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 17712 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17712 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18129 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17733 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 48863 prsthinc 48854 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 48886 df-mndtc 48886 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17756 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 48881 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 48899 oppgoppchom 48898 oppgoppcid 48900 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17828 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17816 invisoinvl 17837 |
| [Adamek] p. 28 | Example 3.13 | idinv 17836 idiso 17835 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17821 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17795 df-iso 17796 dfiso2 17819 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17802 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17853 |
| [Adamek] p. 29 | Definition 3.15 | cic 17846 df-cic 17843 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17908 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17817 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17818 isoco 17824 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17908 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17931 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17924 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 48819 prsthinc 48854 thincciso 48848 thinccisod 48849 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 48886 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17938 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18164 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18222 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17958 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17957 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18222 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17982 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17988 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17987 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18207 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18207 |
| [Adamek] p. 39 | Definition 3.41 | funcoppc 17925 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18152 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17976 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17975 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18161 |
| [Adamek] p. 40 | Definition 3.47 | df-catc 18152 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17888 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17889 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17900 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17859 |
| [Adamek] p. 49 | Remark 4.4(2) | ressffth 17991 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 17997 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 18020 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 18024 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 17998 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 18026 |
| [Adamek] p. 101 | Definition 7.1 | df-inito 18037 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21507 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 18038 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 18065 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 18069 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 18039 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21508 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 18072 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17794 |
| [Adamek] p. 185 | Section 10.67 | updjud 9971 |
| [Adamek] p. 478 | Item Rng | df-ringc 20662 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 48397 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 48419 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14605 df-pfx 14705 df-substr 14675 df-word 14549 lencl 14567 wrd0 14573 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24744 df-nmoo 30773 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32181 hmopidmchi 32179 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32229 pjcmul2i 32230 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 31946 unoplin 31948 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 31947 unopadj2 31966 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 32041 lnopunii 32040 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32114 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 27975 |
| [Alling] p. 184 | Axiom B | bdayfo 27736 |
| [Alling] p. 184 | Axiom O | sltso 27735 |
| [Alling] p. 184 | Axiom SD | nodense 27751 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27837 |
| [Alling] p. 185 | Theorem | conway 27858 |
| [Alling] p. 185 | Axiom FE | noeta 27802 |
| [Alling] p. 186 | Theorem 4 | slerec 27878 |
| [Alling], p. 2 | Definition | rp-brsslt 43412 |
| [Alling], p. 3 | Note | nla0001 43415 nla0002 43413 nla0003 43414 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11442 addcan2d 11462 addcan2i 11452 addcand 11461 addcani 11451 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11495 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11554 negsubd 11623 negsubi 11584 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11556 negnegd 11608 negnegi 11576 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11693 subdid 11716 subdii 11709 subdir 11694 subdird 11717 subdiri 11710 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11437 mul01d 11457 mul01i 11448 mul02 11436 mul02d 11456 mul02i 11447 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11897 mulcan2d 11894 mulcand 11893 mulcani 11899 |
| [Apostol] p. 18 | Theorem I.8 | receu 11905 xreceu 32888 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11935 divrecd 12043 divreci 12009 divreczi 12002 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11961 recreci 11996 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11900 mul0ord 11910 mul0ori 11908 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11699 mul2negd 11715 mul2negi 11708 mulneg1 11696 mulneg1d 11713 mulneg1i 11706 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11979 divadddivd 12084 divadddivi 12026 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11964 divmuldivd 12081 divmuldivi 12024 rdivmuldivd 20429 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11965 divdivdivd 12087 divdivdivi 12027 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 13054 rpaddcld 13089 rpmulcl 13055 rpmulcld 13090 |
| [Apostol] p. 20 | Axiom 8 | rpneg 13064 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 13067 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11384 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11853 ltadd1dd 11871 ltadd1i 11814 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12114 ltmul1a 12113 ltmul1i 12183 ltmul1ii 12193 ltmul2 12115 ltmul2d 13116 ltmul2dd 13130 ltmul2i 12186 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11780 msqgt0d 11827 msqgt0i 11797 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11782 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11766 lt0neg1d 11829 ltneg 11760 ltnegd 11838 ltnegi 11804 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11745 lt2addd 11883 lt2addi 11822 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 13032 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12110 recgt0d 12199 recgt0i 12170 recgt0ii 12171 |
| [Apostol] p. 22 | Definition of integers | df-z 12611 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12277 |
| [Apostol] p. 22 | Definition of rationals | df-q 12988 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9491 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12519 |
| [Apostol] p. 26 | Theorem I.29 | arch 12520 archd 45104 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12718 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12521 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12986 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12985 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13237 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16372 zneo 12698 zneoALTV 47593 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26786 msqsqrtd 15475 resqrtth 15290 sqrtth 15399 sqrtthi 15405 sqsqrtd 15474 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12266 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12952 |
| [Apostol] p. 361 | Remark | crreczi 14263 |
| [Apostol] p. 363 | Remark | absgt0i 15434 |
| [Apostol] p. 363 | Example | abssubd 15488 abssubi 15438 |
| [ApostolNT] p. 7 | Remark | fmtno0 47464 fmtno1 47465 fmtno2 47474 fmtno3 47475 fmtno4 47476 fmtno5fac 47506 fmtnofz04prm 47501 |
| [ApostolNT] p. 7 | Definition | df-fmtno 47452 |
| [ApostolNT] p. 8 | Definition | df-ppi 27157 |
| [ApostolNT] p. 14 | Definition | df-dvds 16287 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16303 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16327 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16322 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16316 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16318 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16304 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16305 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16310 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16344 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16346 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16348 |
| [ApostolNT] p. 15 | Definition | df-gcd 16528 dfgcd2 16579 |
| [ApostolNT] p. 16 | Definition | isprm2 16715 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16686 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16948 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16546 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16580 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16582 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16561 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16553 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16744 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16746 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16961 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16955 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16436 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16620 |
| [ApostolNT] p. 24 | Definition | df-mu 27158 |
| [ApostolNT] p. 25 | Definition | df-phi 16799 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27248 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16823 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16809 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16813 |
| [ApostolNT] p. 32 | Definition | df-vma 27155 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27250 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27274 |
| [ApostolNT] p. 38 | Remark | df-sgm 27159 |
| [ApostolNT] p. 38 | Definition | df-sgm 27159 |
| [ApostolNT] p. 75 | Definition | df-chp 27156 df-cht 27154 |
| [ApostolNT] p. 104 | Definition | congr 16697 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16290 |
| [ApostolNT] p. 106 | Definition | moddvds 16297 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16379 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16380 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13924 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13962 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14273 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16321 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16700 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17107 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16702 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16816 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16834 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16817 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27129 |
