi 11873 rdivmuldivd 20324 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11814 divdivdivd 11936 divdivdivi 11876 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 12906 rpaddcld 12941 rpmulcl 12907 rpmulcld 12942 |
| [Apostol] p. 20 | Axiom 8 | rpneg 12916 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 12919 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11231 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11702 ltadd1dd 11720 ltadd1i 11663 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 11963 ltmul1a 11962 ltmul1i 12032 ltmul1ii 12042 ltmul2 11964 ltmul2d 12968 ltmul2dd 12982 ltmul2i 12035 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11629 msqgt0d 11676 msqgt0i 11646 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11631 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11615 lt0neg1d 11678 ltneg 11609 ltnegd 11687 ltnegi 11653 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11594 lt2addd 11732 lt2addi 11671 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 12883 |
| [Apostol] p. 21 | Exercise 4 | recgt0 11959 recgt0d 12048 recgt0i 12019 recgt0ii 12020 |
| [Apostol] p. 22 | Definition of integers | df-z 12461 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12131 |
| [Apostol] p. 22 | Definition of rationals | df-q 12839 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9333 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12369 |
| [Apostol] p. 26 | Theorem I.29 | arch 12370 archd 45178 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12568 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12371 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12837 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12836 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13090 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16242 zneo 12548 zneoALTV 47679 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26659 msqsqrtd 15342 resqrtth 15154 sqrtth 15264 sqrtthi 15270 sqsqrtd 15341 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12120 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12803 |
| [Apostol] p. 361 | Remark | crreczi 14127 |
| [Apostol] p. 363 | Remark | absgt0i 15299 |
| [Apostol] p. 363 | Example | abssubd 15355 abssubi 15303 |
| [ApostolNT] p. 7 | Remark | fmtno0 47550 fmtno1 47551 fmtno2 47560 fmtno3 47561 fmtno4 47562 fmtno5fac 47592 fmtnofz04prm 47587 |
| [ApostolNT] p. 7 | Definition | df-fmtno 47538 |
| [ApostolNT] p. 8 | Definition | df-ppi 27030 |
| [ApostolNT] p. 14 | Definition | df-dvds 16156 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16172 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16197 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16192 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16185 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16187 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16173 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16174 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16179 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16214 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16216 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16218 |
| [ApostolNT] p. 15 | Definition | df-gcd 16398 dfgcd2 16449 |
| [ApostolNT] p. 16 | Definition | isprm2 16585 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16556 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16819 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16416 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16450 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16452 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16431 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16423 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16614 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16616 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16832 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16826 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16306 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16490 |
| [ApostolNT] p. 24 | Definition | df-mu 27031 |
| [ApostolNT] p. 25 | Definition | df-phi 16669 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27121 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16694 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16679 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16683 |
| [ApostolNT] p. 32 | Definition | df-vma 27028 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27123 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27147 |
| [ApostolNT] p. 38 | Remark | df-sgm 27032 |
| [ApostolNT] p. 38 | Definition | df-sgm 27032 |
| [ApostolNT] p. 75 | Definition | df-chp 27029 df-cht 27027 |
| [ApostolNT] p. 104 | Definition | congr 16567 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16159 |
| [ApostolNT] p. 106 | Definition | moddvds 16166 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16249 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16250 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13784 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13824 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14137 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16191 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16570 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 16978 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16572 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16686 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16705 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16687 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27002 |
| [ApostolNT] p. 179 | Definition | df-lgs 27226 lgsprme0 27270 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27271 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27247 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27262 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27319 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27338 2lgsoddprm 27347 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27305 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27314 |
| [ApostolNT] p. 188 | Definition | df-lgs 27226 lgs1 27272 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27263 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27265 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27273 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27274 |
| [Baer] p. 40 | Property (b) | mapdord 41656 |
| [Baer] p. 40 | Property (c) | mapd11 41657 |
| [Baer] p. 40 | Property (e) | mapdin 41680 mapdlsm 41682 |
| [Baer] p. 40 | Property (f) | mapd0 41683 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 41643 mapd1o 41666 |
| [Baer] p. 41 | Property (g) | mapdat 41685 |
| [Baer] p. 44 | Part (1) | mapdpg 41724 |
| [Baer] p. 45 | Part (2) | hdmap1eq 41819 mapdheq 41746 mapdheq2 41747 mapdheq2biN 41748 |
| [Baer] p. 45 | Part (3) | baerlem3 41731 |
| [Baer] p. 46 | Part (4) | mapdheq4 41750 mapdheq4lem 41749 |
| [Baer] p. 46 | Part (5) | baerlem5a 41732 baerlem5abmN 41736 baerlem5amN 41734 baerlem5b 41733 baerlem5bmN 41735 |
| [Baer] p. 47 | Part (6) | hdmap1l6 41839 hdmap1l6a 41827 hdmap1l6e 41832 hdmap1l6f 41833 hdmap1l6g 41834 hdmap1l6lem1 41825 hdmap1l6lem2 41826 mapdh6N 41765 mapdh6aN 41753 mapdh6eN 41758 mapdh6fN 41759 mapdh6gN 41760 mapdh6lem1N 41751 mapdh6lem2N 41752 |
| [Baer] p. 48 | Part 9 | hdmapval 41846 |
| [Baer] p. 48 | Part 10 | hdmap10 41858 |
| [Baer] p. 48 | Part 11 | hdmapadd 41861 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 41835 mapdh6hN 41761 |
| [Baer] p. 48 | Part (7) | mapdh75cN 41771 mapdh75d 41772 mapdh75e 41770 mapdh75fN 41773 mapdh7cN 41767 mapdh7dN 41768 mapdh7eN 41766 mapdh7fN 41769 |
| [Baer] p. 48 | Part (8) | mapdh8 41806 mapdh8a 41793 mapdh8aa 41794 mapdh8ab 41795 mapdh8ac 41796 mapdh8ad 41797 mapdh8b 41798 mapdh8c 41799 mapdh8d 41801 mapdh8d0N 41800 mapdh8e 41802 mapdh8g 41803 mapdh8i 41804 mapdh8j 41805 |
| [Baer] p. 48 | Part (9) | mapdh9a 41807 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 41787 |
| [Baer] p. 49 | Part 12 | hdmap11 41866 hdmapeq0 41862 hdmapf1oN 41883 hdmapneg 41864 hdmaprnN 41882 hdmaprnlem1N 41867 hdmaprnlem3N 41868 hdmaprnlem3uN 41869 hdmaprnlem4N 41871 hdmaprnlem6N 41872 hdmaprnlem7N 41873 hdmaprnlem8N 41874 hdmaprnlem9N 41875 hdmapsub 41865 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 41886 hdmap14lem10 41895 hdmap14lem1a 41884 hdmap14lem2N 41887 hdmap14lem2a 41885 hdmap14lem3 41888 hdmap14lem8 41893 hdmap14lem9 41894 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 41896 hdmap14lem12 41897 hdmap14lem13 41898 hdmap14lem14 41899 hdmap14lem15 41900 hgmapval 41905 |
| [Baer] p. 50 | Part 15 | hgmapadd 41912 hgmapmul 41913 hgmaprnlem2N 41915 hgmapvs 41909 |
| [Baer] p. 50 | Part 16 | hgmaprnN 41919 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 41935 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 41936 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 41937 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 41938 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 41940 hgmapvv 41944 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 41939 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 41941 |
| [Baer] p. 111 | Line 15 | hdmapg 41948 hdmapglem7 41947 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26660 2irrexpqALT 26730 |
| [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 5223 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5232 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37077 sepex 5236 |
| [BellMachover] p. 466 | Problem | axpow2 5303 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5304 |
| [BellMachover] p. 466 | Axiom Union | axun2 7665 |
| [BellMachover] p. 468 | Definition | df-ord 6305 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6320 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6327 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6322 |
| [BellMachover] p. 471 | Definition of N | df-om 7792 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7729 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6307 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9527 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7807 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9649 |
| [BellMachover] p. 478 | Definition | rankval2 9703 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9667 r1ord3g 9664 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9477 |
| [BellMachover] p. 488 | Axiom AC | ac5 10360 dfac4 10005 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 9993 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 39337 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32323 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32365 chirredi 32364 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32353 |
| [Beran] p. 3 | Definition of join | sshjval3 31324 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 31586 cmcm2i 31563 cmcm2ii 31568 cmt2N 39268 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 31587 lecmi 31572 lecmii 31573 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 31561 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 31590 cm2ji 31595 cm2mi 31596 |
| [Beran] p. 95 | Definition | df-sh 31177 issh2 31179 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31056 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31069 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31060 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 31798 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 31800 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 31799 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 31801 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31052 his1i 31070 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31053 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31054 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31055 |
| [Beran] p. 96 | Definition of norm | df-hnorm 30938 dfhnorm2 31092 normval 31094 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31154 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 30943 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31211 |
| [Beran] p. 96 | Definition of converge | df-hlim 30942 hlimi 31158 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31103 norm-i 31099 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31107 norm-ii 31108 normlem0 31079 normlem1 31080 normlem2 31081 normlem3 31082 normlem4 31083 normlem5 31084 normlem6 31085 normlem7 31086 normlem7tALT 31089 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31109 norm-iii 31110 |
| [Beran] p. 98 | Remark 3.4 | bcs 31151 bcsiALT 31149 bcsiHIL 31150 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31091 normpar 31125 normpari 31124 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31116 normpyth 31115 normpythi 31112 |
| [Beran] p. 99 | Remark | lnfn0 32017 lnfn0i 32012 lnop0 31936 lnop0i 31940 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 31996 nmcfnex 32023 nmcfnexi 32021 nmcopex 31999 nmcopexi 31997 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32024 nmcfnlbi 32022 nmcoplb 32000 nmcoplbi 31998 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32026 lnfnconi 32025 lnopcon 32005 lnopconi 32004 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31126 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31123 norm3adifii 31118 norm3dif 31120 norm3difi 31117 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31271 pjhth 31363 pjhtheu 31364 pjpjhth 31395 pjpjhthi 31396 pjth 25359 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31376 ococi 31375 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32031 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32032 riesz4 32034 riesz4i 32033 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32049 cnlnadjeu 32048 cnlnadjeui 32047 cnlnadji 32046 cnlnadjlem1 32037 nmopadjlei 32058 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32061 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32060 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32062 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 31906 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32072 nmopcoadji 32071 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32063 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32073 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32070 pjadj2coi 32174 pjadjcoi 32131 |
| [Beran] p. 107 | Definition | df-ch 31191 isch2 31193 |
| [Beran] p. 107 | Remark 3.12 | choccl 31276 isch3 31211 occl 31274 ocsh 31253 shoccl 31275 shocsh 31254 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31378 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31302 |
| [Beran] p. 109 | Property (i) | pjadj2 32157 pjadj3 32158 pjadji 31655 pjadjii 31644 |
| [Beran] p. 109 | Property (ii) | pjidmco 32151 pjidmcoi 32147 pjidmi 31643 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32143 |
| [Beran] p. 111 | Remark | ho0val 31720 pjch1 31640 |
| [Beran] p. 111 | Definition | df-hfmul 31704 df-hfsum 31703 df-hodif 31702 df-homul 31701 df-hosum 31700 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 31641 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 31664 pjchi 31402 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31409 pjoc2i 31408 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 31650 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32135 pjssmii 31651 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32134 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32133 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32138 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32136 pjssge0ii 31652 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32137 pjdifnormii 31653 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1777 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1775 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1778 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1773 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34295 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34303 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34301 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34305 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34325 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34356 df-sitm 34334 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34356 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34333 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29019 isuhgrop 29041 isusgrop 29133 isuspgrop 29132 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 47871 df-subgr 29239 uhgrspan1 29274 uhgrspansubgr 29262 |
| [Bollobas] p. 3 | Definition | df-gric 47891 gricuspgr 47928 isuspgrim 47906 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29426 df-clnbgr 47829 df-cusgr 29383 df-nbgr 29304 fusgrmaxsize 29436 |
| [Bollobas] p. 4 | Definition | df-upwlks 48144 df-wlks 29571 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 29522 finsumvtxdgeven 29524 fusgr1th 29523 fusgrvtxdgonume 29526 vtxdgoddnumeven 29525 |
| [Bollobas] p. 5 | Notation | df-pths 29685 |
| [Bollobas] p. 5 | Definition | df-crcts 29757 df-cycls 29758 df-trls 29662 df-wlkson 29572 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29030 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 48210 df-cllaw 48196 df-mgm 18540 df-mgm2 48229 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 48211 df-asslaw 48198 df-sgrp 18619 df-sgrp2 48231 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 48230 df-comlaw 48197 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18635 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 32997 mndlactf1o 33001 mndractf1 32999 mndractf1o 33002 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20146 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20064 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 33636 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 33640 assarrginv 33639 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 33681 fldextrspunfld 33679 fldextrspunlem1 33678 fldextrspunlem2 33680 fldextrspunlsp 33677 fldextrspunlsplem 33676 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 33492 dfufd2 33505 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7216 fcofo 7217 |
| [BourbakiTop1] p. | Remark | xnegmnf 13101 xnegpnf 13100 |
| [BourbakiTop1] p. | Remark | rexneg 13102 |
| [BourbakiTop1] p. | Remark 3 | ust0 24128 ustfilxp 24121 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 23998 |
| [BourbakiTop1] p. | Criterion | ishmeo 23667 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24191 iducn 24190 snfil 23772 |
| [BourbakiTop1] p. | Example 2 | neifil 23788 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 23975 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24211 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 33960 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23771 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24183 df-ust 24109 filintn0 23769 filn0 23770 istgp 23985 ucnprima 24189 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24194 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24205 df-usp 24165 df-utop 24139 trust 24137 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 33859 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23024 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23177 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24114 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24117 |
| [BourbakiTop1] p. | Property V_ii | innei 23033 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23041 neissex 23035 |
| [BourbakiTop1] p. | Proposition 1 | neips 23021 neiss 23017 ucncn 24192 ustund 24130 ustuqtop 24154 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23175 neiptopreu 23041 utop2nei 24158 utop3cls 24159 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24199 uspreg 24181 utopreg 24160 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23599 imasncls 23600 imasnopn 23598 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 23908 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24116 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24118 |
| [BourbakiTop1] p. | Property V_iii | elnei 23019 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24210 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24115 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24119 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23295 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23754 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 22802 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 33856 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 46079 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 46081 stoweid 46080 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 46018 stoweidlem10 46027 stoweidlem14 46031 stoweidlem15 46032 stoweidlem35 46052 stoweidlem36 46053 stoweidlem37 46054 stoweidlem38 46055 stoweidlem40 46057 stoweidlem41 46058 stoweidlem43 46060 stoweidlem44 46061 stoweidlem46 46063 stoweidlem5 46022 stoweidlem50 46067 stoweidlem52 46069 stoweidlem53 46070 stoweidlem55 46072 stoweidlem56 46073 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 46040 stoweidlem24 46041 stoweidlem27 46044 stoweidlem28 46045 stoweidlem30 46047 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 46051 stoweidlem59 46076 stoweidlem60 46077 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 46062 stoweidlem49 46066 stoweidlem7 46024 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 46048 stoweidlem39 46056 stoweidlem42 46059 stoweidlem48 46065 stoweidlem51 46068 stoweidlem54 46071 stoweidlem57 46074 stoweidlem58 46075 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 46042 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 46034 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 46028 stoweidlem13 46030 stoweidlem26 46043 stoweidlem61 46078 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 46035 |