| [ApostolNT] p. 179 | Definition | df-lgs 27353 lgsprme0 27397 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27398 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27374 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27389 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27446 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27465 2lgsoddprm 27474 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27432 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27441 |
| [ApostolNT] p. 188 | Definition | df-lgs 27353 lgs1 27399 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27390 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27392 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27400 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27401 |
| [Baer] p. 40 | Property (b) | mapdord 41620 |
| [Baer] p. 40 | Property (c) | mapd11 41621 |
| [Baer] p. 40 | Property (e) | mapdin 41644 mapdlsm 41646 |
| [Baer] p. 40 | Property (f) | mapd0 41647 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 41607 mapd1o 41630 |
| [Baer] p. 41 | Property (g) | mapdat 41649 |
| [Baer] p. 44 | Part (1) | mapdpg 41688 |
| [Baer] p. 45 | Part (2) | hdmap1eq 41783 mapdheq 41710 mapdheq2 41711 mapdheq2biN 41712 |
| [Baer] p. 45 | Part (3) | baerlem3 41695 |
| [Baer] p. 46 | Part (4) | mapdheq4 41714 mapdheq4lem 41713 |
| [Baer] p. 46 | Part (5) | baerlem5a 41696 baerlem5abmN 41700 baerlem5amN 41698 baerlem5b 41697 baerlem5bmN 41699 |
| [Baer] p. 47 | Part (6) | hdmap1l6 41803 hdmap1l6a 41791 hdmap1l6e 41796 hdmap1l6f 41797 hdmap1l6g 41798 hdmap1l6lem1 41789 hdmap1l6lem2 41790 mapdh6N 41729 mapdh6aN 41717 mapdh6eN 41722 mapdh6fN 41723 mapdh6gN 41724 mapdh6lem1N 41715 mapdh6lem2N 41716 |
| [Baer] p. 48 | Part 9 | hdmapval 41810 |
| [Baer] p. 48 | Part 10 | hdmap10 41822 |
| [Baer] p. 48 | Part 11 | hdmapadd 41825 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 41799 mapdh6hN 41725 |
| [Baer] p. 48 | Part (7) | mapdh75cN 41735 mapdh75d 41736 mapdh75e 41734 mapdh75fN 41737 mapdh7cN 41731 mapdh7dN 41732 mapdh7eN 41730 mapdh7fN 41733 |
| [Baer] p. 48 | Part (8) | mapdh8 41770 mapdh8a 41757 mapdh8aa 41758 mapdh8ab 41759 mapdh8ac 41760 mapdh8ad 41761 mapdh8b 41762 mapdh8c 41763 mapdh8d 41765 mapdh8d0N 41764 mapdh8e 41766 mapdh8g 41767 mapdh8i 41768 mapdh8j 41769 |
| [Baer] p. 48 | Part (9) | mapdh9a 41771 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 41751 |
| [Baer] p. 49 | Part 12 | hdmap11 41830 hdmapeq0 41826 hdmapf1oN 41847 hdmapneg 41828 hdmaprnN 41846 hdmaprnlem1N 41831 hdmaprnlem3N 41832 hdmaprnlem3uN 41833 hdmaprnlem4N 41835 hdmaprnlem6N 41836 hdmaprnlem7N 41837 hdmaprnlem8N 41838 hdmaprnlem9N 41839 hdmapsub 41829 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 41850 hdmap14lem10 41859 hdmap14lem1a 41848 hdmap14lem2N 41851 hdmap14lem2a 41849 hdmap14lem3 41852 hdmap14lem8 41857 hdmap14lem9 41858 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 41860 hdmap14lem12 41861 hdmap14lem13 41862 hdmap14lem14 41863 hdmap14lem15 41864 hgmapval 41869 |
| [Baer] p. 50 | Part 15 | hgmapadd 41876 hgmapmul 41877 hgmaprnlem2N 41879 hgmapvs 41873 |
| [Baer] p. 50 | Part 16 | hgmaprnN 41883 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 41899 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 41900 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 41901 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 41902 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 41904 hgmapvv 41908 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 41903 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 41905 |
| [Baer] p. 111 | Line 15 | hdmapg 41912 hdmapglem7 41911 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26787 2irrexpqALT 26857 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 23 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2566 |
| [BellMachover] p. 460 | Notation | df-mo 2537 |
| [BellMachover] p. 460 | Definition | mo3 2561 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2705 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2709 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5292 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5301 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37046 sepex 5305 |
| [BellMachover] p. 466 | Problem | axpow2 5372 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5373 |
| [BellMachover] p. 466 | Axiom Union | axun2 7755 |
| [BellMachover] p. 468 | Definition | df-ord 6388 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6403 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6410 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6405 |
| [BellMachover] p. 471 | Definition of N | df-om 7887 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7820 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6390 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9679 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7902 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9801 |
| [BellMachover] p. 478 | Definition | rankval2 9855 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9819 r1ord3g 9816 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9632 |
| [BellMachover] p. 488 | Axiom AC | ac5 10514 dfac4 10159 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10147 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 39300 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32381 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32423 chirredi 32422 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32411 |
| [Beran] p. 3 | Definition of join | sshjval3 31382 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 31644 cmcm2i 31621 cmcm2ii 31626 cmt2N 39231 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 31645 lecmi 31630 lecmii 31631 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 31619 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 31648 cm2ji 31653 cm2mi 31654 |
| [Beran] p. 95 | Definition | df-sh 31235 issh2 31237 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31114 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31127 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31118 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 31856 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 31858 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 31857 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 31859 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31110 his1i 31128 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31111 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31112 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31113 |
| [Beran] p. 96 | Definition of norm | df-hnorm 30996 dfhnorm2 31150 normval 31152 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31212 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 31001 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31269 |
| [Beran] p. 96 | Definition of converge | df-hlim 31000 hlimi 31216 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31161 norm-i 31157 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31165 norm-ii 31166 normlem0 31137 normlem1 31138 normlem2 31139 normlem3 31140 normlem4 31141 normlem5 31142 normlem6 31143 normlem7 31144 normlem7tALT 31147 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31167 norm-iii 31168 |
| [Beran] p. 98 | Remark 3.4 | bcs 31209 bcsiALT 31207 bcsiHIL 31208 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31149 normpar 31183 normpari 31182 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31174 normpyth 31173 normpythi 31170 |
| [Beran] p. 99 | Remark | lnfn0 32075 lnfn0i 32070 lnop0 31994 lnop0i 31998 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32054 nmcfnex 32081 nmcfnexi 32079 nmcopex 32057 nmcopexi 32055 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32082 nmcfnlbi 32080 nmcoplb 32058 nmcoplbi 32056 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32084 lnfnconi 32083 lnopcon 32063 lnopconi 32062 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31184 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31181 norm3adifii 31176 norm3dif 31178 norm3difi 31175 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31329 pjhth 31421 pjhtheu 31422 pjpjhth 31453 pjpjhthi 31454 pjth 25486 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31434 ococi 31433 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32089 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32090 riesz4 32092 riesz4i 32091 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32107 cnlnadjeu 32106 cnlnadjeui 32105 cnlnadji 32104 cnlnadjlem1 32095 nmopadjlei 32116 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32119 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32118 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32120 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 31964 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32130 nmopcoadji 32129 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32121 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32131 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32128 pjadj2coi 32232 pjadjcoi 32189 |
| [Beran] p. 107 | Definition | df-ch 31249 isch2 31251 |
| [Beran] p. 107 | Remark 3.12 | choccl 31334 isch3 31269 occl 31332 ocsh 31311 shoccl 31333 shocsh 31312 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31436 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31360 |
| [Beran] p. 109 | Property (i) | pjadj2 32215 pjadj3 32216 pjadji 31713 pjadjii 31702 |
| [Beran] p. 109 | Property (ii) | pjidmco 32209 pjidmcoi 32205 pjidmi 31701 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32201 |
| [Beran] p. 111 | Remark | ho0val 31778 pjch1 31698 |
| [Beran] p. 111 | Definition | df-hfmul 31762 df-hfsum 31761 df-hodif 31760 df-homul 31759 df-hosum 31758 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 31699 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 31722 pjchi 31460 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31467 pjoc2i 31466 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 31708 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32193 pjssmii 31709 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32192 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32191 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32196 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32194 pjssge0ii 31710 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32195 pjdifnormii 31711 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1772 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1770 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1773 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1768 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34273 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34281 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34279 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34283 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34303 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34334 df-sitm 34312 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34334 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34311 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29079 isuhgrop 29101 isusgrop 29193 isuspgrop 29192 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 47784 df-subgr 29299 uhgrspan1 29334 uhgrspansubgr 29322 |
| [Bollobas] p. 3 | Definition | df-gric 47804 gricuspgr 47824 isuspgrim 47812 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29486 df-clnbgr 47743 df-cusgr 29443 df-nbgr 29364 fusgrmaxsize 29496 |
| [Bollobas] p. 4 | Definition | df-upwlks 47977 df-wlks 29631 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 29582 finsumvtxdgeven 29584 fusgr1th 29583 fusgrvtxdgonume 29586 vtxdgoddnumeven 29585 |
| [Bollobas] p. 5 | Notation | df-pths 29748 |