| [Bruck] p. 1 | Section I.1 | df-clintop 48210 df-mgm 18540 df-mgm2 48229 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18619 df-sgrp2 48231 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 18944 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5171 |
| [Church] p. 129 | Section II.24 | df-ifp 1063 dfifp2 1064 |
| [Clemente] p. 10 | Definition IT | natded 30373 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30373 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30373 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30373 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30373 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30373 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30373 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30373 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30373 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30373 |
| [Clemente] p. 14 | Proof 5.11 | natded 30373 |
| [Clemente] p. 14 | Definition E` `n | natded 30373 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30375 ex-natded5.2 30374 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30378 ex-natded5.3 30377 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30380 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30382 ex-natded5.7 30381 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30384 ex-natded5.8 30383 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30386 ex-natded5.13 30385 |
| [Clemente] p. 32 | Definition I` `n | natded 30373 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30373 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30373 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30373 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30387 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30388 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30390 ex-natded9.26 30389 |
| [Cohen] p. 301 | Remark | relogoprlem 26520 |
| [Cohen] p. 301 | Property 2 | relogmul 26521 relogmuld 26554 |
| [Cohen] p. 301 | Property 3 | relogdiv 26522 relogdivd 26555 |
| [Cohen] p. 301 | Property 4 | relogexp 26525 |
| [Cohen] p. 301 | Property 1a | log1 26514 |
| [Cohen] p. 301 | Property 1b | loge 26515 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26717 |
| [Cohen4] p. 349 | Property | relogbf 26721 |
| [Cohen4] p. 352 | Definition | elogb 26700 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26707 |
| [Cohen4] p. 361 | Property 3 | logbrec 26712 relogbdiv 26709 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26705 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26710 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26698 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26699 |
| [Cohen4] p. 367 | Property | logbchbase 26701 |
| [Cohen4] p. 377 | Property 2 | logblt 26714 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34288 sxbrsigalem4 34290 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18455 acsinfd 18454 acsinfdimd 18456 acsmap2d 18453 acsmapd 18452 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34293 |
| [Connell] p. 57 | Definition | df-scmat 22399 df-scmatalt 48410 |
| [Conway] p. 4 | Definition | slerec 27753 slerecd 27754 |
| [Conway] p. 5 | Definition | addsval 27898 addsval2 27899 df-adds 27896 df-muls 28039 df-negs 27956 |
| [Conway] p. 7 | Theorem | 0slt1s 27766 |
| [Conway] p. 12 | Theorem 12 | pw2cut2 28375 |
| [Conway] p. 16 | Theorem 0(i) | ssltright 27809 |
| [Conway] p. 16 | Theorem 0(ii) | ssltleft 27808 |
| [Conway] p. 16 | Theorem 0(iii) | slerflex 27695 |
| [Conway] p. 17 | Theorem 3 | addsass 27941 addsassd 27942 addscom 27902 addscomd 27903 addsrid 27900 addsridd 27901 |
| [Conway] p. 17 | Definition | df-0s 27761 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 27979 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 27976 negsidd 27977 |
| [Conway] p. 18 | Theorem 5 | sleadd1 27925 sleadd1d 27931 |
| [Conway] p. 18 | Definition | df-1s 27762 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 27971 negscld 27972 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 27916 |
| [Conway] p. 19 | Note | mulsunif2 28102 |
| [Conway] p. 19 | Theorem 7 | addsdi 28087 addsdid 28088 addsdird 28089 mulnegs1d 28092 mulnegs2d 28093 mulsass 28098 mulsassd 28099 mulscom 28071 mulscomd 28072 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28066 mulscld 28067 |
| [Conway] p. 19 | Theorem 8(iii) | slemuld 28070 sltmul 28068 sltmuld 28069 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28076 mulsgt0d 28077 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28149 |
| [Conway] p. 23 | Theorem 11 | eqscut3 27758 |
| [Conway] p. 24 | Definition | df-reno 28389 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28394 remulscl 28397 renegscl 28393 |
| [Conway] p. 27 | Definition | df-ons 28182 elons2 28188 |
| [Conway] p. 27 | Theorem 14 | sltonex 28192 |
| [Conway] p. 28 | Theorem 15 | onscutlt 28194 onswe 28199 |
| [Conway] p. 29 | Remark | madebday 27838 newbday 27840 oldbday 27839 |
| [Conway] p. 29 | Definition | df-made 27781 df-new 27783 df-old 27782 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13757 |
| [Crawley] p. 1 | Definition of poset | df-poset 18211 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 39404 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 40208 dalaw 39904 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 41979 |
| [Crawley] p. 111 | Definition of set W | df-watsN 40008 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 40124 df-ldil 40122 isldil 40128 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 40123 df-trnN 40125 isltrn 40137 ltrnu 40139 |
| [Crawley] p. 112 | Lemma A | cdlema1N 39809 cdlema2N 39810 exatleN 39422 |
| [Crawley] p. 112 | Lemma B | 1cvrat 39494 cdlemb 39812 cdlemb2 40059 cdlemb3 40624 idltrn 40168 l1cvat 39073 lhpat 40061 lhpat2 40063 lshpat 39074 ltrnel 40157 ltrnmw 40169 |
| [Crawley] p. 112 | Lemma C | cdlemc1 40209 cdlemc2 40210 ltrnnidn 40192 trlat 40187 trljat1 40184 trljat2 40185 trljat3 40186 trlne 40203 trlnidat 40191 trlnle 40204 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 40009 |
| [Crawley] p. 113 | Lemma C | cdlemc 40215 cdlemc3 40211 cdlemc4 40212 |
| [Crawley] p. 113 | Lemma D | cdlemd 40225 cdlemd1 40216 cdlemd2 40217 cdlemd3 40218 cdlemd4 40219 cdlemd5 40220 cdlemd6 40221 cdlemd7 40222 cdlemd8 40223 cdlemd9 40224 cdleme31sde 40403 cdleme31se 40400 cdleme31se2 40401 cdleme31snd 40404 cdleme32a 40459 cdleme32b 40460 cdleme32c 40461 cdleme32d 40462 cdleme32e 40463 cdleme32f 40464 cdleme32fva 40455 cdleme32fva1 40456 cdleme32fvcl 40458 cdleme32le 40465 cdleme48fv 40517 cdleme4gfv 40525 cdleme50eq 40559 cdleme50f 40560 cdleme50f1 40561 cdleme50f1o 40564 cdleme50laut 40565 cdleme50ldil 40566 cdleme50lebi 40558 cdleme50rn 40563 cdleme50rnlem 40562 cdlemeg49le 40529 cdlemeg49lebilem 40557 |
| [Crawley] p. 113 | Lemma E | cdleme 40578 cdleme00a 40227 cdleme01N 40239 cdleme02N 40240 cdleme0a 40229 cdleme0aa 40228 cdleme0b 40230 cdleme0c 40231 cdleme0cp 40232 cdleme0cq 40233 cdleme0dN 40234 cdleme0e 40235 cdleme0ex1N 40241 cdleme0ex2N 40242 cdleme0fN 40236 cdleme0gN 40237 cdleme0moN 40243 cdleme1 40245 cdleme10 40272 cdleme10tN 40276 cdleme11 40288 cdleme11a 40278 cdleme11c 40279 cdleme11dN 40280 cdleme11e 40281 cdleme11fN 40282 cdleme11g 40283 cdleme11h 40284 cdleme11j 40285 cdleme11k 40286 cdleme11l 40287 cdleme12 40289 cdleme13 40290 cdleme14 40291 cdleme15 40296 cdleme15a 40292 cdleme15b 40293 cdleme15c 40294 cdleme15d 40295 cdleme16 40303 cdleme16aN 40277 cdleme16b 40297 cdleme16c 40298 cdleme16d 40299 cdleme16e 40300 cdleme16f 40301 cdleme16g 40302 cdleme19a 40321 cdleme19b 40322 cdleme19c 40323 cdleme19d 40324 cdleme19e 40325 cdleme19f 40326 cdleme1b 40244 cdleme2 40246 cdleme20aN 40327 cdleme20bN 40328 cdleme20c 40329 cdleme20d 40330 cdleme20e 40331 cdleme20f 40332 cdleme20g 40333 cdleme20h 40334 cdleme20i 40335 cdleme20j 40336 cdleme20k 40337 cdleme20l 40340 cdleme20l1 40338 cdleme20l2 40339 cdleme20m 40341 cdleme20y 40320 cdleme20zN 40319 cdleme21 40355 cdleme21d 40348 cdleme21e 40349 cdleme22a 40358 cdleme22aa 40357 cdleme22b 40359 cdleme22cN 40360 cdleme22d 40361 cdleme22e 40362 cdleme22eALTN 40363 cdleme22f 40364 cdleme22f2 40365 cdleme22g 40366 cdleme23a 40367 cdleme23b 40368 cdleme23c 40369 cdleme26e 40377 cdleme26eALTN 40379 cdleme26ee 40378 cdleme26f 40381 cdleme26f2 40383 cdleme26f2ALTN 40382 cdleme26fALTN 40380 cdleme27N 40387 cdleme27a 40385 cdleme27cl 40384 cdleme28c 40390 cdleme3 40255 cdleme30a 40396 cdleme31fv 40408 cdleme31fv1 40409 cdleme31fv1s 40410 cdleme31fv2 40411 cdleme31id 40412 cdleme31sc 40402 cdleme31sdnN 40405 cdleme31sn 40398 cdleme31sn1 40399 cdleme31sn1c 40406 cdleme31sn2 40407 cdleme31so 40397 cdleme35a 40466 cdleme35b 40468 cdleme35c 40469 cdleme35d 40470 cdleme35e 40471 cdleme35f 40472 cdleme35fnpq 40467 cdleme35g 40473 cdleme35h 40474 cdleme35h2 40475 cdleme35sn2aw 40476 cdleme35sn3a 40477 cdleme36a 40478 cdleme36m 40479 cdleme37m 40480 cdleme38m 40481 cdleme38n 40482 cdleme39a 40483 cdleme39n 40484 cdleme3b 40247 cdleme3c 40248 cdleme3d 40249 cdleme3e 40250 cdleme3fN 40251 cdleme3fa 40254 cdleme3g 40252 cdleme3h 40253 cdleme4 40256 cdleme40m 40485 cdleme40n 40486 cdleme40v 40487 cdleme40w 40488 cdleme41fva11 40495 cdleme41sn3aw 40492 cdleme41sn4aw 40493 cdleme41snaw 40494 cdleme42a 40489 cdleme42b 40496 cdleme42c 40490 cdleme42d 40491 cdleme42e 40497 cdleme42f 40498 cdleme42g 40499 cdleme42h 40500 cdleme42i 40501 cdleme42k 40502 cdleme42ke 40503 cdleme42keg 40504 cdleme42mN 40505 cdleme42mgN 40506 cdleme43aN 40507 cdleme43bN 40508 cdleme43cN 40509 cdleme43dN 40510 cdleme5 40258 cdleme50ex 40577 cdleme50ltrn 40575 cdleme51finvN 40574 cdleme51finvfvN 40573 cdleme51finvtrN 40576 cdleme6 40259 cdleme7 40267 cdleme7a 40261 cdleme7aa 40260 cdleme7b 40262 cdleme7c 40263 cdleme7d 40264 cdleme7e 40265 cdleme7ga 40266 cdleme8 40268 cdleme8tN 40273 cdleme9 40271 cdleme9a 40269 cdleme9b 40270 cdleme9tN 40275 cdleme9taN 40274 cdlemeda 40316 cdlemedb 40315 cdlemednpq 40317 cdlemednuN 40318 cdlemefr27cl 40421 cdlemefr32fva1 40428 cdlemefr32fvaN 40427 cdlemefrs32fva 40418 cdlemefrs32fva1 40419 cdlemefs27cl 40431 cdlemefs32fva1 40441 cdlemefs32fvaN 40440 cdlemesner 40314 cdlemeulpq 40238 |
| [Crawley] p. 114 | Lemma E | 4atex 40094 4atexlem7 40093 cdleme0nex 40308 cdleme17a 40304 cdleme17c 40306 cdleme17d 40516 cdleme17d1 40307 cdleme17d2 40513 cdleme18a 40309 cdleme18b 40310 cdleme18c 40311 cdleme18d 40313 cdleme4a 40257 |
| [Crawley] p. 115 | Lemma E | cdleme21a 40343 cdleme21at 40346 cdleme21b 40344 cdleme21c 40345 cdleme21ct 40347 cdleme21f 40350 cdleme21g 40351 cdleme21h 40352 cdleme21i 40353 cdleme22gb 40312 |
| [Crawley] p. 116 | Lemma F | cdlemf 40581 cdlemf1 40579 cdlemf2 40580 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 40585 cdlemg16 40675 cdlemg28 40722 cdlemg28a 40711 cdlemg28b 40721 cdlemg3a 40615 cdlemg42 40747 cdlemg43 40748 cdlemg44 40751 cdlemg44a 40749 cdlemg46 40753 cdlemg47 40754 cdlemg9 40652 ltrnco 40737 ltrncom 40756 tgrpabl 40769 trlco 40745 |
| [Crawley] p. 116 | Definition of G | df-tgrp 40761 |
| [Crawley] p. 117 | Lemma G | cdlemg17 40695 cdlemg17b 40680 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 40774 df-edring 40775 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 40778 |
| [Crawley] p. 118 | Remark | tendopltp 40798 |
| [Crawley] p. 118 | Lemma H | cdlemh 40835 cdlemh1 40833 cdlemh2 40834 |
| [Crawley] p. 118 | Lemma I | cdlemi 40838 cdlemi1 40836 cdlemi2 40837 |
| [Crawley] p. 118 | Lemma J | cdlemj1 40839 cdlemj2 40840 cdlemj3 40841 tendocan 40842 |
| [Crawley] p. 118 | Lemma K | cdlemk 40992 cdlemk1 40849 cdlemk10 40861 cdlemk11 40867 cdlemk11t 40964 cdlemk11ta 40947 cdlemk11tb 40949 cdlemk11tc 40963 cdlemk11u-2N 40907 cdlemk11u 40889 cdlemk12 40868 cdlemk12u-2N 40908 cdlemk12u 40890 cdlemk13-2N 40894 cdlemk13 40870 cdlemk14-2N 40896 cdlemk14 40872 cdlemk15-2N 40897 cdlemk15 40873 cdlemk16-2N 40898 cdlemk16 40875 cdlemk16a 40874 cdlemk17-2N 40899 cdlemk17 40876 cdlemk18-2N 40904 cdlemk18-3N 40918 cdlemk18 40886 cdlemk19-2N 40905 cdlemk19 40887 cdlemk19u 40988 cdlemk1u 40877 cdlemk2 40850 cdlemk20-2N 40910 cdlemk20 40892 cdlemk21-2N 40909 cdlemk21N 40891 cdlemk22-3 40919 cdlemk22 40911 cdlemk23-3 40920 cdlemk24-3 40921 cdlemk25-3 40922 cdlemk26-3 40924 cdlemk26b-3 40923 cdlemk27-3 40925 cdlemk28-3 40926 cdlemk29-3 40929 cdlemk3 40851 cdlemk30 40912 cdlemk31 40914 cdlemk32 40915 cdlemk33N 40927 cdlemk34 40928 cdlemk35 40930 cdlemk36 40931 cdlemk37 40932 cdlemk38 40933 cdlemk39 40934 cdlemk39u 40986 cdlemk4 40852 cdlemk41 40938 cdlemk42 40959 cdlemk42yN 40962 cdlemk43N 40981 cdlemk45 40965 cdlemk46 40966 cdlemk47 40967 cdlemk48 40968 cdlemk49 40969 cdlemk5 40854 cdlemk50 40970 cdlemk51 40971 cdlemk52 40972 cdlemk53 40975 cdlemk54 40976 cdlemk55 40979 cdlemk55u 40984 cdlemk56 40989 cdlemk5a 40853 cdlemk5auN 40878 cdlemk5u 40879 cdlemk6 40855 cdlemk6u 40880 cdlemk7 40866 cdlemk7u-2N 40906 cdlemk7u 40888 cdlemk8 40856 cdlemk9 40857 cdlemk9bN 40858 cdlemki 40859 cdlemkid 40954 cdlemkj-2N 40900 cdlemkj 40881 cdlemksat 40864 cdlemksel 40863 cdlemksv 40862 cdlemksv2 40865 cdlemkuat 40884 cdlemkuel-2N 40902 cdlemkuel-3 40916 cdlemkuel 40883 cdlemkuv-2N 40901 cdlemkuv2-2 40903 cdlemkuv2-3N 40917 cdlemkuv2 40885 cdlemkuvN 40882 cdlemkvcl 40860 cdlemky 40944 cdlemkyyN 40980 tendoex 40993 |
| [Crawley] p. 120 | Remark | dva1dim 41003 |
| [Crawley] p. 120 | Lemma L | cdleml1N 40994 cdleml2N 40995 cdleml3N 40996 cdleml4N 40997 cdleml5N 40998 cdleml6 40999 cdleml7 41000 cdleml8 41001 cdleml9 41002 dia1dim 41079 |
| [Crawley] p. 120 | Lemma M | dia11N 41066 diaf11N 41067 dialss 41064 diaord 41065 dibf11N 41179 djajN 41155 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 41050 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 41136 dia2dimlem1 41082 dia2dimlem2 41083 dia2dimlem3 41084 dia2dimlem4 41085 dia2dimlem5 41086 diaf1oN 41148 diarnN 41147 dvheveccl 41130 dvhopN 41134 |
| [Crawley] p. 121 | Lemma N | cdlemn 41230 cdlemn10 41224 cdlemn11 41229 cdlemn11a 41225 cdlemn11b 41226 cdlemn11c 41227 cdlemn11pre 41228 cdlemn2 41213 cdlemn2a 41214 cdlemn3 41215 cdlemn4 41216 cdlemn4a 41217 cdlemn5 41219 cdlemn5pre 41218 cdlemn6 41220 cdlemn7 41221 cdlemn8 41222 cdlemn9 41223 diclspsn 41212 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 41191 |
| [Crawley] p. 122 | Lemma N | dih11 41283 dihf11 41285 dihjust 41235 dihjustlem 41234 dihord 41282 dihord1 41236 dihord10 41241 dihord11b 41240 dihord11c 41242 dihord2 41245 dihord2a 41237 dihord2b 41238 dihord2cN 41239 dihord2pre 41243 dihord2pre2 41244 dihordlem6 41231 dihordlem7 41232 dihordlem7b 41233 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 41248 dihfval 41249 dihval 41250 |
| [Diestel] p. 3 | Definition | df-gric 47891 df-grim 47888 isuspgrim 47906 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29383 df-nbgr 29304 |
| [Diestel] p. 3 | Definition by | df-grisom 47887 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 47871 df-subgr 29239 uhgrspan1 29274 uhgrspansubgr 29262 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 29526 vtxdgoddnumeven 29525 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29030 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 33867 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 33879 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 33871 zarcls1 33872 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 33882 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 33885 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 33888 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3903 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9532 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8747 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9540 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9865 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10438 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5241 |
| [Enderton] p. 19 | Definition | df-tp 4579 |
| [Enderton] p. 26 | Exercise 5 | unissb 4889 |
| [Enderton] p. 26 | Exercise 10 | pwel 5317 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5507 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5025 iinin2 5024 iinun2 5019 iunin1 5018 iunin1f 32527 iunin2 5017 uniin1 32521 uniin2 32522 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5023 iundif2 5020 |
| [Enderton] p. 32 | Exercise 20 | unineq 4236 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5044 |
| [Enderton] p. 33 | Exercise 25 | iununi 5045 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5052 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7699 iunpwss 5053 |
| [Enderton] p. 36 | Definition | opthwiener 5452 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5389 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4894 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5408 rnex 7835 rnexg 7827 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5852 rnuni 6092 |
| [Enderton] p. 42 | Definition of a function | dffun7 6504 dffun8 6505 |
| [Enderton] p. 43 | Definition of function value | funfv2 6905 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6546 |
| [Enderton] p. 44 | Definition (d) | dfima2 6008 dfima3 6009 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6914 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10356 ac7g 10357 df-ac 9999 dfac2 10015 dfac2a 10013 dfac2b 10014 dfac3 10004 dfac7 10016 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7175 |
| [Enderton] p. 52 | Definition | df-map 8747 |
| [Enderton] p. 53 | Exercise 21 | coass 6209 |
| [Enderton] p. 53 | Exercise 27 | dmco 6198 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6553 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6048 |
| [Enderton] p. 54 | Remark | ixpf 8839 ixpssmap 8851 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8817 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10366 ac9s 10376 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 38626 erref 8637 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 38629 erthi 8673 |
| [Enderton] p. 57 | Definition | df-ec 8619 |
| [Enderton] p. 58 | Definition | df-qs 8623 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8619 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5848 |
| [Enderton] p. 68 | Definition of successor | df-suc 6308 |
| [Enderton] p. 71 | Definition | df-tr 5197 dftr4 5202 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6383 unisucg 6382 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6383 unisucg 6382 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5211 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5213 trintALT 44892 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8514 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8516 onasuc 8438 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7344 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8515 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8517 onmsuc 8439 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8532 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8519 nnacom 8527 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8533 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8534 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8536 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8520 nnmsucr 8535 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8548 |
| [Enderton] p. 129 | Definition | df-en 8865 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7295 |
| [Enderton] p. 133 | Exercise 1 | xpomen 9898 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16114 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9111 |
| [Enderton] p. 135 | Corollary 6C | php3 9113 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9110 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9141 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9143 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9073 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9077 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9049 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10063 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10064 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10059 dju1en 10055 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9222 unifi 9223 unifi2 9224 |
| [Enderton] p. 144 | Corollary 6K | undif2 4425 unfi 9075 unfi2 9189 |
| [Enderton] p. 145 | Figure 38 | ffoss 7873 |
| [Enderton] p. 145 | Definition | df-dom 8866 |
| [Enderton] p. 146 | Example 1 | domen 8879 domeng 8880 |
| [Enderton] p. 146 | Example 3 | nndomo 9121 nnsdom 9539 nnsdomg 9178 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10067 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9050 xpdom1 8984 xpdom1g 8982 xpdom2g 8981 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9056 |
| [Enderton] p. 151 | Theorem 6M | zorn 10390 zorng 10387 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10375 dfac5 10012 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10458 |
| [Enderton] p. 164 | Example | infdif 10091 |
| [Enderton] p. 168 | Definition | df-po 5522 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6417 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6349 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6416 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6357 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7764 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7709 |
| [Enderton] p. 194 | Remark | onprc 7706 |
| [Enderton] p. 194 | Exercise 16 | suc11 6411 |
| [Enderton] p. 197 | Definition | df-card 9824 |
| [Enderton] p. 197 | Theorem 7P | carden 10434 |
| [Enderton] p. 200 | Exercise 25 | tfis 7780 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9661 |