| [Bollobas] p. 5 | Definition | df-crcts 29818 df-cycls 29819 df-trls 29724 df-wlkson 29632 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29090 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 48043 df-cllaw 48029 df-mgm 18665 df-mgm2 48062 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 48044 df-asslaw 48031 df-sgrp 18744 df-sgrp2 48064 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 48063 df-comlaw 48030 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18760 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33013 mndlactf1o 33017 mndractf1 33015 mndractf1o 33018 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20252 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20170 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 33660 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 33664 assarrginv 33663 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 33544 dfufd2 33557 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7306 fcofo 7307 |
| [BourbakiTop1] p. | Remark | xnegmnf 13248 xnegpnf 13247 |
| [BourbakiTop1] p. | Remark | rexneg 13249 |
| [BourbakiTop1] p. | Remark 3 | ust0 24243 ustfilxp 24236 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24113 |
| [BourbakiTop1] p. | Criterion | ishmeo 23782 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24308 iducn 24307 snfil 23887 |
| [BourbakiTop1] p. | Example 2 | neifil 23903 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 24090 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24328 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 33917 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23886 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24300 df-ust 24224 filintn0 23884 filn0 23885 istgp 24100 ucnprima 24306 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24311 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24322 df-usp 24281 df-utop 24255 trust 24253 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 33816 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23139 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23292 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24229 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24232 |
| [BourbakiTop1] p. | Property V_ii | innei 23148 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23156 neissex 23150 |
| [BourbakiTop1] p. | Proposition 1 | neips 23136 neiss 23132 ucncn 24309 ustund 24245 ustuqtop 24270 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23290 neiptopreu 23156 utop2nei 24274 utop3cls 24275 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24316 uspreg 24298 utopreg 24276 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23714 imasncls 23715 imasnopn 23713 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 24023 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24231 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24233 |
| [BourbakiTop1] p. | Property V_iii | elnei 23134 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24327 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24230 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24234 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23410 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23869 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 22915 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 33813 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 46017 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 46019 stoweid 46018 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 45956 stoweidlem10 45965 stoweidlem14 45969 stoweidlem15 45970 stoweidlem35 45990 stoweidlem36 45991 stoweidlem37 45992 stoweidlem38 45993 stoweidlem40 45995 stoweidlem41 45996 stoweidlem43 45998 stoweidlem44 45999 stoweidlem46 46001 stoweidlem5 45960 stoweidlem50 46005 stoweidlem52 46007 stoweidlem53 46008 stoweidlem55 46010 stoweidlem56 46011 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 45978 stoweidlem24 45979 stoweidlem27 45982 stoweidlem28 45983 stoweidlem30 45985 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 45989 stoweidlem59 46014 stoweidlem60 46015 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 46000 stoweidlem49 46004 stoweidlem7 45962 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 45986 stoweidlem39 45994 stoweidlem42 45997 stoweidlem48 46003 stoweidlem51 46006 stoweidlem54 46009 stoweidlem57 46012 stoweidlem58 46013 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 45980 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 45972 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 45966 stoweidlem13 45968 stoweidlem26 45981 stoweidlem61 46016 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 45973 |
| [Bruck] p. 1 | Section I.1 | df-clintop 48043 df-mgm 18665 df-mgm2 48062 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18744 df-sgrp2 48064 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 19069 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5231 |
| [Church] p. 129 | Section II.24 | df-ifp 1063 dfifp2 1064 |
| [Clemente] p. 10 | Definition IT | natded 30431 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30431 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30431 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30431 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30431 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30431 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30431 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30431 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30431 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30431 |
| [Clemente] p. 14 | Proof 5.11 | natded 30431 |
| [Clemente] p. 14 | Definition E` `n | natded 30431 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30433 ex-natded5.2 30432 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30436 ex-natded5.3 30435 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30438 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30440 ex-natded5.7 30439 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30442 ex-natded5.8 30441 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30444 ex-natded5.13 30443 |
| [Clemente] p. 32 | Definition I` `n | natded 30431 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30431 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30431 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30431 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30445 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30446 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30448 ex-natded9.26 30447 |
| [Cohen] p. 301 | Remark | relogoprlem 26647 |
| [Cohen] p. 301 | Property 2 | relogmul 26648 relogmuld 26681 |
| [Cohen] p. 301 | Property 3 | relogdiv 26649 relogdivd 26682 |
| [Cohen] p. 301 | Property 4 | relogexp 26652 |
| [Cohen] p. 301 | Property 1a | log1 26641 |
| [Cohen] p. 301 | Property 1b | loge 26642 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26844 |
| [Cohen4] p. 349 | Property | relogbf 26848 |
| [Cohen4] p. 352 | Definition | elogb 26827 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26834 |
| [Cohen4] p. 361 | Property 3 | logbrec 26839 relogbdiv 26836 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26832 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26837 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26825 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26826 |
| [Cohen4] p. 367 | Property | logbchbase 26828 |
| [Cohen4] p. 377 | Property 2 | logblt 26841 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34266 sxbrsigalem4 34268 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18614 acsinfd 18613 acsinfdimd 18615 acsmap2d 18612 acsmapd 18611 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34271 |
| [Connell] p. 57 | Definition | df-scmat 22512 df-scmatalt 48244 |
| [Conway] p. 4 | Definition | slerec 27878 |
| [Conway] p. 5 | Definition | addsval 28009 addsval2 28010 df-adds 28007 df-muls 28147 df-negs 28067 |
| [Conway] p. 7 | Theorem | 0slt1s 27888 |
| [Conway] p. 16 | Theorem 0(i) | ssltright 27924 |
| [Conway] p. 16 | Theorem 0(ii) | ssltleft 27923 |
| [Conway] p. 16 | Theorem 0(iii) | slerflex 27822 |
| [Conway] p. 17 | Theorem 3 | addsass 28052 addsassd 28053 addscom 28013 addscomd 28014 addsrid 28011 addsridd 28012 |
| [Conway] p. 17 | Definition | df-0s 27883 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 28090 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 28087 negsidd 28088 |
| [Conway] p. 18 | Theorem 5 | sleadd1 28036 sleadd1d 28042 |
| [Conway] p. 18 | Definition | df-1s 27884 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 28082 negscld 28083 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 28027 |
| [Conway] p. 19 | Note | mulsunif2 28210 |
| [Conway] p. 19 | Theorem 7 | addsdi 28195 addsdid 28196 addsdird 28197 mulnegs1d 28200 mulnegs2d 28201 mulsass 28206 mulsassd 28207 mulscom 28179 mulscomd 28180 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28174 mulscld 28175 |
| [Conway] p. 19 | Theorem 8(iii) | slemuld 28178 sltmul 28176 sltmuld 28177 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28184 mulsgt0d 28185 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28256 |
| [Conway] p. 24 | Definition | df-reno 28440 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28445 remulscl 28448 renegscl 28444 |
| [Conway] p. 27 | Definition | df-ons 28289 elons2 28295 |
| [Conway] p. 27 | Theorem 14 | sltonex 28298 |
| [Conway] p. 29 | Remark | madebday 27952 newbday 27954 oldbday 27953 |
| [Conway] p. 29 | Definition | df-made 27900 df-new 27902 df-old 27901 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13897 |
| [Crawley] p. 1 | Definition of poset | df-poset 18370 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 39368 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 40172 dalaw 39868 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 41947 |
| [Crawley] p. 111 | Definition of set W | df-watsN 39972 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 40088 df-ldil 40086 isldil 40092 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 40087 df-trnN 40089 isltrn 40101 ltrnu 40103 |
| [Crawley] p. 112 | Lemma A | cdlema1N 39773 cdlema2N 39774 exatleN 39386 |
| [Crawley] p. 112 | Lemma B | 1cvrat 39458 cdlemb 39776 cdlemb2 40023 cdlemb3 40588 idltrn 40132 l1cvat 39036 lhpat 40025 lhpat2 40027 lshpat 39037 ltrnel 40121 ltrnmw 40133 |
| [Crawley] p. 112 | Lemma C | cdlemc1 40173 cdlemc2 40174 ltrnnidn 40156 trlat 40151 trljat1 40148 trljat2 40149 trljat3 40150 trlne 40167 trlnidat 40155 trlnle 40168 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 39973 |
| [Crawley] p. 113 | Lemma C | cdlemc 40179 cdlemc3 40175 cdlemc4 40176 |
| [Crawley] p. 113 | Lemma D | cdlemd 40189 cdlemd1 40180 cdlemd2 40181 cdlemd3 40182 cdlemd4 40183 cdlemd5 40184 cdlemd6 40185 cdlemd7 40186 cdlemd8 40187 cdlemd9 40188 cdleme31sde 40367 cdleme31se 40364 cdleme31se2 40365 cdleme31snd 40368 cdleme32a 40423 cdleme32b 40424 cdleme32c 40425 cdleme32d 40426 cdleme32e 40427 cdleme32f 40428 cdleme32fva 40419 cdleme32fva1 40420 cdleme32fvcl 40422 cdleme32le 40429 cdleme48fv 40481 cdleme4gfv 40489 cdleme50eq 40523 cdleme50f 40524 cdleme50f1 40525 cdleme50f1o 40528 cdleme50laut 40529 cdleme50ldil 40530 cdleme50lebi 40522 cdleme50rn 40527 cdleme50rnlem 40526 cdlemeg49le 40493 cdlemeg49lebilem 40521 |