| [Enderton] p. 202 | Definition | df-r1 9649 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9671 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9752 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9491 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9742 rankprb 9736 rankpw 9728 rankpwi 9708 rankuniss 9751 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9503 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9504 |
| [Enderton] p. 212 | Definition of aleph | alephval3 9993 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 9959 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 9973 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8256 |
| [Enderton] p. 222 | Definition of kard | karden 9780 kardex 9779 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8507 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8509 |
| [Enderton] p. 240 | Exercise 25 | oarec 8472 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10133 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17540 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17482 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18451 mrieqv2d 17537 mrieqvd 17536 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17541 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17546 mreexexlem2d 17543 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18457 mreexfidimd 17548 |
| [Frege1879] p. 11 | Statement | df3or2 43780 |
| [Frege1879] p. 12 | Statement | df3an2 43781 dfxor4 43778 dfxor5 43779 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 43802 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 43803 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 43807 |
| [Frege1879] p. 31 | Proposition 4 | frege4 43811 |
| [Frege1879] p. 32 | Proposition 5 | frege5 43812 |
| [Frege1879] p. 33 | Proposition 6 | frege6 43818 |
| [Frege1879] p. 34 | Proposition 7 | frege7 43820 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 43821 axfrege8 43819 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 90 wl-luk-pm2.04 37458 |
| [Frege1879] p. 35 | Proposition 9 | frege9 43824 |
| [Frege1879] p. 36 | Proposition 10 | frege10 43832 |
| [Frege1879] p. 36 | Proposition 11 | frege11 43826 |
| [Frege1879] p. 37 | Proposition 12 | frege12 43825 |
| [Frege1879] p. 37 | Proposition 13 | frege13 43834 |
| [Frege1879] p. 37 | Proposition 14 | frege14 43835 |
| [Frege1879] p. 38 | Proposition 15 | frege15 43838 |
| [Frege1879] p. 38 | Proposition 16 | frege16 43828 |
| [Frege1879] p. 39 | Proposition 17 | frege17 43833 |
| [Frege1879] p. 39 | Proposition 18 | frege18 43830 |
| [Frege1879] p. 39 | Proposition 19 | frege19 43836 |
| [Frege1879] p. 40 | Proposition 20 | frege20 43840 |
| [Frege1879] p. 40 | Proposition 21 | frege21 43839 |
| [Frege1879] p. 41 | Proposition 22 | frege22 43831 |
| [Frege1879] p. 42 | Proposition 23 | frege23 43837 |
| [Frege1879] p. 42 | Proposition 24 | frege24 43827 |
| [Frege1879] p. 42 | Proposition 25 | frege25 43829 rp-frege25 43817 |
| [Frege1879] p. 42 | Proposition 26 | frege26 43822 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 43842 |
| [Frege1879] p. 43 | Proposition 27 | frege27 43823 |
| [Frege1879] p. 43 | Proposition 28 | con3 153 |
| [Frege1879] p. 43 | Proposition 29 | frege29 43843 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 43846 axfrege31 43845 |
| [Frege1879] p. 44 | Proposition 30 | frege30 43844 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 130 |
| [Frege1879] p. 44 | Proposition 32 | frege32 43847 |
| [Frege1879] p. 44 | Proposition 33 | frege33 43848 |
| [Frege1879] p. 45 | Proposition 34 | frege34 43849 |
| [Frege1879] p. 45 | Proposition 35 | frege35 43850 |
| [Frege1879] p. 45 | Proposition 36 | frege36 43851 |
| [Frege1879] p. 46 | Proposition 37 | frege37 43852 |
| [Frege1879] p. 46 | Proposition 38 | frege38 43853 |
| [Frege1879] p. 46 | Proposition 39 | frege39 43854 |
| [Frege1879] p. 46 | Proposition 40 | frege40 43855 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 43857 axfrege41 43856 |
| [Frege1879] p. 47 | Proposition 41 | notnot 142 |
| [Frege1879] p. 47 | Proposition 42 | frege42 43858 |
| [Frege1879] p. 47 | Proposition 43 | frege43 43859 |
| [Frege1879] p. 47 | Proposition 44 | frege44 43860 |
| [Frege1879] p. 47 | Proposition 45 | frege45 43861 |
| [Frege1879] p. 48 | Proposition 46 | frege46 43862 |
| [Frege1879] p. 48 | Proposition 47 | frege47 43863 |
| [Frege1879] p. 49 | Proposition 48 | frege48 43864 |
| [Frege1879] p. 49 | Proposition 49 | frege49 43865 |
| [Frege1879] p. 49 | Proposition 50 | frege50 43866 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 43869 ax-frege52c 43900 frege52aid 43870 frege52b 43901 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 43874 ax-frege54c 43904 frege54b 43905 |
| [Frege1879] p. 50 | Proposition 51 | frege51 43867 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3741 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 43872 frege53aid 43871 frege53b 43902 frege53c 43926 |
| [Frege1879] p. 50 | Proposition 54 | biid 261 eqid 2730 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 43880 frege55aid 43877 frege55b 43909 frege55c 43930 frege55cor1a 43881 frege55lem2a 43879 frege55lem2b 43908 frege55lem2c 43929 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 43883 frege56aid 43882 frege56b 43910 frege56c 43931 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 43887 ax-frege58b 43913 frege58bid 43914 frege58c 43933 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 43885 frege57aid 43884 frege57b 43911 frege57c 43932 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3752 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 43889 frege59b 43916 frege59c 43934 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 43890 frege60b 43917 frege60c 43935 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 43891 frege61b 43918 frege61c 43936 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 43892 frege62b 43919 frege62c 43937 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 43893 frege63b 43920 frege63c 43938 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 43894 frege64b 43921 frege64c 43939 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 43895 frege65b 43922 frege65c 43940 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 43896 frege66b 43923 frege66c 43941 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 43897 frege67b 43924 frege67c 43942 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 43898 frege68b 43925 frege68c 43943 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 43944 |
| [Frege1879] p. 58 | Proposition 70 | frege70 43945 |
| [Frege1879] p. 59 | Proposition 71 | frege71 43946 |
| [Frege1879] p. 59 | Proposition 72 | frege72 43947 |
| [Frege1879] p. 59 | Proposition 73 | frege73 43948 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 43951 |
| [Frege1879] p. 60 | Proposition 74 | frege74 43949 |
| [Frege1879] p. 60 | Proposition 75 | frege75 43950 |
| [Frege1879] p. 62 | Proposition 77 | frege77 43952 frege77d 43758 |
| [Frege1879] p. 63 | Proposition 78 | frege78 43953 |
| [Frege1879] p. 63 | Proposition 79 | frege79 43954 |
| [Frege1879] p. 63 | Proposition 80 | frege80 43955 |
| [Frege1879] p. 63 | Proposition 81 | frege81 43956 frege81d 43759 |
| [Frege1879] p. 64 | Proposition 82 | frege82 43957 |
| [Frege1879] p. 65 | Proposition 83 | frege83 43958 frege83d 43760 |
| [Frege1879] p. 65 | Proposition 84 | frege84 43959 |
| [Frege1879] p. 66 | Proposition 85 | frege85 43960 |
| [Frege1879] p. 66 | Proposition 86 | frege86 43961 |
| [Frege1879] p. 66 | Proposition 87 | frege87 43962 frege87d 43762 |
| [Frege1879] p. 67 | Proposition 88 | frege88 43963 |
| [Frege1879] p. 68 | Proposition 89 | frege89 43964 |
| [Frege1879] p. 68 | Proposition 90 | frege90 43965 |
| [Frege1879] p. 68 | Proposition 91 | frege91 43966 frege91d 43763 |
| [Frege1879] p. 69 | Proposition 92 | frege92 43967 |
| [Frege1879] p. 70 | Proposition 93 | frege93 43968 |
| [Frege1879] p. 70 | Proposition 94 | frege94 43969 |
| [Frege1879] p. 70 | Proposition 95 | frege95 43970 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 43974 |
| [Frege1879] p. 71 | Proposition 96 | frege96 43971 frege96d 43761 |
| [Frege1879] p. 71 | Proposition 97 | frege97 43972 frege97d 43764 |
| [Frege1879] p. 71 | Proposition 98 | frege98 43973 frege98d 43765 |
| [Frege1879] p. 72 | Proposition 100 | frege100 43975 |
| [Frege1879] p. 72 | Proposition 101 | frege101 43976 |
| [Frege1879] p. 72 | Proposition 102 | frege102 43977 frege102d 43766 |
| [Frege1879] p. 73 | Proposition 103 | frege103 43978 |
| [Frege1879] p. 73 | Proposition 104 | frege104 43979 |
| [Frege1879] p. 73 | Proposition 105 | frege105 43980 |
| [Frege1879] p. 73 | Proposition 106 | frege106 43981 frege106d 43767 |
| [Frege1879] p. 74 | Proposition 107 | frege107 43982 |
| [Frege1879] p. 74 | Proposition 108 | frege108 43983 frege108d 43768 |
| [Frege1879] p. 74 | Proposition 109 | frege109 43984 frege109d 43769 |
| [Frege1879] p. 75 | Proposition 110 | frege110 43985 |
| [Frege1879] p. 75 | Proposition 111 | frege111 43986 frege111d 43771 |
| [Frege1879] p. 76 | Proposition 112 | frege112 43987 |
| [Frege1879] p. 76 | Proposition 113 | frege113 43988 |
| [Frege1879] p. 76 | Proposition 114 | frege114 43989 frege114d 43770 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 43990 |
| [Frege1879] p. 77 | Proposition 116 | frege116 43991 |
| [Frege1879] p. 78 | Proposition 117 | frege117 43992 |
| [Frege1879] p. 78 | Proposition 118 | frege118 43993 |
| [Frege1879] p. 78 | Proposition 119 | frege119 43994 |
| [Frege1879] p. 78 | Proposition 120 | frege120 43995 |
| [Frege1879] p. 79 | Proposition 121 | frege121 43996 |
| [Frege1879] p. 79 | Proposition 122 | frege122 43997 frege122d 43772 |
| [Frege1879] p. 79 | Proposition 123 | frege123 43998 |
| [Frege1879] p. 80 | Proposition 124 | frege124 43999 frege124d 43773 |
| [Frege1879] p. 81 | Proposition 125 | frege125 44000 |
| [Frege1879] p. 81 | Proposition 126 | frege126 44001 frege126d 43774 |
| [Frege1879] p. 82 | Proposition 127 | frege127 44002 |
| [Frege1879] p. 83 | Proposition 128 | frege128 44003 |
| [Frege1879] p. 83 | Proposition 129 | frege129 44004 frege129d 43775 |
| [Frege1879] p. 84 | Proposition 130 | frege130 44005 |
| [Frege1879] p. 85 | Proposition 131 | frege131 44006 frege131d 43776 |
| [Frege1879] p. 86 | Proposition 132 | frege132 44007 |
| [Frege1879] p. 86 | Proposition 133 | frege133 44008 frege133d 43777 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 46330 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 46653 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 46353 |
| [Fremlin1] p. 14 | Definition 112A | ismea 46468 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 46488 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 46479 meadjunre 46493 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 46480 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 46481 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 46477 meaiunle 46486 meaiunlelem 46485 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 46498 meaiuninc2 46499 meaiuninc3 46502 meaiuninc3v 46501 meaiunincf 46500 meaiuninclem 46497 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 46504 meaiininc2 46505 meaiininclem 46503 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 46523 caragendifcl 46531 caratheodory 46545 omelesplit 46535 |
| [Fremlin1] p. 19 | Definition 113A | isome 46511 isomennd 46548 isomenndlem 46547 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 46533 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 46552 voncmpl 46638 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 46515 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 46540 carageniuncllem1 46538 carageniuncllem2 46539 caragenuncl 46530 caragenuncllem 46529 caragenunicl 46541 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 46549 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 46543 caratheodorylem2 46544 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 46552 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 46611 hoidmv1lelem1 46608 hoidmv1lelem2 46609 hoidmv1lelem3 46610 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 46655 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 46611 hoidmvle 46617 hoidmvlelem1 46612 hoidmvlelem2 46613 hoidmvlelem3 46614 hoidmvlelem4 46615 hoidmvlelem5 46616 hsphoidmvle2 46602 hsphoif 46593 hsphoival 46596 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 46565 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 46573 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 46600 hoidmvn0val 46601 hoidmvval 46594 hoidmvval0 46604 hoidmvval0b 46607 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 46605 hsphoidmvle 46603 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 46554 df-voln 46556 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 46621 ovn0 46583 ovn0lem 46582 ovnf 46580 ovnome 46590 ovnssle 46578 ovnsslelem 46577 ovnsupge0 46574 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 46620 ovnhoilem1 46618 ovnhoilem2 46619 vonhoi 46684 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 46637 hoidifhspf 46635 hoidifhspval 46625 hoidifhspval2 46632 hoidifhspval3 46636 hspmbl 46646 hspmbllem1 46643 hspmbllem2 46644 hspmbllem3 46645 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 46638 vonmea 46591 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 46589 ovnsubadd2 46663 ovnsubadd2lem 46662 ovnsubaddlem1 46587 ovnsubaddlem2 46588 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 46648 hoimbl2 46682 hoimbllem 46647 hspdifhsp 46633 opnvonmbl 46651 opnvonmbllem2 46650 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 46653 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 46696 iccvonmbllem 46695 ioovonmbl 46694 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 46702 vonicclem2 46701 vonioo 46699 vonioolem2 46698 vonn0icc 46705 vonn0icc2 46709 vonn0ioo 46704 vonn0ioo2 46707 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 46706 snvonmbl 46703 vonct 46710 vonsn 46708 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 46376 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 46375 subsaliuncllem 46374 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 46742 salpreimalegt 46726 salpreimaltle 46743 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 46745 issmff 46751 issmflem 46744 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 46762 issmflelem 46761 smfpreimale 46771 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 46773 issmfgtlem 46772 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 46713 issmf 46745 issmff 46751 issmfge 46787 issmfgelem 46786 issmfgt 46773 issmfgtlem 46772 issmfle 46762 issmflelem 46761 issmflem 46744 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 46724 salpreimagtlt 46747 salpreimalelt 46746 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 46787 issmfgelem 46786 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 46770 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 46768 cnfsmf 46757 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 46784 decsmflem 46783 incsmf 46759 incsmflem 46758 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 46718 pimconstlt1 46719 smfconst 46766 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 46782 smfaddlem1 46780 smfaddlem2 46781 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 46813 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 46812 smfmullem1 46808 smfmullem2 46809 smfmullem3 46810 smfmullem4 46811 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 46814 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 46817 smfpimbor1lem2 46816 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 46819 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 46807 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 46806 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 46815 smfresal 46805 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 46794 smflim2 46823 smflimlem1 46788 smflimlem2 46789 smflimlem3 46790 smflimlem4 46791 smflimlem5 46792 smflimlem6 46793 smflimmpt 46827 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 46831 smfsuplem1 46828 smfsuplem2 46829 smfsuplem3 46830 smfsupmpt 46832 smfsupxr 46833 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 46835 smfinflem 46834 smfinfmpt 46836 |
| [Fremlin1] p. 39 | Remark 121G | smflim 46794 smflim2 46823 smflimmpt 46827 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 46825 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 46855 smfdivdmmbl2 46858 smfinfdmmbl 46866 smfinfdmmbllem 46865 smfsupdmmbl 46862 smfsupdmmbllem 46861 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 46845 smflimsuplem2 46838 smflimsuplem6 46842 smflimsuplem7 46843 smflimsuplem8 46844 smflimsupmpt 46846 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 46848 smfliminflem 46847 smfliminfmpt 46849 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 46713 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 46859 fsupdm2 46860 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 46850 adddmmbl2 46851 finfdm 46863 finfdm2 46864 fsupdm 46859 fsupdm2 46860 muldmmbl 46852 muldmmbl2 46853 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 46863 finfdm2 46864 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25457 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25500 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25510 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 37717 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 37720 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9523 inf1 9507 inf2 9508 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10794 enqer 10804 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10799 df-nq 10795 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10791 df-plq 10797 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7578 df-mpq 10792 df-mq 10798 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10800 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10858 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10859 ltbtwnnq 10861 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10854 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10855 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10862 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10864 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 10876 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 10878 |
| [Gleason] p. 122 | Definition | df-1p 10865 |
| [Gleason] p. 122 | Remark (1) | prub 10877 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 10916 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10868 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 10915 psslinpr 10914 supexpr 10937 suplem1pr 10935 suplem2pr 10936 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 10901 addclprlem1 10899 addclprlem2 10900 df-plp 10866 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 10905 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 10904 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 10917 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 10926 ltexprlem1 10919 ltexprlem2 10920 ltexprlem3 10921 ltexprlem4 10922 ltexprlem5 10923 ltexprlem6 10924 ltexprlem7 10925 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 10928 ltaprlem 10927 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 10929 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 10930 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10867 mulclpr 10903 mulclprlem 10902 reclem2pr 10931 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 10912 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 10907 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 10906 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 10911 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 10934 reclem3pr 10932 reclem4pr 10933 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 10938 enrer 10946 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 10943 df-1r 10944 df-nr 10939 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 10941 df-plr 10940 negexsr 10985 recexsr 10990 recexsrlem 10986 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 10942 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12112 creur 12111 cru 12109 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11071 axcnre 11047 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15014 crimd 15131 crimi 15092 crre 15013 crred 15130 crrei 15091 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15016 remimd 15097 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15183 absval2d 15347 absval2i 15297 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15040 cjaddd 15119 cjaddi 15087 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15041 cjmuld 15120 cjmuli 15088 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15039 cjcjd 15098 cjcji 15070 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15038 cjreb 15022 cjrebd 15101 cjrebi 15073 cjred 15125 rere 15021 rereb 15019 rerebd 15100 rerebi 15072 rered 15123 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15047 addcjd 15111 addcji 15082 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15137 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15178 abscjd 15352 abscji 15301 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15188 abs00d 15348 abs00i 15298 absne0d 15349 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15221 releabsd 15353 releabsi 15302 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15193 absmuld 15356 absmuli 15304 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15181 sqabsaddi 15305 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15230 abstrid 15358 abstrii 15308 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 13961 exp0 13964 expp1 13967 expp1d 14046 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26608 cxpaddd 26646 expadd 14003 expaddd 14047 expaddz 14005 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26617 cxpmuld 26666 expmul 14006 expmuld 14048 expmulz 14007 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26614 mulcxpd 26657 mulexp 14000 mulexpd 14060 mulexpz 14001 |