| [Crawley] p. 113 | Lemma E | cdleme 40542 cdleme00a 40191 cdleme01N 40203 cdleme02N 40204 cdleme0a 40193 cdleme0aa 40192 cdleme0b 40194 cdleme0c 40195 cdleme0cp 40196 cdleme0cq 40197 cdleme0dN 40198 cdleme0e 40199 cdleme0ex1N 40205 cdleme0ex2N 40206 cdleme0fN 40200 cdleme0gN 40201 cdleme0moN 40207 cdleme1 40209 cdleme10 40236 cdleme10tN 40240 cdleme11 40252 cdleme11a 40242 cdleme11c 40243 cdleme11dN 40244 cdleme11e 40245 cdleme11fN 40246 cdleme11g 40247 cdleme11h 40248 cdleme11j 40249 cdleme11k 40250 cdleme11l 40251 cdleme12 40253 cdleme13 40254 cdleme14 40255 cdleme15 40260 cdleme15a 40256 cdleme15b 40257 cdleme15c 40258 cdleme15d 40259 cdleme16 40267 cdleme16aN 40241 cdleme16b 40261 cdleme16c 40262 cdleme16d 40263 cdleme16e 40264 cdleme16f 40265 cdleme16g 40266 cdleme19a 40285 cdleme19b 40286 cdleme19c 40287 cdleme19d 40288 cdleme19e 40289 cdleme19f 40290 cdleme1b 40208 cdleme2 40210 cdleme20aN 40291 cdleme20bN 40292 cdleme20c 40293 cdleme20d 40294 cdleme20e 40295 cdleme20f 40296 cdleme20g 40297 cdleme20h 40298 cdleme20i 40299 cdleme20j 40300 cdleme20k 40301 cdleme20l 40304 cdleme20l1 40302 cdleme20l2 40303 cdleme20m 40305 cdleme20y 40284 cdleme20zN 40283 cdleme21 40319 cdleme21d 40312 cdleme21e 40313 cdleme22a 40322 cdleme22aa 40321 cdleme22b 40323 cdleme22cN 40324 cdleme22d 40325 cdleme22e 40326 cdleme22eALTN 40327 cdleme22f 40328 cdleme22f2 40329 cdleme22g 40330 cdleme23a 40331 cdleme23b 40332 cdleme23c 40333 cdleme26e 40341 cdleme26eALTN 40343 cdleme26ee 40342 cdleme26f 40345 cdleme26f2 40347 cdleme26f2ALTN 40346 cdleme26fALTN 40344 cdleme27N 40351 cdleme27a 40349 cdleme27cl 40348 cdleme28c 40354 cdleme3 40219 cdleme30a 40360 cdleme31fv 40372 cdleme31fv1 40373 cdleme31fv1s 40374 cdleme31fv2 40375 cdleme31id 40376 cdleme31sc 40366 cdleme31sdnN 40369 cdleme31sn 40362 cdleme31sn1 40363 cdleme31sn1c 40370 cdleme31sn2 40371 cdleme31so 40361 cdleme35a 40430 cdleme35b 40432 cdleme35c 40433 cdleme35d 40434 cdleme35e 40435 cdleme35f 40436 cdleme35fnpq 40431 cdleme35g 40437 cdleme35h 40438 cdleme35h2 40439 cdleme35sn2aw 40440 cdleme35sn3a 40441 cdleme36a 40442 cdleme36m 40443 cdleme37m 40444 cdleme38m 40445 cdleme38n 40446 cdleme39a 40447 cdleme39n 40448 cdleme3b 40211 cdleme3c 40212 cdleme3d 40213 cdleme3e 40214 cdleme3fN 40215 cdleme3fa 40218 cdleme3g 40216 cdleme3h 40217 cdleme4 40220 cdleme40m 40449 cdleme40n 40450 cdleme40v 40451 cdleme40w 40452 cdleme41fva11 40459 cdleme41sn3aw 40456 cdleme41sn4aw 40457 cdleme41snaw 40458 cdleme42a 40453 cdleme42b 40460 cdleme42c 40454 cdleme42d 40455 cdleme42e 40461 cdleme42f 40462 cdleme42g 40463 cdleme42h 40464 cdleme42i 40465 cdleme42k 40466 cdleme42ke 40467 cdleme42keg 40468 cdleme42mN 40469 cdleme42mgN 40470 cdleme43aN 40471 cdleme43bN 40472 cdleme43cN 40473 cdleme43dN 40474 cdleme5 40222 cdleme50ex 40541 cdleme50ltrn 40539 cdleme51finvN 40538 cdleme51finvfvN 40537 cdleme51finvtrN 40540 cdleme6 40223 cdleme7 40231 cdleme7a 40225 cdleme7aa 40224 cdleme7b 40226 cdleme7c 40227 cdleme7d 40228 cdleme7e 40229 cdleme7ga 40230 cdleme8 40232 cdleme8tN 40237 cdleme9 40235 cdleme9a 40233 cdleme9b 40234 cdleme9tN 40239 cdleme9taN 40238 cdlemeda 40280 cdlemedb 40279 cdlemednpq 40281 cdlemednuN 40282 cdlemefr27cl 40385 cdlemefr32fva1 40392 cdlemefr32fvaN 40391 cdlemefrs32fva 40382 cdlemefrs32fva1 40383 cdlemefs27cl 40395 cdlemefs32fva1 40405 cdlemefs32fvaN 40404 cdlemesner 40278 cdlemeulpq 40202 |
| [Crawley] p. 114 | Lemma E | 4atex 40058 4atexlem7 40057 cdleme0nex 40272 cdleme17a 40268 cdleme17c 40270 cdleme17d 40480 cdleme17d1 40271 cdleme17d2 40477 cdleme18a 40273 cdleme18b 40274 cdleme18c 40275 cdleme18d 40277 cdleme4a 40221 |
| [Crawley] p. 115 | Lemma E | cdleme21a 40307 cdleme21at 40310 cdleme21b 40308 cdleme21c 40309 cdleme21ct 40311 cdleme21f 40314 cdleme21g 40315 cdleme21h 40316 cdleme21i 40317 cdleme22gb 40276 |
| [Crawley] p. 116 | Lemma F | cdlemf 40545 cdlemf1 40543 cdlemf2 40544 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 40549 cdlemg16 40639 cdlemg28 40686 cdlemg28a 40675 cdlemg28b 40685 cdlemg3a 40579 cdlemg42 40711 cdlemg43 40712 cdlemg44 40715 cdlemg44a 40713 cdlemg46 40717 cdlemg47 40718 cdlemg9 40616 ltrnco 40701 ltrncom 40720 tgrpabl 40733 trlco 40709 |
| [Crawley] p. 116 | Definition of G | df-tgrp 40725 |
| [Crawley] p. 117 | Lemma G | cdlemg17 40659 cdlemg17b 40644 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 40738 df-edring 40739 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 40742 |
| [Crawley] p. 118 | Remark | tendopltp 40762 |
| [Crawley] p. 118 | Lemma H | cdlemh 40799 cdlemh1 40797 cdlemh2 40798 |
| [Crawley] p. 118 | Lemma I | cdlemi 40802 cdlemi1 40800 cdlemi2 40801 |
| [Crawley] p. 118 | Lemma J | cdlemj1 40803 cdlemj2 40804 cdlemj3 40805 tendocan 40806 |
| [Crawley] p. 118 | Lemma K | cdlemk 40956 cdlemk1 40813 cdlemk10 40825 cdlemk11 40831 cdlemk11t 40928 cdlemk11ta 40911 cdlemk11tb 40913 cdlemk11tc 40927 cdlemk11u-2N 40871 cdlemk11u 40853 cdlemk12 40832 cdlemk12u-2N 40872 cdlemk12u 40854 cdlemk13-2N 40858 cdlemk13 40834 cdlemk14-2N 40860 cdlemk14 40836 cdlemk15-2N 40861 cdlemk15 40837 cdlemk16-2N 40862 cdlemk16 40839 cdlemk16a 40838 cdlemk17-2N 40863 cdlemk17 40840 cdlemk18-2N 40868 cdlemk18-3N 40882 cdlemk18 40850 cdlemk19-2N 40869 cdlemk19 40851 cdlemk19u 40952 cdlemk1u 40841 cdlemk2 40814 cdlemk20-2N 40874 cdlemk20 40856 cdlemk21-2N 40873 cdlemk21N 40855 cdlemk22-3 40883 cdlemk22 40875 cdlemk23-3 40884 cdlemk24-3 40885 cdlemk25-3 40886 cdlemk26-3 40888 cdlemk26b-3 40887 cdlemk27-3 40889 cdlemk28-3 40890 cdlemk29-3 40893 cdlemk3 40815 cdlemk30 40876 cdlemk31 40878 cdlemk32 40879 cdlemk33N 40891 cdlemk34 40892 cdlemk35 40894 cdlemk36 40895 cdlemk37 40896 cdlemk38 40897 cdlemk39 40898 cdlemk39u 40950 cdlemk4 40816 cdlemk41 40902 cdlemk42 40923 cdlemk42yN 40926 cdlemk43N 40945 cdlemk45 40929 cdlemk46 40930 cdlemk47 40931 cdlemk48 40932 cdlemk49 40933 cdlemk5 40818 cdlemk50 40934 cdlemk51 40935 cdlemk52 40936 cdlemk53 40939 cdlemk54 40940 cdlemk55 40943 cdlemk55u 40948 cdlemk56 40953 cdlemk5a 40817 cdlemk5auN 40842 cdlemk5u 40843 cdlemk6 40819 cdlemk6u 40844 cdlemk7 40830 cdlemk7u-2N 40870 cdlemk7u 40852 cdlemk8 40820 cdlemk9 40821 cdlemk9bN 40822 cdlemki 40823 cdlemkid 40918 cdlemkj-2N 40864 cdlemkj 40845 cdlemksat 40828 cdlemksel 40827 cdlemksv 40826 cdlemksv2 40829 cdlemkuat 40848 cdlemkuel-2N 40866 cdlemkuel-3 40880 cdlemkuel 40847 cdlemkuv-2N 40865 cdlemkuv2-2 40867 cdlemkuv2-3N 40881 cdlemkuv2 40849 cdlemkuvN 40846 cdlemkvcl 40824 cdlemky 40908 cdlemkyyN 40944 tendoex 40957 |
| [Crawley] p. 120 | Remark | dva1dim 40967 |
| [Crawley] p. 120 | Lemma L | cdleml1N 40958 cdleml2N 40959 cdleml3N 40960 cdleml4N 40961 cdleml5N 40962 cdleml6 40963 cdleml7 40964 cdleml8 40965 cdleml9 40966 dia1dim 41043 |
| [Crawley] p. 120 | Lemma M | dia11N 41030 diaf11N 41031 dialss 41028 diaord 41029 dibf11N 41143 djajN 41119 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 41014 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 41100 dia2dimlem1 41046 dia2dimlem2 41047 dia2dimlem3 41048 dia2dimlem4 41049 dia2dimlem5 41050 diaf1oN 41112 diarnN 41111 dvheveccl 41094 dvhopN 41098 |
| [Crawley] p. 121 | Lemma N | cdlemn 41194 cdlemn10 41188 cdlemn11 41193 cdlemn11a 41189 cdlemn11b 41190 cdlemn11c 41191 cdlemn11pre 41192 cdlemn2 41177 cdlemn2a 41178 cdlemn3 41179 cdlemn4 41180 cdlemn4a 41181 cdlemn5 41183 cdlemn5pre 41182 cdlemn6 41184 cdlemn7 41185 cdlemn8 41186 cdlemn9 41187 diclspsn 41176 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 41155 |
| [Crawley] p. 122 | Lemma N | dih11 41247 dihf11 41249 dihjust 41199 dihjustlem 41198 dihord 41246 dihord1 41200 dihord10 41205 dihord11b 41204 dihord11c 41206 dihord2 41209 dihord2a 41201 dihord2b 41202 dihord2cN 41203 dihord2pre 41207 dihord2pre2 41208 dihordlem6 41195 dihordlem7 41196 dihordlem7b 41197 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 41212 dihfval 41213 dihval 41214 |
| [Diestel] p. 3 | Definition | df-gric 47804 df-grim 47801 isuspgrim 47812 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29443 df-nbgr 29364 |
| [Diestel] p. 3 | Definition by | df-grisom 47800 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 47784 df-subgr 29299 uhgrspan1 29334 uhgrspansubgr 29322 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 29586 vtxdgoddnumeven 29585 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29090 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 33824 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 33836 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 33828 zarcls1 33829 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 33839 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 33842 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 33845 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3965 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9684 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8866 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9692 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 10017 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10592 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5310 |
| [Enderton] p. 19 | Definition | df-tp 4635 |
| [Enderton] p. 26 | Exercise 5 | unissb 4943 |
| [Enderton] p. 26 | Exercise 10 | pwel 5386 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5580 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5083 iinin2 5082 iinun2 5077 iunin1 5076 iunin1f 32577 iunin2 5075 uniin1 32571 uniin2 32572 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5081 iundif2 5078 |
| [Enderton] p. 32 | Exercise 20 | unineq 4293 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5102 |
| [Enderton] p. 33 | Exercise 25 | iununi 5103 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5110 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7789 iunpwss 5111 |
| [Enderton] p. 36 | Definition | opthwiener 5523 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5460 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4949 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5480 rnex 7932 rnexg 7924 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5927 rnuni 6170 |
| [Enderton] p. 42 | Definition of a function | dffun7 6594 dffun8 6595 |
| [Enderton] p. 43 | Definition of function value | funfv2 6996 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6636 |
| [Enderton] p. 44 | Definition (d) | dfima2 6081 dfima3 6082 |
| [Enderton] p. 47 | Theorem 3H | fvco2 7005 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10510 ac7g 10511 df-ac 10153 dfac2 10169 dfac2a 10167 dfac2b 10168 dfac3 10158 dfac7 10170 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7265 |
| [Enderton] p. 52 | Definition | df-map 8866 |
| [Enderton] p. 53 | Exercise 21 | coass 6286 |
| [Enderton] p. 53 | Exercise 27 | dmco 6275 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6643 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6122 |
| [Enderton] p. 54 | Remark | ixpf 8958 ixpssmap 8970 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8936 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10520 ac9s 10530 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 38591 erref 8763 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 38594 erthi 8796 |
| [Enderton] p. 57 | Definition | df-ec 8745 |
| [Enderton] p. 58 | Definition | df-qs 8749 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8745 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5923 |
| [Enderton] p. 68 | Definition of successor | df-suc 6391 |
| [Enderton] p. 71 | Definition | df-tr 5265 dftr4 5271 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6464 unisucg 6463 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6464 unisucg 6463 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5280 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5282 trintALT 44878 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8640 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8642 onasuc 8564 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7433 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8641 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8643 onmsuc 8565 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8658 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8645 nnacom 8653 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8659 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8660 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8662 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8646 nnmsucr 8661 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8674 |
| [Enderton] p. 129 | Definition | df-en 8984 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7384 |
| [Enderton] p. 133 | Exercise 1 | xpomen 10052 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16245 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9244 |
| [Enderton] p. 135 | Corollary 6C | php3 9246 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9243 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9289 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9291 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9206 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9211 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9179 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10217 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10218 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10213 dju1en 10209 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9380 unifi 9381 unifi2 9382 |
| [Enderton] p. 144 | Corollary 6K | undif2 4482 unfi 9209 unfi2 9345 |
| [Enderton] p. 145 | Figure 38 | ffoss 7968 |
| [Enderton] p. 145 | Definition | df-dom 8985 |
| [Enderton] p. 146 | Example 1 | domen 9000 domeng 9001 |
| [Enderton] p. 146 | Example 3 | nndomo 9266 nnsdom 9691 nnsdomg 9332 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10221 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9180 xpdom1 9109 xpdom1g 9107 xpdom2g 9106 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9186 |
| [Enderton] p. 151 | Theorem 6M | zorn 10544 zorng 10541 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10529 dfac5 10166 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10612 |
| [Enderton] p. 164 | Example | infdif 10245 |
| [Enderton] p. 168 | Definition | df-po 5596 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6499 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6431 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6498 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6439 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7858 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7799 |
| [Enderton] p. 194 | Remark | onprc 7796 |
| [Enderton] p. 194 | Exercise 16 | suc11 6492 |
| [Enderton] p. 197 | Definition | df-card 9976 |
| [Enderton] p. 197 | Theorem 7P | carden 10588 |
| [Enderton] p. 200 | Exercise 25 | tfis 7875 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9813 |
| [Enderton] p. 202 | Definition | df-r1 9801 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9823 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9904 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9643 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9894 rankprb 9888 rankpw 9880 rankpwi 9860 rankuniss 9903 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9655 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9656 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10147 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 10113 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10127 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8379 |
| [Enderton] p. 222 | Definition of kard | karden 9932 kardex 9931 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8633 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8635 |
| [Enderton] p. 240 | Exercise 25 | oarec 8598 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10287 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17686 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17632 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18610 mrieqv2d 17683 mrieqvd 17682 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17687 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17692 mreexexlem2d 17689 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18616 mreexfidimd 17694 |
| [Frege1879] p. 11 | Statement | df3or2 43757 |
| [Frege1879] p. 12 | Statement | df3an2 43758 dfxor4 43755 dfxor5 43756 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 43779 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 43780 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 43784 |
| [Frege1879] p. 31 | Proposition 4 | frege4 43788 |
| [Frege1879] p. 32 | Proposition 5 | frege5 43789 |
| [Frege1879] p. 33 | Proposition 6 | frege6 43795 |
| [Frege1879] p. 34 | Proposition 7 | frege7 43797 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 43798 axfrege8 43796 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 90 wl-luk-pm2.04 37427 |
| [Frege1879] p. 35 | Proposition 9 | frege9 43801 |
| [Frege1879] p. 36 | Proposition 10 | frege10 43809 |
| [Frege1879] p. 36 | Proposition 11 | frege11 43803 |
| [Frege1879] p. 37 | Proposition 12 | frege12 43802 |
| [Frege1879] p. 37 | Proposition 13 | frege13 43811 |
| [Frege1879] p. 37 | Proposition 14 | frege14 43812 |
| [Frege1879] p. 38 | Proposition 15 | frege15 43815 |
| [Frege1879] p. 38 | Proposition 16 | frege16 43805 |
| [Frege1879] p. 39 | Proposition 17 | frege17 43810 |
| [Frege1879] p. 39 | Proposition 18 | frege18 43807 |
| [Frege1879] p. 39 | Proposition 19 | frege19 43813 |
| [Frege1879] p. 40 | Proposition 20 | frege20 43817 |
| [Frege1879] p. 40 | Proposition 21 | frege21 43816 |
| [Frege1879] p. 41 | Proposition 22 | frege22 43808 |
| [Frege1879] p. 42 | Proposition 23 | frege23 43814 |
| [Frege1879] p. 42 | Proposition 24 | frege24 43804 |
| [Frege1879] p. 42 | Proposition 25 | frege25 43806 rp-frege25 43794 |
| [Frege1879] p. 42 | Proposition 26 | frege26 43799 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 43819 |
| [Frege1879] p. 43 | Proposition 27 | frege27 43800 |
| [Frege1879] p. 43 | Proposition 28 | con3 153 |
| [Frege1879] p. 43 | Proposition 29 | frege29 43820 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 43823 axfrege31 43822 |
| [Frege1879] p. 44 | Proposition 30 | frege30 43821 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 130 |
| [Frege1879] p. 44 | Proposition 32 | frege32 43824 |
| [Frege1879] p. 44 | Proposition 33 | frege33 43825 |
| [Frege1879] p. 45 | Proposition 34 | frege34 43826 |
| [Frege1879] p. 45 | Proposition 35 | frege35 43827 |
| [Frege1879] p. 45 | Proposition 36 | frege36 43828 |
| [Frege1879] p. 46 | Proposition 37 | frege37 43829 |
| [Frege1879] p. 46 | Proposition 38 | frege38 43830 |
| [Frege1879] p. 46 | Proposition 39 | frege39 43831 |
| [Frege1879] p. 46 | Proposition 40 | frege40 43832 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 43834 axfrege41 43833 |
| [Frege1879] p. 47 | Proposition 41 | notnot 142 |
| [Frege1879] p. 47 | Proposition 42 | frege42 43835 |
| [Frege1879] p. 47 | Proposition 43 | frege43 43836 |
| [Frege1879] p. 47 | Proposition 44 | frege44 43837 |
| [Frege1879] p. 47 | Proposition 45 | frege45 43838 |
| [Frege1879] p. 48 | Proposition 46 | frege46 43839 |
| [Frege1879] p. 48 | Proposition 47 | frege47 43840 |
| [Frege1879] p. 49 | Proposition 48 | frege48 43841 |
| [Frege1879] p. 49 | Proposition 49 | frege49 43842 |
| [Frege1879] p. 49 | Proposition 50 | frege50 43843 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 43846 ax-frege52c 43877 frege52aid 43847 frege52b 43878 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 43851 ax-frege54c 43881 frege54b 43882 |
| [Frege1879] p. 50 | Proposition 51 | frege51 43844 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3792 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 43849 frege53aid 43848 frege53b 43879 frege53c 43903 |
| [Frege1879] p. 50 | Proposition 54 | biid 261 eqid 2734 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 43857 frege55aid 43854 frege55b 43886 frege55c 43907 frege55cor1a 43858 frege55lem2a 43856 frege55lem2b 43885 frege55lem2c 43906 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 43860 frege56aid 43859 frege56b 43887 frege56c 43908 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 43864 ax-frege58b 43890 frege58bid 43891 frege58c 43910 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 43862 frege57aid 43861 frege57b 43888 frege57c 43909 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3803 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 43866 frege59b 43893 frege59c 43911 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 43867 frege60b 43894 frege60c 43912 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 43868 frege61b 43895 frege61c 43913 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 43869 frege62b 43896 frege62c 43914 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 43870 frege63b 43897 frege63c 43915 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 43871 frege64b 43898 frege64c 43916 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 43872 frege65b 43899 frege65c 43917 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 43873 frege66b 43900 frege66c 43918 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 43874 frege67b 43901 frege67c 43919 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 43875 frege68b 43902 frege68c 43920 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 43921 |
| [Frege1879] p. 58 | Proposition 70 | frege70 43922 |
| [Frege1879] p. 59 | Proposition 71 | frege71 43923 |
| [Frege1879] p. 59 | Proposition 72 | frege72 43924 |
| [Frege1879] p. 59 | Proposition 73 | frege73 43925 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 43928 |
| [Frege1879] p. 60 | Proposition 74 | frege74 43926 |
| [Frege1879] p. 60 | Proposition 75 | frege75 43927 |
| [Frege1879] p. 62 | Proposition 77 | frege77 43929 frege77d 43735 |
| [Frege1879] p. 63 | Proposition 78 | frege78 43930 |
| [Frege1879] p. 63 | Proposition 79 | frege79 43931 |
| [Frege1879] p. 63 | Proposition 80 | frege80 43932 |
| [Frege1879] p. 63 | Proposition 81 | frege81 43933 frege81d 43736 |
| [Frege1879] p. 64 | Proposition 82 | frege82 43934 |
| [Frege1879] p. 65 | Proposition 83 | frege83 43935 frege83d 43737 |
| [Frege1879] p. 65 | Proposition 84 | frege84 43936 |
| [Frege1879] p. 66 | Proposition 85 | frege85 43937 |
| [Frege1879] p. 66 | Proposition 86 | frege86 43938 |
| [Frege1879] p. 66 | Proposition 87 | frege87 43939 frege87d 43739 |
| [Frege1879] p. 67 | Proposition 88 | frege88 43940 |
| [Frege1879] p. 68 | Proposition 89 | frege89 43941 |
| [Frege1879] p. 68 | Proposition 90 | frege90 43942 |
| [Frege1879] p. 68 | Proposition 91 | frege91 43943 frege91d 43740 |
| [Frege1879] p. 69 | Proposition 92 | frege92 43944 |
| [Frege1879] p. 70 | Proposition 93 | frege93 43945 |
| [Frege1879] p. 70 | Proposition 94 | frege94 43946 |
| [Frege1879] p. 70 | Proposition 95 | frege95 43947 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 43951 |
| [Frege1879] p. 71 | Proposition 96 | frege96 43948 frege96d 43738 |
| [Frege1879] p. 71 | Proposition 97 | frege97 43949 frege97d 43741 |
| [Frege1879] p. 71 | Proposition 98 | frege98 43950 frege98d 43742 |
| [Frege1879] p. 72 | Proposition 100 | frege100 43952 |
| [Frege1879] p. 72 | Proposition 101 | frege101 43953 |
| [Frege1879] p. 72 | Proposition 102 | frege102 43954 frege102d 43743 |
| [Frege1879] p. 73 | Proposition 103 | frege103 43955 |
| [Frege1879] p. 73 | Proposition 104 | frege104 43956 |
| [Frege1879] p. 73 | Proposition 105 | frege105 43957 |
| [Frege1879] p. 73 | Proposition 106 | frege106 43958 frege106d 43744 |
| [Frege1879] p. 74 | Proposition 107 | frege107 43959 |
| [Frege1879] p. 74 | Proposition 108 | frege108 43960 frege108d 43745 |
| [Frege1879] p. 74 | Proposition 109 | frege109 43961 frege109d 43746 |
| [Frege1879] p. 75 | Proposition 110 | frege110 43962 |
| [Frege1879] p. 75 | Proposition 111 | frege111 43963 frege111d 43748 |
| [Frege1879] p. 76 | Proposition 112 | frege112 43964 |
| [Frege1879] p. 76 | Proposition 113 | frege113 43965 |
| [Frege1879] p. 76 | Proposition 114 | frege114 43966 frege114d 43747 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 43967 |
| [Frege1879] p. 77 | Proposition 116 | frege116 43968 |
| [Frege1879] p. 78 | Proposition 117 | frege117 43969 |
| [Frege1879] p. 78 | Proposition 118 | frege118 43970 |
| [Frege1879] p. 78 | Proposition 119 | frege119 43971 |
| [Frege1879] p. 78 | Proposition 120 | frege120 43972 |
| [Frege1879] p. 79 | Proposition 121 | frege121 43973 |
| [Frege1879] p. 79 | Proposition 122 | frege122 43974 frege122d 43749 |
| [Frege1879] p. 79 | Proposition 123 | frege123 43975 |
| [Frege1879] p. 80 | Proposition 124 | frege124 43976 frege124d 43750 |
| [Frege1879] p. 81 | Proposition 125 | frege125 43977 |
| [Frege1879] p. 81 | Proposition 126 | frege126 43978 frege126d 43751 |
| [Frege1879] p. 82 | Proposition 127 | frege127 43979 |