| [Gleason] p. 140 | Exercise 1 | znnen 16113 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13401 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15531 rlimadd 15542 rlimdiv 15545 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15533 rlimsub 15543 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15532 rlimmul 15544 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15536 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15482 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15503 climcj 15504 climim 15506 climre 15505 rlimabs 15508 rlimcj 15509 rlimim 15511 rlimre 15510 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11143 df-xr 11142 ltxr 13006 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15370 limsupval 15373 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15569 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15578 caucvgb 15579 caucvgbf 45506 caucvgr 15575 climcau 15570 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15715 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15782 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15235 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13724 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21278 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24251 xmet0 24250 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24267 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24258 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24260 mstri 24377 xmettri 24259 xmstri 24376 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24290 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23556 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25230 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24448 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24774 addcn2 15493 mulcn 24776 mulcn2 15495 subcn 24775 subcn2 15494 |
| [Gleason] p. 295 | Remark | bcval3 14205 bcval4 14206 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14220 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14203 df-bc 14202 |
| [Gleason] p. 296 | Remark | bcn0 14209 bcnn 14211 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15729 |
| [Gleason] p. 308 | Equation 2 | ef0 15990 |
| [Gleason] p. 308 | Equation 3 | efcj 15991 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 15997 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16002 |
| [Gleason] p. 310 | Equation 14 | sinadd 16065 |
| [Gleason] p. 310 | Equation 15 | cosadd 16066 |
| [Gleason] p. 311 | Equation 17 | sincossq 16077 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16082 sinbnd 16081 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14115 sqeqori 14113 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 15971 |
| [Godowski] p. 730 | Equation SF | goeqi 32243 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 31638 |
| [Golan] p. 1 | Remark | srgisid 20120 |
| [Golan] p. 1 | Definition | df-srg 20098 |
| [Golan] p. 149 | Definition | df-slmd 33160 |
| [Gonshor] p. 7 | Definition | df-scut 27716 |
| [Gonshor] p. 9 | Theorem 2.5 | slerec 27753 slerecd 27754 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 27857 cofcut1d 27858 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 27859 cofcut2d 27860 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 27861 cofcutr1d 27862 cofcutr2d 27863 |
| [Gonshor] p. 13 | Definition | df-adds 27896 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 27912 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 27938 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28062 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28082 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28371 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28373 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28372 |
| [Gonshor] p. 95 | Theorem 6.1 | addsbday 27953 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36172 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17480 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17482 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 48198 df-cllaw 48196 df-comlaw 48197 |
| [Hall] p. 2 | Section 1.2 | df-clintop 48210 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 48231 |
| [Halmos] p. 28 | Partition ` ` | df-parts 38782 dfmembpart2 38787 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32035 riesz2 32036 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 31911 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32143 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32155 elpjidm 32154 pjnmopi 32118 |
| [Halmos] p. 44 | Remark | pjinormi 31657 pjinormii 31646 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32159 pjrn 31677 pjrni 31672 pjvec 31666 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 31697 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32124 hmopidmpji 32122 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32161 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32150 pjocvec 31667 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32139 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32142 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32145 pjssdif2i 32144 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 31825 |
| [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 1796 |
| [Hatcher] p. 25 | Definition | df-phtpc 24911 df-phtpy 24890 |
| [Hatcher] p. 26 | Definition | df-pco 24925 df-pi1 24928 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 24914 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 24970 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22398 df-dmatalt 48409 |
| [Helfgott] p. 2 | Theorem | tgoldbach 47827 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 47812 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 47824 bgoldbtbnd 47819 bgoldbtbnd 47819 tgblthelfgott 47825 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 34645 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 34646 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 34660 hgt750lemb 34659 hgt750leme 34661 hgt750lemf 34656 hgt750lemg 34657 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 47821 tgoldbachgt 34666 tgoldbachgtALTV 47822 tgoldbachgtd 34665 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 34647 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30463 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 18849 grpoideu 30479 mndideu 18645 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 18879 grpoinveu 30489 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 18910 grpo2inv 30501 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 18923 grpoinvop 30503 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 18945 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1769 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1770 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1772 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32390 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32403 cdj3i 32411 cdj3lem1 32404 cdjreui 32402 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32401 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 41979 |
| [Holland95] p. 14 | Line 15 | hgmapvs 41909 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 41931 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 41932 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 41929 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 41935 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 41854 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 41949 |
| [Holland95] p. 204 | Definition of involution | df-srng 20748 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 39521 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 41546 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 41499 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 39951 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 41395 poml4N 39971 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 41486 pexmidALTN 39996 pexmidN 39987 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 41551 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 39142 ldualset 39143 |
| [Holland95] p. 222 | Item 1 | df-lines 39519 df-pointsN 39520 |
| [Holland95] p. 222 | Item 2 | df-polarityN 39921 |
| [Holland95] p. 223 | Remark | ispsubcl2N 39965 omllaw4 39264 pol1N 39928 polcon3N 39935 |
| [Holland95] p. 223 | Definition | df-psubclN 39953 |
| [Holland95] p. 223 | Equation for polarity | polval2N 39924 |
| [Holmes] p. 40 | Definition | df-xrn 38378 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31054 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32152 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 31933 eigre 31805 eigrei 31804 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 31934 eigorth 31808 eigorthi 31807 |
| [Hughes] p. 137 | Remark (ii) | eigposi 31806 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30279 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30275 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30276 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30277 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30295 frgrregorufr0 30294 frgrregorufrg 30296 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30302 frrusgrord 30311 frrusgrord0 30310 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30058 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30285 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30288 frgrwopreg2 30289 frgrwopregasn 30286 frgrwopregbsn 30287 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30291 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30305 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30308 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30056 numclwlk1 30341 numclwlk1lem1 30339 numclwlk1lem2 30340 numclwwlk1 30331 numclwwlk8 30362 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30282 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 29742 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30317 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30343 numclwwlkovh0 30342 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30351 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 29948 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30355 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30358 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30361 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30373 natded 30373 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30373 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30373 natded 30373 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30373 |
| [Jech] p. 4 | Definition of class | cv 1540 cvjust 2724 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10462 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10460 alephmul 10461 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10459 infmap2 10100 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9699 |
| [Jech] p. 72 | Equation 9.3 | scott0 9771 scottex 9770 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9752 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9776 |
| [Jech] p. 78 | Note | opthprc 5678 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 42927 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 43015 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 43016 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 42939 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 42943 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 42944 rmyp1 42945 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 42946 rmym1 42947 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 42937 rmx1 42938 rmxluc 42948 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 42941 rmy1 42942 rmyluc 42949 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 42951 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 42952 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 42972 jm2.17b 42973 jm2.17c 42974 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 43005 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 43009 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 43000 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 42975 jm2.24nn 42971 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 43014 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 43020 rmygeid 42976 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 43032 |
| [Juillerat] p. 11 | Section *5 | etransc 46300 etransclem47 46298 etransclem48 46299 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 46295 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 46297 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 46283 |
| [Juillerat] p. 13 | Proof | etransclem35 46286 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 46289 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 46275 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 46292 |
| [Juillerat] p. 14 | Proof | etransclem23 46274 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1968 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2013 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2018 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2008 cbvaliw 2007 wl-cbvmotv 37526 wl-motae 37528 wl-moteq 37527 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 1987 spimw 1971 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2034 spw 2035 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31486 chabs1i 31488 chabs2 31487 chabs2i 31489 chjass 31503 chjassi 31456 latabs1 18373 latabs2 18374 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32308 ela 32309 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32253 cvrval2 39292 |
| [Kalmbach] p. 16 | Definition | df-ol 39196 df-oml 39197 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 31554 cmbri 31560 cmtvalN 39229 df-cm 31553 df-cmtN 39195 |
| [Kalmbach] p. 22 | Remark | omllaw5N 39265 pjoml5 31583 pjoml5i 31558 |
| [Kalmbach] p. 22 | Definition | pjoml2 31581 pjoml2i 31555 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 31584 cmcmi 31562 cmcmii 31567 cmtcomN 39267 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 39263 omlsi 31374 pjoml 31406 pjomli 31405 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 39262 |
| [Kalmbach] p. 23 | Remark | cmbr2i 31566 cmcm3 31585 cmcm3i 31564 cmcm3ii 31569 cmcm4i 31565 cmt3N 39269 cmt4N 39270 cmtbr2N 39271 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 31578 cmbr3i 31570 cmtbr3N 39272 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 31588 fh1i 31591 fh2 31589 fh2i 31592 omlfh1N 39276 |
| [Kalmbach] p. 65 | Remark | chjatom 32327 chslej 31468 chsleji 31428 shslej 31350 shsleji 31340 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31465 chocini 31424 chsupcl 31310 chsupval2 31380 h0elch 31225 helch 31213 hsupval2 31379 ocin 31266 ococss 31263 shococss 31264 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31282 |
| [Kalmbach] p. 66 | Remark | df-pjh 31365 pjssmi 32135 pjssmii 31651 |
| [Kalmbach] p. 67 | Lemma 3 | osum 31615 osumi 31612 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32170 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32370 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32280 |
| [Kalmbach] p. 140 | Remark | hatomic 32330 hatomici 32329 hatomistici 32332 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 39337 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32351 lsatexch 39061 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32325 cvlcvr1 39357 cvr1 39428 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32344 cvexchi 32339 cvrexch 39438 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32334 hlrelat 39420 hlrelat5N 39419 lrelat 39032 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21071 lsmsatcv 39028 spansncv 31623 spansncvi 31622 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 39047 spansncv2 32263 |
| [Kalmbach] p. 266 | Definition | df-st 32181 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 31819 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10529 fpwwe2 10526 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10530 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10537 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10532 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10534 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10547 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10551 gchxpidm 10552 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10563 gchhar 10562 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10098 unxpwdom 9470 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10553 |
| [Kreyszig] p. 3 | Property M1 | metcl 24240 xmetcl 24239 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24247 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24480 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11830 muleqadd 11753 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24346 |
| [Kreyszig] p. 19 | Remark | mopntopon 24347 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24406 mopnm 24352 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24404 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24409 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24450 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23166 lmmbr 25178 lmmbr2 25179 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23288 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25233 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25196 iscmet2 25214 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25236 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23369 metelcls 25225 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25226 metcld2 25227 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25019 lmodvneg1 20831 nvinv 30609 vcm 30546 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25015 lmod0vs 20821 slmd0vs 33183 vc0 30544 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20822 slmdvs0 33184 vcz 30545 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 30661 ngpmet 24511 nrmmetd 24482 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 30656 imsdval2 30657 ncvspds 25081 ngpds 24512 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24497 nvnd 30658 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24526 nmge0 24525 nvge0 30643 nvz 30639 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24532 nvabs 30642 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 30771 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 30715 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 30777 blocni 30775 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 30776 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25124 ipeq0 21568 ipz 30689 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25136 pythi 30820 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 30824 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25158 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15755 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25356 minveco 30854 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 30720 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25249 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 30843 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32093 leopg 32092 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32111 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 30888 |
| [Kulpa] p. 547 | Theorem | poimir 37672 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 37671 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 37670 |
| [Kulpa] p. 548 | Theorem | broucube 37673 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 37665 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 37666 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2382 axnul 5241 |
| [Kunen] p. 11 | Axiom 3 | axnul 5241 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 7882 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8757 mapvalg 8755 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10405 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7866 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9649 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9691 r1elssi 9690 |
| [Kunen] p. 107 | Exercise 4 | rankop 9743 rankopb 9737 rankuni 9748 rankxplim 9764 rankxpsuc 9767 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 44966 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 44974 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 44973 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 44975 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 44980 rexabso 44981 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 44987 n0abso 44988 ssabso 44986 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 44989 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 44999 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 44994 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 44997 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 44998 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 44993 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 45005 wfaxpr 45010 wfaxreg 45012 wfaxrep 45006 wfaxsep 45007 wfaxun 45011 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 44996 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 45009 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 45005 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 45004 omelaxinf2 45001 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 45014 wfaxinf2 45013 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 45027 permaxext 45017 permaxinf2 45025 permaxnul 45020 permaxpow 45021 permaxpr 45022 permaxrep 45018 permaxsep 45019 permaxun 45023 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 45015 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 45026 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4952 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 33668 |