| [Frege1879] p. 83 | Proposition 128 | frege128 43980 |
| [Frege1879] p. 83 | Proposition 129 | frege129 43981 frege129d 43752 |
| [Frege1879] p. 84 | Proposition 130 | frege130 43982 |
| [Frege1879] p. 85 | Proposition 131 | frege131 43983 frege131d 43753 |
| [Frege1879] p. 86 | Proposition 132 | frege132 43984 |
| [Frege1879] p. 86 | Proposition 133 | frege133 43985 frege133d 43754 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 46268 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 46591 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 46291 |
| [Fremlin1] p. 14 | Definition 112A | ismea 46406 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 46426 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 46417 meadjunre 46431 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 46418 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 46419 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 46415 meaiunle 46424 meaiunlelem 46423 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 46436 meaiuninc2 46437 meaiuninc3 46440 meaiuninc3v 46439 meaiunincf 46438 meaiuninclem 46435 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 46442 meaiininc2 46443 meaiininclem 46441 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 46461 caragendifcl 46469 caratheodory 46483 omelesplit 46473 |
| [Fremlin1] p. 19 | Definition 113A | isome 46449 isomennd 46486 isomenndlem 46485 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 46471 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 46490 voncmpl 46576 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 46453 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 46478 carageniuncllem1 46476 carageniuncllem2 46477 caragenuncl 46468 caragenuncllem 46467 caragenunicl 46479 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 46487 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 46481 caratheodorylem2 46482 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 46490 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 46549 hoidmv1lelem1 46546 hoidmv1lelem2 46547 hoidmv1lelem3 46548 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 46593 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 46549 hoidmvle 46555 hoidmvlelem1 46550 hoidmvlelem2 46551 hoidmvlelem3 46552 hoidmvlelem4 46553 hoidmvlelem5 46554 hsphoidmvle2 46540 hsphoif 46531 hsphoival 46534 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 46503 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 46511 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 46538 hoidmvn0val 46539 hoidmvval 46532 hoidmvval0 46542 hoidmvval0b 46545 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 46543 hsphoidmvle 46541 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 46492 df-voln 46494 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 46559 ovn0 46521 ovn0lem 46520 ovnf 46518 ovnome 46528 ovnssle 46516 ovnsslelem 46515 ovnsupge0 46512 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 46558 ovnhoilem1 46556 ovnhoilem2 46557 vonhoi 46622 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 46575 hoidifhspf 46573 hoidifhspval 46563 hoidifhspval2 46570 hoidifhspval3 46574 hspmbl 46584 hspmbllem1 46581 hspmbllem2 46582 hspmbllem3 46583 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 46576 vonmea 46529 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 46527 ovnsubadd2 46601 ovnsubadd2lem 46600 ovnsubaddlem1 46525 ovnsubaddlem2 46526 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 46586 hoimbl2 46620 hoimbllem 46585 hspdifhsp 46571 opnvonmbl 46589 opnvonmbllem2 46588 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 46591 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 46634 iccvonmbllem 46633 ioovonmbl 46632 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 46640 vonicclem2 46639 vonioo 46637 vonioolem2 46636 vonn0icc 46643 vonn0icc2 46647 vonn0ioo 46642 vonn0ioo2 46645 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 46644 snvonmbl 46641 vonct 46648 vonsn 46646 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 46314 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 46313 subsaliuncllem 46312 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 46680 salpreimalegt 46664 salpreimaltle 46681 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 46683 issmff 46689 issmflem 46682 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 46700 issmflelem 46699 smfpreimale 46709 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 46711 issmfgtlem 46710 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 46651 issmf 46683 issmff 46689 issmfge 46725 issmfgelem 46724 issmfgt 46711 issmfgtlem 46710 issmfle 46700 issmflelem 46699 issmflem 46682 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 46662 salpreimagtlt 46685 salpreimalelt 46684 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 46725 issmfgelem 46724 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 46708 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 46706 cnfsmf 46695 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 46722 decsmflem 46721 incsmf 46697 incsmflem 46696 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 46656 pimconstlt1 46657 smfconst 46704 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 46720 smfaddlem1 46718 smfaddlem2 46719 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 46751 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 46750 smfmullem1 46746 smfmullem2 46747 smfmullem3 46748 smfmullem4 46749 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 46752 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 46755 smfpimbor1lem2 46754 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 46757 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 46745 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 46744 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 46753 smfresal 46743 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 46732 smflim2 46761 smflimlem1 46726 smflimlem2 46727 smflimlem3 46728 smflimlem4 46729 smflimlem5 46730 smflimlem6 46731 smflimmpt 46765 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 46769 smfsuplem1 46766 smfsuplem2 46767 smfsuplem3 46768 smfsupmpt 46770 smfsupxr 46771 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 46773 smfinflem 46772 smfinfmpt 46774 |
| [Fremlin1] p. 39 | Remark 121G | smflim 46732 smflim2 46761 smflimmpt 46765 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 46763 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 46793 smfdivdmmbl2 46796 smfinfdmmbl 46804 smfinfdmmbllem 46803 smfsupdmmbl 46800 smfsupdmmbllem 46799 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 46783 smflimsuplem2 46776 smflimsuplem6 46780 smflimsuplem7 46781 smflimsuplem8 46782 smflimsupmpt 46784 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 46786 smfliminflem 46785 smfliminfmpt 46787 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 46651 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 46797 fsupdm2 46798 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 46788 adddmmbl2 46789 finfdm 46801 finfdm2 46802 fsupdm 46797 fsupdm2 46798 muldmmbl 46790 muldmmbl2 46791 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 46801 finfdm2 46802 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25584 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25627 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25637 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 37684 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 37687 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9675 inf1 9659 inf2 9660 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10948 enqer 10958 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10953 df-nq 10949 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10945 df-plq 10951 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7669 df-mpq 10946 df-mq 10952 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10954 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 11012 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 11013 ltbtwnnq 11015 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 11008 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 11009 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 11016 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 11018 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 11030 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 11032 |
| [Gleason] p. 122 | Definition | df-1p 11019 |
| [Gleason] p. 122 | Remark (1) | prub 11031 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 11070 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 11022 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 11069 psslinpr 11068 supexpr 11091 suplem1pr 11089 suplem2pr 11090 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 11055 addclprlem1 11053 addclprlem2 11054 df-plp 11020 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 11059 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 11058 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 11071 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 11080 ltexprlem1 11073 ltexprlem2 11074 ltexprlem3 11075 ltexprlem4 11076 ltexprlem5 11077 ltexprlem6 11078 ltexprlem7 11079 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 11082 ltaprlem 11081 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 11083 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 11084 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 11021 mulclpr 11057 mulclprlem 11056 reclem2pr 11085 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 11066 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 11061 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 11060 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 11065 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 11088 reclem3pr 11086 reclem4pr 11087 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 11092 enrer 11100 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 11097 df-1r 11098 df-nr 11093 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 11095 df-plr 11094 negexsr 11139 recexsr 11144 recexsrlem 11140 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 11096 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12258 creur 12257 cru 12255 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11225 axcnre 11201 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15150 crimd 15267 crimi 15228 crre 15149 crred 15266 crrei 15227 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15152 remimd 15233 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15319 absval2d 15480 absval2i 15432 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15176 cjaddd 15255 cjaddi 15223 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15177 cjmuld 15256 cjmuli 15224 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15175 cjcjd 15234 cjcji 15206 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15174 cjreb 15158 cjrebd 15237 cjrebi 15209 cjred 15261 rere 15157 rereb 15155 rerebd 15236 rerebi 15208 rered 15259 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15183 addcjd 15247 addcji 15218 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15273 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15314 abscjd 15485 abscji 15436 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15324 abs00d 15481 abs00i 15433 absne0d 15482 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15356 releabsd 15486 releabsi 15437 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15329 absmuld 15489 absmuli 15439 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15317 sqabsaddi 15440 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15365 abstrid 15491 abstrii 15443 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14099 exp0 14102 expp1 14105 expp1d 14183 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26735 cxpaddd 26773 expadd 14141 expaddd 14184 expaddz 14143 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26744 cxpmuld 26793 expmul 14144 expmuld 14185 expmulz 14145 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26741 mulcxpd 26784 mulexp 14138 mulexpd 14197 mulexpz 14139 |
| [Gleason] p. 140 | Exercise 1 | znnen 16244 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13545 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15664 rlimadd 15675 rlimdiv 15678 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15666 rlimsub 15676 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15665 rlimmul 15677 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15669 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15615 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15636 climcj 15637 climim 15639 climre 15638 rlimabs 15641 rlimcj 15642 rlimim 15644 rlimre 15643 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11297 df-xr 11296 ltxr 13154 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15503 limsupval 15506 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15702 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15711 caucvgb 15712 caucvgbf 45439 caucvgr 15708 climcau 15703 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15848 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15915 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15370 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13864 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21375 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24368 xmet0 24367 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24384 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24375 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24377 mstri 24494 xmettri 24376 xmstri 24493 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24407 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23671 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25357 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24568 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24900 addcn2 15626 mulcn 24902 mulcn2 15628 subcn 24901 subcn2 15627 |
| [Gleason] p. 295 | Remark | bcval3 14341 bcval4 14342 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14356 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14339 df-bc 14338 |
| [Gleason] p. 296 | Remark | bcn0 14345 bcnn 14347 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15862 |
| [Gleason] p. 308 | Equation 2 | ef0 16123 |
| [Gleason] p. 308 | Equation 3 | efcj 16124 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16129 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16133 |
| [Gleason] p. 310 | Equation 14 | sinadd 16196 |
| [Gleason] p. 310 | Equation 15 | cosadd 16197 |
| [Gleason] p. 311 | Equation 17 | sincossq 16208 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16213 sinbnd 16212 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14251 sqeqori 14249 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16104 |
| [Godowski] p. 730 | Equation SF | goeqi 32301 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 31696 |
| [Golan] p. 1 | Remark | srgisid 20226 |
| [Golan] p. 1 | Definition | df-srg 20204 |
| [Golan] p. 149 | Definition | df-slmd 33189 |
| [Gonshor] p. 7 | Definition | df-scut 27842 |
| [Gonshor] p. 9 | Theorem 2.5 | slerec 27878 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 27968 cofcut1d 27969 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 27970 cofcut2d 27971 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 27972 cofcutr1d 27973 cofcutr2d 27974 |
| [Gonshor] p. 13 | Definition | df-adds 28007 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 28023 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 28049 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28170 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28190 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28430 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28434 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28433 |
| [Gonshor] p. 95 | Theorem 6.1 | addsbday 28064 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36140 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17630 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17632 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 48031 df-cllaw 48029 df-comlaw 48030 |
| [Hall] p. 2 | Section 1.2 | df-clintop 48043 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 48064 |
| [Halmos] p. 28 | Partition ` ` | df-parts 38746 dfmembpart2 38751 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32093 riesz2 32094 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 31969 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32201 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32213 elpjidm 32212 pjnmopi 32176 |
| [Halmos] p. 44 | Remark | pjinormi 31715 pjinormii 31704 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32217 pjrn 31735 pjrni 31730 pjvec 31724 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 31755 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32182 hmopidmpji 32180 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32219 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32208 pjocvec 31725 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32197 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32200 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32203 pjssdif2i 32202 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 31883 |
| [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 1791 |
| [Hatcher] p. 25 | Definition | df-phtpc 25037 df-phtpy 25016 |
| [Hatcher] p. 26 | Definition | df-pco 25051 df-pi1 25054 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 25040 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 25096 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22511 df-dmatalt 48243 |
| [Helfgott] p. 2 | Theorem | tgoldbach 47741 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 47726 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 47738 bgoldbtbnd 47733 bgoldbtbnd 47733 tgblthelfgott 47739 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 34635 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 34636 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 34650 hgt750lemb 34649 hgt750leme 34651 hgt750lemf 34646 hgt750lemg 34647 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 47735 tgoldbachgt 34656 tgoldbachgtALTV 47736 tgoldbachgtd 34655 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 34637 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30521 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 18974 grpoideu 30537 mndideu 18770 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 19004 grpoinveu 30547 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 19035 grpo2inv 30559 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 19048 grpoinvop 30561 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 19070 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1764 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1765 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1767 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32448 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32461 cdj3i 32469 cdj3lem1 32462 cdjreui 32460 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32459 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 41947 |
| [Holland95] p. 14 | Line 15 | hgmapvs 41873 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 41895 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 41896 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 41893 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 41899 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 41818 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 41913 |
| [Holland95] p. 204 | Definition of involution | df-srng 20857 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 39485 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 41510 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 41463 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 39915 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 41359 poml4N 39935 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 41450 pexmidALTN 39960 pexmidN 39951 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 41515 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 39105 ldualset 39106 |
| [Holland95] p. 222 | Item 1 | df-lines 39483 df-pointsN 39484 |
| [Holland95] p. 222 | Item 2 | df-polarityN 39885 |
| [Holland95] p. 223 | Remark | ispsubcl2N 39929 omllaw4 39227 pol1N 39892 polcon3N 39899 |
| [Holland95] p. 223 | Definition | df-psubclN 39917 |
| [Holland95] p. 223 | Equation for polarity | polval2N 39888 |
| [Holmes] p. 40 | Definition | df-xrn 38352 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31112 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32210 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 31991 eigre 31863 eigrei 31862 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 31992 eigorth 31866 eigorthi 31865 |
| [Hughes] p. 137 | Remark (ii) | eigposi 31864 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30337 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30333 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30334 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30335 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30353 frgrregorufr0 30352 frgrregorufrg 30354 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30360 frrusgrord 30369 frrusgrord0 30368 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30116 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30343 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30346 frgrwopreg2 30347 frgrwopregasn 30344 frgrwopregbsn 30345 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30349 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30363 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30366 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30114 numclwlk1 30399 numclwlk1lem1 30397 numclwlk1lem2 30398 numclwwlk1 30389 numclwwlk8 30420 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30340 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 29803 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30375 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30401 numclwwlkovh0 30400 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30409 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 30006 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30413 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30416 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30419 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30431 natded 30431 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30431 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30431 natded 30431 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30431 |
| [Jech] p. 4 | Definition of class | cv 1535 cvjust 2728 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10616 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10614 alephmul 10615 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10613 infmap2 10254 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9851 |
| [Jech] p. 72 | Equation 9.3 | scott0 9923 scottex 9922 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9904 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9928 |
| [Jech] p. 78 | Note | opthprc 5752 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 42903 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 42991 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 42992 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 42915 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 42919 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 42920 rmyp1 42921 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 42922 rmym1 42923 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 42913 rmx1 42914 rmxluc 42924 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 42917 rmy1 42918 rmyluc 42925 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 42927 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 42928 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 42948 jm2.17b 42949 jm2.17c 42950 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 42981 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 42985 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 42976 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 42951 jm2.24nn 42947 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 42990 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 42996 rmygeid 42952 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 43008 |