| [Lang] p. | Definition | df-rn 5625 |
| [Lang] p. 3 | Statement | lidrideqd 18569 mndbn0 18650 |
| [Lang] p. 3 | Definition | df-mnd 18635 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18587 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18741 |
| [Lang] p. 5 | Equation | gsumreidx 19822 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 48192 |
| [Lang] p. 6 | Example | nn0mnd 48189 |
| [Lang] p. 6 | Equation | gsumxp2 19885 |
| [Lang] p. 6 | Statement | cycsubm 19107 |
| [Lang] p. 6 | Definition | mulgnn0gsum 18985 |
| [Lang] p. 6 | Observation | mndlsmidm 19575 |
| [Lang] p. 7 | Definition | dfgrp2e 18868 |
| [Lang] p. 30 | Definition | df-tocyc 33066 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33111 |
| [Lang] p. 32 | Property (b) | cyc3conja 33116 cycpmconjv 33101 |
| [Lang] p. 53 | Definition | df-cat 17566 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 17996 cat1lem 17995 |
| [Lang] p. 54 | Definition | df-iso 17648 |
| [Lang] p. 57 | Definition | df-inito 17883 df-termo 17884 |
| [Lang] p. 58 | Example | irinitoringc 21409 |
| [Lang] p. 58 | Statement | initoeu1 17910 termoeu1 17917 |
| [Lang] p. 62 | Definition | df-func 17757 |
| [Lang] p. 65 | Definition | df-nat 17845 |
| [Lang] p. 91 | Note | df-ringc 20554 |
| [Lang] p. 92 | Statement | mxidlprm 33425 |
| [Lang] p. 92 | Definition | isprmidlc 33402 |
| [Lang] p. 128 | Remark | dsmmlmod 21675 |
| [Lang] p. 129 | Proof | lincscm 48441 lincscmcl 48443 lincsum 48440 lincsumcl 48442 |
| [Lang] p. 129 | Statement | lincolss 48445 |
| [Lang] p. 129 | Observation | dsmmfi 21668 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 33630 qusdimsum 33631 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 33610 |
| [Lang] p. 147 | Definition | snlindsntor 48482 |
| [Lang] p. 504 | Statement | mat1 22355 matring 22351 |
| [Lang] p. 504 | Definition | df-mamu 22299 |
| [Lang] p. 505 | Statement | mamuass 22310 mamutpos 22366 matassa 22352 mattposvs 22363 tposmap 22365 |
| [Lang] p. 513 | Definition | mdet1 22509 mdetf 22503 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22599 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22495 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22519 |
| [Lang] p. 515 | Definition | df-minmar1 22543 smadiadetr 22583 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22518 mdetralt 22516 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22531 |
| [Lang] p. 518 | Definition | df-madu 22542 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22553 madurid 22552 matinv 22585 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 22798 |
| [Lang], p. 224 | Proposition 1.1 | extdgfialg 33697 finextalg 33701 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 33666 fedgmul 33634 |
| [Lang], p. 225 | Proposition 1.4 | algextdeg 33728 |
| [Lang], p. 561 | Remark | chpmatply1 22740 |
| [Lang], p. 561 | Definition | df-chpmat 22735 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 44346 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 44341 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 44347 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5241 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2709 |
| [Levy] p. 59 | Definition | df-ttrcl 9593 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9636 |
| [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 10269 |
| [Levy58] p. 2 | Definition II | df-fin2 10169 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10168 |
| [Levy58] p. 2 | Definition III | df-fin3 10171 |
| [Levy58] p. 3 | Definition V | df-fin5 10172 |
| [Levy58] p. 3 | Definition IV | df-fin4 10170 |
| [Levy58] p. 4 | Definition VI | df-fin6 10173 |
| [Levy58] p. 4 | Definition VII | df-fin7 10174 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10298 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27618 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27629 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27661 nosupbnd1 27646 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27663 nosupbnd2 27648 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27667 noetasuplem4 27668 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27664 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1769 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1770 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1772 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32378 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32382 mdsymi 32381 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32376 mdsymlem6 32378 mdsymlem7 32379 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32380 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32283 ssdmd2 32284 ssmd1 32281 ssmd2 32282 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32279 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32251 df-md 32250 mdbr 32264 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32301 mdslj1i 32289 mdslj2i 32290 mdslle1i 32287 mdslle2i 32288 mdslmd1i 32299 mdslmd2i 32300 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32291 mdsl2bi 32293 mdsl2i 32292 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32305 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32302 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32303 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32280 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32285 mdsl3 32286 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32304 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32399 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 39339 hlrelat1 39418 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 39057 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32306 cvmdi 32294 cvnbtwn4 32259 cvrnbtwn4 39297 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32307 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 39358 cvp 32345 cvrp 39434 lcvp 39058 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32369 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32368 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 39351 hlexch4N 39410 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32371 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 39461 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 39767 atpsubN 39771 df-pointsN 39520 pointpsubN 39769 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 39522 pmap11 39780 pmaple 39779 pmapsub 39786 pmapval 39775 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 39783 pmap1N 39785 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 39788 pmapglb2N 39789 pmapglb2xN 39790 pmapglbx 39787 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 39870 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 39495 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 39814 paddclN 39860 paddidm 39859 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 39496 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 39856 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 39495 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 39496 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19580 lsmmod2 19581 lssats 39030 shatomici 32328 shatomistici 32331 shmodi 31360 shmodsi 31359 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32270 mdsymlem7 32379 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 31559 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31463 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32385 |
| [Margaris] p. 40 | Rule C | exlimiv 1931 |
| [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 1781 df-or 848 dfbi2 474 |
| [Margaris] p. 51 | Theorem 1 | idALT 23 |
| [Margaris] p. 56 | Theorem 3 | conventions 30370 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 44926 |
| [Margaris] p. 60 | Theorem 8 | jcn 162 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 44927 |
| [Margaris] p. 79 | Rule C | exinst01 44637 exinst11 44638 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1977 19.2g 2190 r19.2z 4443 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2204 rr19.3v 3620 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2161 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1827 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1782 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2183 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2207 19.9h 2287 exlimd 2220 exlimdh 2291 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2164 excomim 2165 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2327 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30371 conventions-labels 30371 conventions-labels 30371 conventions-labels 30371 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1828 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 44390 albi 1819 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2227 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2228 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 44392 exbi 1848 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2231 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 44389 2alimdv 1919 alimd 2214 alimdh 1818 alimdv 1917 ax-4 1810 ralimdaa 3231 ralimdv 3144 ralimdva 3142 ralimdvva 3177 sbcimdv 3808 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2209 19.21h 2288 19.21t 2208 19.21vv 44388 alrimd 2217 alrimdd 2216 alrimdh 1864 alrimdv 1930 alrimi 2215 alrimih 1825 alrimiv 1928 alrimivv 1929 hbralrimi 3120 r19.21be 3223 r19.21bi 3222 ralrimd 3235 ralrimdv 3128 ralrimdva 3130 ralrimdvv 3174 ralrimdvva 3185 ralrimi 3228 ralrimia 3229 ralrimiv 3121 ralrimiva 3122 ralrimivv 3171 ralrimivva 3173 ralrimivvva 3176 ralrimivw 3126 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 44391 2eximdv 1920 exim 1835 eximd 2218 eximdh 1865 eximdv 1918 rexim 3071 reximd2a 3240 reximdai 3232 reximdd 45164 reximddv 3146 reximddv2 3189 reximddv3 3147 reximdv 3145 reximdv2 3140 reximdva 3143 reximdvai 3141 reximdvva 3178 reximi2 3063 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2213 19.23bi 2193 19.23h 2289 19.23t 2212 exlimdv 1934 exlimdvv 1935 exlimexi 44536 exlimiv 1931 exlimivv 1933 rexlimd3 45160 rexlimdv 3129 rexlimdv3a 3135 rexlimdva 3131 rexlimdva2 3133 rexlimdvaa 3132 rexlimdvv 3186 rexlimdvva 3187 rexlimdvvva 3188 rexlimdvw 3136 rexlimiv 3124 rexlimiva 3123 rexlimivv 3172 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 1992 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1881 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1871 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2229 r19.27z 4453 r19.27zv 4454 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2230 19.28vv 44398 r19.28z 4446 r19.28zf 45175 r19.28zv 4449 rr19.28v 3621 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1874 r19.29d2r 3117 r19.29imd 3095 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1882 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2236 19.31vv 44396 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2235 r19.32 47108 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 44394 19.33 1885 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 1993 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1878 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2232 19.36vv 44395 r19.36zv 4455 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2234 19.37vv 44397 r19.37zv 4450 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1840 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 1991 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1888 19.40 1887 r19.40 3096 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2237 19.41rg 44562 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2238 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1883 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2239 r19.44zv 4452 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2240 r19.45zv 4451 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2604 |
| [Mayet] p. 370 | Remark | jpi 32240 largei 32237 stri 32227 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32182 ishst 32184 |
| [Mayet3] p. 10 | Theorem | hstrbi 32236 hstri 32235 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 31698 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 31699 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32248 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31302 chsupcl 31310 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32330 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32324 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32351 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 40001 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18385 latj32 18383 latjass 18381 |
| [Megill] p. 444 | Axiom C5 | ax-5 1911 ax5ALT 38925 |
| [Megill] p. 444 | Section 7 | conventions 30370 |
| [Megill] p. 445 | Lemma L12 | aecom-o 38919 ax-c11n 38906 axc11n 2425 |
| [Megill] p. 446 | Lemma L17 | equtrr 2023 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 38914 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 38946 hbnae 2431 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2480 sbid 2257 sbidd-misc 49730 sbidd 49729 |
| [Megill] p. 448 | Remark 9.6 | axc14 2462 |
| [Megill] p. 448 | Scheme C4' | ax-c4 38902 |
| [Megill] p. 448 | Scheme C5' | ax-c5 38901 sp 2185 |
| [Megill] p. 448 | Scheme C6' | ax-11 2159 |
| [Megill] p. 448 | Scheme C7' | ax-c7 38903 |
| [Megill] p. 448 | Scheme C8' | ax-7 2009 |
| [Megill] p. 448 | Scheme C9' | ax-c9 38908 |
| [Megill] p. 448 | Scheme C10' | ax-6 1968 ax-c10 38904 |
| [Megill] p. 448 | Scheme C11' | ax-c11 38905 |
| [Megill] p. 448 | Scheme C12' | ax-8 2112 |
| [Megill] p. 448 | Scheme C13' | ax-9 2120 |
| [Megill] p. 448 | Scheme C14' | ax-c14 38909 |
| [Megill] p. 448 | Scheme C15' | ax-c15 38907 |
| [Megill] p. 448 | Scheme C16' | ax-c16 38910 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 38922 dral1 2438 dral2-o 38948 dral2 2437 drex1 2440 drex2 2441 drsb1 2494 drsb2 2268 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2175 sbequ 2085 sbid2v 2508 |
| [Megill] p. 450 | Example in Appendix | hba1-o 38915 hba1 2294 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 46902 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 23 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3828 rspsbca 3829 stdpc4 2070 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 38902 ra4 3835 stdpc5 2210 |
| [Mendelson] p. 81 | Rule C | exlimiv 1931 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2029 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2252 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3737 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5452 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4346 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4347 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4225 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4282 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4226 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4089 |
| [Mendelson] p. 231 | Definition of union | dfun3 4224 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5390 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4854 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5505 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4566 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5506 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4881 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5764 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6212 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7703 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6308 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8505 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9048 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 8969 xpsneng 8970 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 8976 xpcomeng 8977 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 8979 |
| [Mendelson] p. 255 | Definition | brsdom 8892 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 8972 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8749 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 8954 mapsnend 8953 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9054 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9053 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8801 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 8957 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 8973 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10062 djucomen 10061 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10066 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10060 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8441 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8468 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10442 |
| [Mendelson] p. 281 | Definition | df-r1 9649 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9698 |
| [Mendelson] p. 287 | Axiom system MK | ru 3737 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30229 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30264 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30266 vdgn1frgrv3 30267 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30268 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30261 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30254 2pthfrgrrn 30252 2pthfrgrrn2 30253 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31222 |
| [Monk1] p. 22 | Remark | conventions 30370 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30370 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4187 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5721 ssrelf 32588 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5722 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5152 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6206 coi2 6207 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5858 rn0 5863 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 6085 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5632 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5866 rnxp 6114 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5713 xp0 6102 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6023 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6020 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7839 imaexg 7838 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6017 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7003 funfvop 6978 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6871 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6882 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6523 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7183 dff13f 7184 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7148 funrnex 7881 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7176 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6171 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4912 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 7933 df-1st 7916 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 7934 df-2nd 7917 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9739 ranksnb 9712 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9740 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9741 rankunb 9735 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9723 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9649 r1val2 9722 |
| [Monk1] p. 117 | Lemma | zorn2 10389 zorn2g 10386 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9871 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10444 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9866 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1810 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2009 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2179 ax-c15 38907 ax12v2 2181 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 38902 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2159 |
| [Monk2] p. 109 | Lemma 15 | equvini 2454 equvinv 2030 eqvinop 5425 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1911 ax5ALT 38925 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2143 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2159 |
| [Monk2] p. 114 | Lemma 21 | sp 2185 |
| [Monk2] p. 114 | Lemma 22 | axc4 2321 hba1-o 38915 hba1 2294 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2155 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2178 nfra2 3340 nfra2w 3266 |
| [Moore] p. 53 | Part I | df-mre 17480 |
| [Munkres] p. 77 | Example 2 | distop 22903 indistop 22910 indistopon 22909 |
| [Munkres] p. 77 | Example 3 | fctop 22912 fctop2 22913 |
| [Munkres] p. 77 | Example 4 | cctop 22914 |
| [Munkres] p. 78 | Definition of basis | df-bases 22854 isbasis3g 22857 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17339 tgval2 22864 |
| [Munkres] p. 79 | Remark | tgcl 22877 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 22871 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 22895 tgss3 22894 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 22896 basgen2 22897 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 37362 topdifinfeq 37363 topdifinffin 37361 topdifinfindis 37359 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23068 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 22946 topcld 22943 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 22947 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 22949 |
| [Munkres] p. 94 | Definition of closure | clsval 22945 |
| [Munkres] p. 94 | Definition of interior | ntrval 22944 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 22983 elcls 22981 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 22991 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23056 neindisj 23025 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23058 |
| [Munkres] p. 97 | Definition of limit point | islp2 23053 lpval 23047 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23223 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23135 iscn 23143 iscn2 23146 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23188 cncnp2 23189 cncnpi 23186 df-cnp 23136 iscnp 23145 iscnp2 23147 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24451 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25231 |
| [Nathanson] p. 123 | Remark | reprgt 34624 reprinfz1 34625 reprlt 34622 |
| [Nathanson] p. 123 | Definition | df-repr 34612 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 34644 |
| [Nathanson] p. 123 | Proposition | breprexp 34636 breprexpnat 34637 itgexpif 34609 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32074 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 47820 |
| [Pfenning] p. 17 | Definition XM | natded 30373 |
| [Pfenning] p. 17 | Definition NNC | natded 30373 notnotrd 133 |
| [Pfenning] p. 17 | Definition ` `C | natded 30373 |
| [Pfenning] p. 18 | Rule" | natded 30373 |
| [Pfenning] p. 18 | Definition /\I | natded 30373 |
| [Pfenning] p. 18 | Definition ` `E | natded 30373 natded 30373 natded 30373 natded 30373 natded 30373 |
| [Pfenning] p. 18 | Definition ` `I | natded 30373 natded 30373 natded 30373 natded 30373 natded 30373 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30373 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30373 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30373 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30373 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30373 |
| [Pfenning] p. 127 | Definition =E | natded 30373 |
| [Pfenning] p. 127 | Definition =I | natded 30373 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25122 df-dip 30671 dip0l 30688 ip0l 21566 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25163 ipval 30673 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 30684 ipcj 21564 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25125 dipdir 30812 ipdir 21569 ipdiri 30800 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 30680 nmsq 25114 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 30795 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 30797 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 30798 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25131 dipass 30815 ipass 21575 ipassi 30811 |
| [Prugovecki] p. 186 | Definition of bra | braval 31914 df-bra 31820 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 31821 kbval 31924 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32352 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 39906 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32366 atcvat4i 32367 cvrat3 39460 cvrat4 39461 lsatcvat3 39070 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32252 cvrval 39287 df-cv 32249 df-lcv 39037 lspsncv0 21076 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 39918 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 39919 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2709 rabid 3414 rabidd 45171 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2280 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2722 |
| [Quine] p. 19 | Definition 2.9 | conventions 30370 df-v 3436 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2868 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2865 abid2f 2923 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2277 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2087 sbalex 2244 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2804 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2730 eqid1 30437 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2737 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3740 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3741 dfsbcq2 3742 |
| [Quine] p. 43 | Theorem 6.8 | vex 3438 |
| [Quine] p. 43 | Theorem 6.9 | isset 3448 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3544 spcgv 3549 spcimgf 3503 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3752 spsbcd 3753 |
| [Quine] p. 44 | Theorem 6.12 | elex 3455 |
| [Quine] p. 44 | Theorem 6.13 | elab 3633 elabg 3630 elabgf 3628 |
| [Quine] p. 44 | Theorem 6.14 | noel 4286 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4668 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4577 df-sn 4575 |
| [Quine] p. 49 | Theorem 7.4 | snss 4735 snssg 4734 |
| [Quine] p. 49 | Theorem 7.5 | prss 4770 prssg 4769 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4713 prid1g 4711 prid2 4714 prid2g 4712 snid 4613 snidg 4611 |
| [Quine] p. 51 | Theorem 7.12 | snex 5372 |
| [Quine] p. 51 | Theorem 7.13 | prex 5373 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4876 unisnALT 44937 unisng 4875 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4880 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4887 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4885 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6447 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 47096 dfiota2 6434 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 47105 iotaval 6451 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6457 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6453 |
| [Quine] p. 58 | Definition 9.1 | df-op 4581 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5463 opabidw 5462 opelopab 5480 opelopaba 5474 opelopabaf 5482 opelopabf 5483 opelopabg 5476 opelopabga 5471 opelopabgf 5478 oprabid 7373 oprabidw 7372 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5620 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5622 |
| [Quine] p. 64 | Definition 9.15 | df-id 5509 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6542 |
| [Quine] p. 65 | Theorem 10.4 | funi 6509 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6530 funsng 6528 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6479 |
| [Quine] p. 65 | Definition 10.2 | args 6038 dffv4 6814 |
| [Quine] p. 68 | Definition 10.11 | conventions 30370 df-fv 6485 fv2 6812 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14171 nn0opth2i 14170 nn0opthi 14169 omopthi 8571 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8324 |
| [Quine] p. 232 | Equation i | carddom 10437 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6565 funimaexg 6564 |
| [Quine] p. 331 | Axiom system NF | ru 3737 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31054 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 30671 polid 31129 polid2i 31127 polidi 31128 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 30783 |
| [ReedSimon] p. 195 | Remark | lnophm 31989 lnophmi 31988 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32102 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32104 leopmuli 32103 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32107 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 31822 leoppos 32096 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32106 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32095 |
| [Roman] p. 4 | Definition | df-dmat 22398 df-dmatalt 48409 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20064 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20146 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 48496 |
| [Roman] p. 112 | Note | isldepslvec2 48496 ldepsnlinc 48519 zlmodzxznm 48508 |
| [Roman] p. 112 | Example | zlmodzxzequa 48507 zlmodzxzequap 48510 zlmodzxzldep 48515 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 22798 |
| [Rosenlicht] p. 80 | Theorem | heicant 37674 |
| [Rosser] p. 281 | Definition | df-op 4581 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 34648 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 34649 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 48376 pmtr3ncom 19380 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19376 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19319 cayleyth 19320 |
| [Rudin] p. 164 | Equation 27 | efcan 15995 |
| [Rudin] p. 164 | Equation 30 | efzval 16003 |
| [Rudin] p. 167 | Equation 48 | absefi 16097 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 197 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1772 |
| [Sanford] p. 39 | Rule 4 | mptxor 1770 |
| [Sanford] p. 40 | Rule 1 | mptnan 1769 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6059 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6062 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6058 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6056 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17480 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17481 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17481 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17483 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10020 |
| [Schechter] p. 141 | Definition (MC) | dfac11 43074 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10329 axdc3 10337 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20148 isrngo 37916 |
| [Schechter] p. 276 | Remark 11.6.e | span0 31512 |
| [Schechter] p. 276 | Definition of span | df-span 31279 spanval 31303 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 22901 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6327 onelord 43263 ordelon 6326 ordelord 6324 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 43264 sucidg 6385 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6357 onsuc 7738 ord0 6356 ordsuci 7736 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 43265 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5200 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 43040 elon2 6313 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6308 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5517 epelg 5515 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9480 epirron 43266 ordirr 6320 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 43268 oneptr 43267 ontr1 6349 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6345 oneptri 43269 ordtri3or 6334 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8411 ord0eln0 6358 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6371 onsucss 43278 trsucss 6392 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7743 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6398 ordnbtwn 6397 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 43280 ordnexbtwnsuc 43279 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10284 onsucf1lem 43281 onsucf1o 43284 onsucf1olem 43282 onsucrn 43283 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 43285 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7770 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 43274 ordne0gt0 43273 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 43276 limnsuc 43277 onsucelab 43275 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9528 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7785 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9531 ordom 7801 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9532 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8550 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7708 ssorduni 7707 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8441 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9535 limom 7807 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8380 df1o2 8387 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8426 oa0suclim 43287 oalim 8442 oasuc 8434 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8427 om0suclim 43288 omlim 8443 omsuc 8436 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8432 oe0m1 8431 oe0suclim 43289 oelim 8444 oesuc 8437 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 43241 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 43291 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 43292 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 43293 limexissupab 43295 limiun 43294 limuni 6364 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8448 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8452 om1om1r 43296 om1r 8453 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8445 oaomoecl 43290 oecl 8447 omcl 8446 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 43243 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8454 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8455 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 43297 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 43298 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8521 nnamecl 43299 nnecl 8523 nnmcl 8522 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 43300 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8462 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8463 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8470 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 43302 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 43303 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 43305 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8469 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 43309 omword1 8483 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 43308 oaordnrex 43307 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 43304 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 43310 omword2 8484 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 43311 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 43312 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 43313 omordi 8476 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8478 omord2com 43314 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 43315 df-2o 8381 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 43318 oewordi 8501 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 43319 oeworde 8503 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 43320 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 43321 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 43317 omnord1ex 43316 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 43322 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 43324 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 43328 oenord1ex 43327 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 43329 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8471 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 43323 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8489 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8490 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 43331 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8507 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 43332 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 43333 cantnfub2 43334 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 43337 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 28885 axtgcgrrflx 28433 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 28886 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 28887 axtgcgrid 28434 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28419 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 28898 axtgsegcon 28435 df-trkgcb 28421 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 28909 axtg5seg 28436 df-trkgcb 28421 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 28910 axtgbtwnid 28437 df-trkgb 28420 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 28912 axtgpasch 28438 df-trkgb 28420 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 28931 df-trkg2d 34668 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28441 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28442 df-trkg2d 34668 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 28934 axtgeucl 28443 df-trkge 28422 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 28947 axtgcont 28440 axtgcont1 28439 df-trkgb 28420 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 36000 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 36002 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 36005 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 36009 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 36010 tgcgrcomimp 28448 tgcgrcoml 28450 tgcgrcomr 28449 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 36015 tgcgrtriv 28455 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 36019 tg5segofs 34676 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 34673 df-ofs 35996 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 36021 tgcgrextend 28456 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 36023 tgsegconeq 28457 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36035 btwntriv2 36025 tgbtwntriv2 28458 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 36026 tgbtwncom 28459 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36029 tgbtwntriv1 28462 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36030 tgbtwnswapid 28463 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36036 btwnintr 36032 tgbtwnexch2 28467 tgbtwnintr 28464 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36038 btwnexch3 36033 tgbtwnexch 28469 tgbtwnexch3 28465 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36037 tgbtwnouttr 28468 tgbtwnouttr2 28466 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 28930 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36040 tgbtwndiff 28477 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28470 trisegint 36041 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36057 tgifscgr 28479 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28529 colrot1 28530 colrot2 28531 lncom 28593 lnrot1 28594 lnrot2 28595 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36053 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36058 tgcgrsub 28480 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36068 tgcgrxfr 28489 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28488 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36054 df-cgrg 28482 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28482 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36069 tgbtwnxfr 28501 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36075 colinearperm2 36077 colinearperm3 36076 colinearperm4 36078 colinearperm5 36079 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28504 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36052 tgellng 28524 tglng 28517 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36080 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36088 lnxfr 28537 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36089 lnext 28538 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36093 tgfscgr 28539 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36094 lncgr 28540 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36055 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36096 lnid 28541 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36097 tgidinside 28542 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36114 tgbtwnconn1 28546 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36115 tgbtwnconn2 28547 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36116 tgbtwnconn3 28548 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36122 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36120 legov 28556 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28557 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28570 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36123 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36125 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36127 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36128 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36129 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36126 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36131 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28558 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28560 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28561 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28562 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28563 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36138 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36139 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36134 df-outsideof 36133 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36135 ishlg 28573 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28578 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28580 outsideofrflx 36140 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28574 hlcomd 28575 outsideofcom 36141 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28581 outsideoftr 36142 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 28589 outsideofeu 36144 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36151 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36152 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36145 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36160 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36161 tglineelsb2 28603 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36163 linerflx1 36162 linerflx2 36164 tglinecom 28606 tglinerflx1 28604 tglinerflx2 28605 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36166 tglinethru 28607 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36150 tglng 28517 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28565 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36169 tglinethrueu 28610 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36170 tglineineq 28614 tglineinteq 28616 tglineintmo 28613 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28620 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28621 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 28622 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 28637 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 28633 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 28625 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 28624 ismir 28630 mirbtwn 28629 mircgr 28628 mirfv 28627 mirval 28626 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 28635 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 28636 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 28637 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 28640 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 28641 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 28646 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 28643 mirbtwni 28642 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 28644 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 28656 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 28660 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 28657 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 28658 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 28659 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 28662 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 28663 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 28669 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 28665 israg 28668 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 28670 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 28671 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 28673 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 28674 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 28675 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 28676 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 28677 ragncol 28680 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 28678 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 28684 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 28688 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 28685 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 28667 isperp 28683 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 28686 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 28693 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 28701 colperpexlem2 28702 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 28704 colperpexlem3 28703 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 28709 midex 28708 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 28706 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 28715 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 28710 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 28719 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 28722 opphllem6 28723 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 28725 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28438 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 28726 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 28734 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 28729 hpgbr 28731 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 28736 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 28735 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 28737 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 28738 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 28739 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 28740 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 28741 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 28755 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 28745 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 28759 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 28760 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 28761 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 28762 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 28763 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 28766 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 28768 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 28746 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 28769 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 28772 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 28773 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 28774 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 28775 trgcopyeu 28777 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 28801 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 28780 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 28789 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 28787 cgrahl2 28788 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 28790 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 28791 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 28793 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 28794 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 28797 cgrahl 28798 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 28802 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 28803 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 28804 acopyeu 28805 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 28812 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 28816 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 28809 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 28824 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 28817 isleag 28818 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 28826 tgsas1 28825 tgsas2 28827 tgsas3 28828 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 28830 tgasa1 28829 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 28831 tgsss2 28832 tgsss3 28833 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27202 dchrsum 27200 dchrsum2 27199 sumdchr 27203 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27204 sum2dchr 27205 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 19973 ablfacrp2 19974 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27147 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27148 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27155 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27413 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27416 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27470 vmalogdivsum2 27469 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27460 dirith2 27459 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27458 rpvmasum 27457 rpvmasum2 27443 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27418 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27456 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27423 dchrisumlem1 27420 dchrisumlem2 27421 dchrisumlem3 27422 dchrisumlema 27419 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27426 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27455 dchrmusumlem 27453 dchrvmasumlem 27454 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27425 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27427 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27451 dchrisum0re 27444 dchrisumn0 27452 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27437 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27441 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27442 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27497 pntrsumbnd2 27498 pntrsumo1 27496 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27461 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27463 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27465 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27468 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27473 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27474 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27479 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27481 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27482 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27490 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27491 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27488 selberg3lem2 27489 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27492 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27486 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27499 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27500 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27501 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27515 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27527 pntlemb 27528 pntlemc 27526 pntlemd 27525 pntlemg 27529 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27527 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27519 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27524 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27527 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27540 pntleml 27542 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 33746 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 33733 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 33765 constrinvcl 33776 constrmulcl 33774 constrnegcl 33766 constrsqrtcl 33782 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 33752 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 33762 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 33784 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 33794 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4254 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4353 dif0 4326 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4440 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4423 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4245 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4246 |
| [Stoll] p. 20 | Remark | invdif 4227 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4583 |
| [Stoll] p. 43 | Definition | uniiun 5005 |
| [Stoll] p. 44 | Definition | intiin 5006 |
| [Stoll] p. 45 | Definition | df-iin 4942 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4941 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 401 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4254 |
| [Strang] p. 242 | Section 6.3 | expgrowth 44347 |
| [Suppes] p. 22 | Theorem 2 | eq0 4298 eq0f 4295 |
| [Suppes] p. 22 | Theorem 4 | eqss 3948 eqssd 3950 eqssi 3949 |
| [Suppes] p. 23 | Theorem 5 | ss0 4350 ss0b 4349 |
| [Suppes] p. 23 | Theorem 6 | sstr 3941 sstrALT2 44846 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4051 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4052 |
| [Suppes] p. 23 | Theorem 9 | psstr 4055 |
| [Suppes] p. 23 | Theorem 10 | pssss 4046 |
| [Suppes] p. 25 | Theorem 12 | elin 3916 elun 4101 |
| [Suppes] p. 26 | Theorem 15 | inidm 4175 |
| [Suppes] p. 26 | Theorem 16 | in0 4343 |
| [Suppes] p. 27 | Theorem 23 | unidm 4105 |
| [Suppes] p. 27 | Theorem 24 | un0 4342 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4126 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4134 |
| [Suppes] p. 27 | Theorem 27 | unss 4138 |
| [Suppes] p. 27 | Theorem 28 | indir 4234 |
| [Suppes] p. 27 | Theorem 29 | undir 4235 |
| [Suppes] p. 28 | Theorem 32 | difid 4324 |
| [Suppes] p. 29 | Theorem 33 | difin 4220 |
| [Suppes] p. 29 | Theorem 34 | indif 4228 |
| [Suppes] p. 29 | Theorem 35 | undif1 4424 |
| [Suppes] p. 29 | Theorem 36 | difun2 4429 |
| [Suppes] p. 29 | Theorem 37 | difin0 4422 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4420 |
| [Suppes] p. 29 | Theorem 39 | difundi 4238 |
| [Suppes] p. 29 | Theorem 40 | difindi 4240 |
| [Suppes] p. 30 | Theorem 41 | nalset 5249 |
| [Suppes] p. 39 | Theorem 61 | uniss 4865 |
| [Suppes] p. 39 | Theorem 65 | uniop 5453 |
| [Suppes] p. 41 | Theorem 70 | intsn 4932 |
| [Suppes] p. 42 | Theorem 71 | intpr 4930 intprg 4929 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5409 |
| [Suppes] p. 42 | Theorem 78 | intun 4928 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4980 dfiun2g 4978 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4981 |
| [Suppes] p. 47 | Theorem 86 | elpw 4552 elpw2 5270 elpw2g 5269 elpwg 4551 elpwgdedVD 44928 |
| [Suppes] p. 47 | Theorem 87 | pwid 4570 |
| [Suppes] p. 47 | Theorem 89 | pw0 4762 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4763 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5629 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5771 xpindir 5772 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5683 xpundir 5684 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9478 |
| [Suppes] p. 58 | Theorem 2 | relss 5720 |
| [Suppes] p. 59 | Theorem 4 | eldm 5838 eldm2 5839 eldm2g 5837 eldmg 5836 |
| [Suppes] p. 59 | Definition 3 | df-dm 5624 |
| [Suppes] p. 60 | Theorem 6 | dmin 5849 |
| [Suppes] p. 60 | Theorem 8 | rnun 6089 |
| [Suppes] p. 60 | Theorem 9 | rnin 6090 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5826 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5820 brcnvg 5817 |
| [Suppes] p. 62 | Equation 5 | elcnv 5814 elcnv2 5815 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6050 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6088 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6086 |
| [Suppes] p. 63 | Definition | dftrrels2 38591 |
| [Suppes] p. 63 | Theorem 20 | co02 6204 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5911 |
| [Suppes] p. 63 | Definition 7 | df-co 5623 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5823 |
| [Suppes] p. 64 | Theorem 27 | coass 6209 |
| [Suppes] p. 65 | Theorem 31 | resundi 5939 |
| [Suppes] p. 65 | Theorem 34 | elima 6011 elima2 6012 elima3 6013 elimag 6010 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6093 |
| [Suppes] p. 66 | Theorem 40 | dminss 6097 |
| [Suppes] p. 66 | Theorem 41 | imainss 6098 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6101 |
| [Suppes] p. 81 | Definition 34 | dfec2 8620 |
| [Suppes] p. 82 | Theorem 72 | elec 8663 elecALTV 38280 elecg 8661 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 38627 erth 8671 erth2 8672 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 38630 erdisj 8674 |
| [Suppes] p. 83 | Definition 35, | df-parts 38782 dfmembpart2 38787 |
| [Suppes] p. 89 | Theorem 96 | map0b 8802 |
| [Suppes] p. 89 | Theorem 97 | map0 8806 map0g 8803 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8807 mapsnd 8805 |
| [Suppes] p. 89 | Theorem 99 | mapss 8808 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 9951 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 9950 |
| [Suppes] p. 92 | Theorem 1 | enref 8902 enrefg 8901 |
| [Suppes] p. 92 | Theorem 2 | ensym 8920 ensymb 8919 ensymi 8921 |
| [Suppes] p. 92 | Theorem 3 | entr 8923 |
| [Suppes] p. 92 | Theorem 4 | unen 8962 |
| [Suppes] p. 94 | Theorem 15 | endom 8896 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 8917 |
| [Suppes] p. 94 | Theorem 17 | domtr 8924 |
| [Suppes] p. 95 | Theorem 18 | sbth 9005 |
| [Suppes] p. 97 | Theorem 23 | canth2 9038 canth2g 9039 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9009 df-sdom 8867 dfsdom2 9008 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9022 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9011 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9010 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9020 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8899 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9023 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9018 |
| [Suppes] p. 98 | Exercise 4 | fundmen 8948 fundmeng 8949 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 8983 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9019 |
| [Suppes] p. 104 | Theorem 37 | fofi 9192 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9198 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9198 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10434 |
| [Suppes] p. 130 | Definition 3 | df-tr 5197 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7708 |
| [Suppes] p. 134 | Definition 6 | df-suc 6308 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7825 finds 7821 finds1 7824 finds2 7823 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9537 isfinite2 9177 isfiniteg 9179 unbnn 9175 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10801 df-ltpq 10793 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7788 tfinds 7785 tfinds2 7789 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8461 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8463 |
| [Suppes] p. 211 | Theorem 25 | oaass 8471 |
| [Suppes] p. 225 | Definition 8 | iscard2 9861 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10446 |
| [Suppes] p. 228 | Theorem 59 | harcard 9863 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 9949 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6354 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7721 onminsb 7722 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10455 |
| [Suppes] p. 229 | Theorem 65 | alephcard 9953 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 9960 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 9954 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9825 |
| [Suppes] p. 242 | Theorem 6 | weth 10378 |
| [Suppes] p. 242 | Theorem 8 | entric 10440 |
| [Suppes] p. 242 | Theorem 9 | carden 10434 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 35708 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 35712 |
| [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 7345 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3737 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5357 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4599 elpr2 4601 elpr2g 4600 elprg 4597 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4589 elsn2 4616 elsn2g 4615 elsng 4588 velsn 4590 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5405 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4584 sneqr 4790 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4595 dfsn2 4587 dfsn2ALT 4596 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7669 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5414 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5402 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5387 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7672 unexg 7671 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4642 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4858 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3907 df-un 3905 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4874 uniprg 4873 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5313 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4640 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6374 elsucg 6372 sstr2 3939 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4106 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4157 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4120 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4176 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4232 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4233 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3920 df-ss 3917 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4550 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4135 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3918 sseqin2 4171 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3955 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4185 inss2 4186 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 3997 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4868 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5388 sspwimp 44929 sspwimpALT 44936 sspwimpALT2 44939 sspwimpcf 44931 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5395 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5215 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3394 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5243 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3903 |
| [TakeutiZaring] p. 20 | Definition 5.14 | dfnul2 4284 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4324 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4301 n0f 4297 neq0 4300 neq0f 4296 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9477 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9617 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9619 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3436 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5251 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4348 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5257 ssexg 5259 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5253 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9486 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9480 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4314 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4083 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4248 undif3VD 44893 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4084 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4091 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3046 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3055 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7681 xpexg 7678 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5621 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6548 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6724 fun11 6551 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6490 svrelfun 6549 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5825 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5827 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5626 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5627 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5623 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6138 dfrel2 6133 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5630 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5749 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5756 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5769 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 5951 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5931 opelresi 5933 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 5958 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5947 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 5952 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6519 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6054 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6517 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6726 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2603 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30370 df-fv 6485 fv3 6835 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7850 cnvexg 7849 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7834 dmexg 7826 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7835 rnexg 7827 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 44465 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7845 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6830 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 47184 tz6.12-1-afv2 47251 tz6.12-1 6840 tz6.12-afv 47183 tz6.12-afv2 47250 tz6.12 6841 tz6.12c-afv2 47252 tz6.12c 6839 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 47247 tz6.12-2 6805 tz6.12i-afv2 47253 tz6.12i 6843 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6480 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6481 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6483 wfo 6475 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6482 wf1 6474 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6484 wf1o 6476 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 6959 eqfnfv2 6960 eqfnfv2f 6963 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6915 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7146 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7144 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6565 funimaexg 6564 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5090 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5523 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5575 dffr3 6045 eliniseg 6040 iniseg 6043 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5514 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5591 fr3nr 7700 frirr 5590 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5567 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7702 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5578 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5600 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6290 tz6.26i 6291 wefrc 5608 wereu2 5611 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6292 wfii 6293 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6486 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7258 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7259 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7265 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7266 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7267 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7271 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7278 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7280 |
| [TakeutiZaring] p. 35 | Notation | wtr 5196 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 44466 tz7.2 5597 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5201 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6315 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6323 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6324 ordelordALT 44549 ordelordALTVD 44878 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6330 ordelssne 6329 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6328 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6332 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7710 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7711 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6306 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6334 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 44561 ordon 7705 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7706 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7778 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6350 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5198 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7720 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7756 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6408 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6407 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7707 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4887 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6308 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6384 sucidg 6385 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7738 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6398 ordnbtwn 6397 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7753 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6307 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7806 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7811 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7766 ordelsuc 7745 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7747 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7776 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7793 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7814 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7815 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7816 |
| [TakeutiZaring] p. 43 | Remark | omon 7803 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9520 omex 9528 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7801 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7820 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7817 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7818 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7796 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4910 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5214 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4911 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5280 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7723 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6353 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4896 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9545 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7718 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8290 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8311 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8312 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8313 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8320 tz7.44-2 8321 tz7.44-3 8322 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8282 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8277 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8261 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8359 tz7.49c 8360 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8357 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8356 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8358 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2650 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 9894 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 9895 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8442 oasuc 8434 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7786 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8445 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8426 oa0r 8448 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8446 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8458 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8529 nnaordi 8528 oaord 8457 oaordi 8456 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 4996 uniss2 4890 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8460 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8465 oawordex 8467 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8521 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8558 |
| [TakeutiZaring] p. 60 | Remark | oancom 9536 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8470 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8526 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8462 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8429 omlim 8443 omsuc 8436 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8427 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8523 nnmcl 8522 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8542 nnmordi 8541 omord 8478 omordi 8476 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8479 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8546 omwordri 8482 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8449 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8452 om1r 8453 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8485 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8487 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8488 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8489 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8490 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8518 oe0 8432 oelim 8444 oesuc 8437 onesuc 8440 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8430 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8496 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8497 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8431 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8455 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8498 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8504 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8502 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8503 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8507 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8509 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9613 tz9.1 9614 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9649 r10 9653 r1lim 9657 r1limg 9656 r1suc 9655 r1sucg 9654 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9665 r1ord2 9666 r1ordg 9663 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9675 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9700 tz9.13 9676 tz9.13g 9677 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9650 rankval 9701 rankvalb 9682 rankvalg 9702 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9724 rankelb 9709 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9738 rankval3 9725 rankval3b 9711 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9714 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9680 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9719 rankr1c 9706 rankr1g 9717 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9720 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9734 rankssb 9733 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9727 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9726 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10358 dfac3 10004 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 9913 numth 10355 numth2 10354 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10429 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10430 cardid2 9838 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9845 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10434 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9844 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9829 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9850 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9842 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9058 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 8935 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9063 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 8987 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9848 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 9981 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9110 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9118 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 9982 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9115 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 9971 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 9949 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9857 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10099 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9202 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8868 isfi 8893 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9119 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10417 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 8980 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10409 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10069 unxpdom 9138 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9859 cardsdomelir 9858 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9140 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 9897 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8747 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10445 infxpidm2 9900 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10090 infxp 10097 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 8992 pw2f1o 8990 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9051 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10370 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10365 ac6s5 10374 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10426 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10427 uniimadomf 10428 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10157 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10152 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10137 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10134 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10140 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10147 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10156 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10465 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10135 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10159 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 9980 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 9979 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 9991 alephfp2 9992 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10582 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 9995 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10452 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10466 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10467 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 38901 |
| [Tarski] p. 67 | Scheme B5 | sp 2185 |
| [Tarski] p. 68 | Lemma 6 | avril1 30433 equid 2013 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2018 |
| [Tarski] p. 70 | Lemma 14 | spim 2386 spime 2388 spimew 1972 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2179 ax-c15 38907 ax12i 1967 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2087 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1969 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1911 ax5ALT 38925 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2009 ax-8 2112 ax-9 2120 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28435 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28436 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28438 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28438 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28439 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16144 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 37678 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 37680 |
| [Weierstrass] p. 272 | Definition | df-mdet 22493 mdetuni 22530 |
| [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 37458 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 43812 imim2 58 wl-luk-imim2 37453 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 47029 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 37456 |
| [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 44938 wl-luk-notnotr 37457 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 146 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 43842 axfrege28 43841 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 37450 |
| [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 30371 pm2.27 42 wl-luk-pm2.27 37448 |
| [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 38370 |
| [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 44370 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 44371 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1871 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 44372 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 44373 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 44374 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1894 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 44375 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 44376 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 44377 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 44378 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 44379 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 44381 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 44382 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 44383 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 44380 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2092 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 44386 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 44387 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2072 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2162 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1830 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1831 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 44388 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 44389 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 44390 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 44391 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 44393 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 44392 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1888 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 44395 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 44396 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 44394 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1829 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 44397 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 44398 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1847 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 44399 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2345 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1861 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 44404 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 44400 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 44401 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 44402 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 44403 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 44408 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 44405 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 44406 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 44407 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 44409 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2563 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 44419 pm13.13b 44420 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 44421 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3007 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3008 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3619 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 44427 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 44428 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 44422 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 44564 pm13.193 44423 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 44424 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 44425 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 44426 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 44433 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 44432 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 44431 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3802 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 44434 pm14.122b 44435 pm14.122c 44436 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 44437 pm14.123b 44438 pm14.123c 44439 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 44441 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 44440 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 44442 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6458 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 44443 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6459 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 44444 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 44446 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2627 eupickbi 2630 sbaniota 44447 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 44445 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2578 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 44448 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30370 df-fv 6485 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 9886 pm54.43lem 9885 |
| [Young] p. 141 | Definition of operator ordering | leop2 32094 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32100 idleop 32101 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 42840 |
| [vandenDries] p. 43 | Theorem 62 | pellex 42847 pellexlem1 42841 |