| [Juillerat] p. 11 | Section *5 | etransc 46238 etransclem47 46236 etransclem48 46237 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 46233 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 46235 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 46221 |
| [Juillerat] p. 13 | Proof | etransclem35 46224 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 46227 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 46213 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 46230 |
| [Juillerat] p. 14 | Proof | etransclem23 46212 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1964 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2008 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2013 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2003 cbvaliw 2002 wl-cbvmotv 37493 wl-motae 37495 wl-moteq 37494 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 1992 spimw 1967 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2029 spw 2030 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31544 chabs1i 31546 chabs2 31545 chabs2i 31547 chjass 31561 chjassi 31514 latabs1 18532 latabs2 18533 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32366 ela 32367 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32311 cvrval2 39255 |
| [Kalmbach] p. 16 | Definition | df-ol 39159 df-oml 39160 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 31612 cmbri 31618 cmtvalN 39192 df-cm 31611 df-cmtN 39158 |
| [Kalmbach] p. 22 | Remark | omllaw5N 39228 pjoml5 31641 pjoml5i 31616 |
| [Kalmbach] p. 22 | Definition | pjoml2 31639 pjoml2i 31613 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 31642 cmcmi 31620 cmcmii 31625 cmtcomN 39230 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 39226 omlsi 31432 pjoml 31464 pjomli 31463 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 39225 |
| [Kalmbach] p. 23 | Remark | cmbr2i 31624 cmcm3 31643 cmcm3i 31622 cmcm3ii 31627 cmcm4i 31623 cmt3N 39232 cmt4N 39233 cmtbr2N 39234 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 31636 cmbr3i 31628 cmtbr3N 39235 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 31646 fh1i 31649 fh2 31647 fh2i 31650 omlfh1N 39239 |
| [Kalmbach] p. 65 | Remark | chjatom 32385 chslej 31526 chsleji 31486 shslej 31408 shsleji 31398 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31523 chocini 31482 chsupcl 31368 chsupval2 31438 h0elch 31283 helch 31271 hsupval2 31437 ocin 31324 ococss 31321 shococss 31322 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31340 |
| [Kalmbach] p. 66 | Remark | df-pjh 31423 pjssmi 32193 pjssmii 31709 |
| [Kalmbach] p. 67 | Lemma 3 | osum 31673 osumi 31670 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32228 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32428 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32338 |
| [Kalmbach] p. 140 | Remark | hatomic 32388 hatomici 32387 hatomistici 32390 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 39300 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32409 lsatexch 39024 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32383 cvlcvr1 39320 cvr1 39392 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32402 cvexchi 32397 cvrexch 39402 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32392 hlrelat 39384 hlrelat5N 39383 lrelat 38995 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21160 lsmsatcv 38991 spansncv 31681 spansncvi 31680 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 39010 spansncv2 32321 |
| [Kalmbach] p. 266 | Definition | df-st 32239 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 31877 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10683 fpwwe2 10680 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10684 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10691 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10686 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10688 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10701 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10705 gchxpidm 10706 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10717 gchhar 10716 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10252 unxpwdom 9626 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10707 |
| [Kreyszig] p. 3 | Property M1 | metcl 24357 xmetcl 24356 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24364 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24600 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11981 muleqadd 11904 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24463 |
| [Kreyszig] p. 19 | Remark | mopntopon 24464 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24526 mopnm 24469 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24524 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24529 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24570 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23281 lmmbr 25305 lmmbr2 25306 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23403 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25360 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25323 iscmet2 25341 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25363 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23484 metelcls 25352 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25353 metcld2 25354 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25145 lmodvneg1 20919 nvinv 30667 vcm 30604 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25141 lmod0vs 20909 slmd0vs 33212 vc0 30602 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20910 slmdvs0 33213 vcz 30603 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 30719 ngpmet 24631 nrmmetd 24602 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 30714 imsdval2 30715 ncvspds 25208 ngpds 24632 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24617 nvnd 30716 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24646 nmge0 24645 nvge0 30701 nvz 30697 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24652 nvabs 30700 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 30829 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 30773 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 30835 blocni 30833 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 30834 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25251 ipeq0 21673 ipz 30747 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25263 pythi 30878 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 30882 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25285 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15888 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25483 minveco 30912 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 30778 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25376 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 30901 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32151 leopg 32150 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32169 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 30946 |
| [Kulpa] p. 547 | Theorem | poimir 37639 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 37638 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 37637 |
| [Kulpa] p. 548 | Theorem | broucube 37640 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 37632 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 37633 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2385 axnul 5310 |
| [Kunen] p. 11 | Axiom 3 | axnul 5310 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 7977 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8876 mapvalg 8874 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10559 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7961 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9801 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9843 r1elssi 9842 |
| [Kunen] p. 107 | Exercise 4 | rankop 9895 rankopb 9889 rankuni 9900 rankxplim 9916 rankxpsuc 9919 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 44937 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 44946 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 44947 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 44945 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 44948 wfaxpr 44951 wfaxrep 44949 wfaxsep 44950 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 5008 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 33689 |
| [Lang] p. | Definition | df-rn 5699 |
| [Lang] p. 3 | Statement | lidrideqd 18694 mndbn0 18775 |
| [Lang] p. 3 | Definition | df-mnd 18760 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18712 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18866 |
| [Lang] p. 5 | Equation | gsumreidx 19949 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 48025 |
| [Lang] p. 6 | Example | nn0mnd 48022 |
| [Lang] p. 6 | Equation | gsumxp2 20012 |
| [Lang] p. 6 | Statement | cycsubm 19232 |
| [Lang] p. 6 | Definition | mulgnn0gsum 19110 |
| [Lang] p. 6 | Observation | mndlsmidm 19702 |
| [Lang] p. 7 | Definition | dfgrp2e 18993 |
| [Lang] p. 30 | Definition | df-tocyc 33109 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33154 |
| [Lang] p. 32 | Property (b) | cyc3conja 33159 cycpmconjv 33144 |
| [Lang] p. 53 | Definition | df-cat 17712 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18150 cat1lem 18149 |
| [Lang] p. 54 | Definition | df-iso 17796 |
| [Lang] p. 57 | Definition | df-inito 18037 df-termo 18038 |
| [Lang] p. 58 | Example | irinitoringc 21507 |
| [Lang] p. 58 | Statement | initoeu1 18064 termoeu1 18071 |
| [Lang] p. 62 | Definition | df-func 17908 |
| [Lang] p. 65 | Definition | df-nat 17997 |
| [Lang] p. 91 | Note | df-ringc 20662 |
| [Lang] p. 92 | Statement | mxidlprm 33477 |
| [Lang] p. 92 | Definition | isprmidlc 33454 |
| [Lang] p. 128 | Remark | dsmmlmod 21782 |
| [Lang] p. 129 | Proof | lincscm 48275 lincscmcl 48277 lincsum 48274 lincsumcl 48276 |
| [Lang] p. 129 | Statement | lincolss 48279 |
| [Lang] p. 129 | Observation | dsmmfi 21775 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 33654 qusdimsum 33655 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 33634 |
| [Lang] p. 147 | Definition | snlindsntor 48316 |
| [Lang] p. 504 | Statement | mat1 22468 matring 22464 |
| [Lang] p. 504 | Definition | df-mamu 22410 |
| [Lang] p. 505 | Statement | mamuass 22421 mamutpos 22479 matassa 22465 mattposvs 22476 tposmap 22478 |
| [Lang] p. 513 | Definition | mdet1 22622 mdetf 22616 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22712 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22608 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22632 |
| [Lang] p. 515 | Definition | df-minmar1 22656 smadiadetr 22696 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22631 mdetralt 22629 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22644 |
| [Lang] p. 518 | Definition | df-madu 22655 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22666 madurid 22665 matinv 22698 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 22911 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 33688 fedgmul 33658 |
| [Lang], p. 561 | Remark | chpmatply1 22853 |
| [Lang], p. 561 | Definition | df-chpmat 22848 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 44329 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 44324 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 44330 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5310 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2712 |
| [Levy] p. 59 | Definition | df-ttrcl 9745 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9788 |
| [Levy] p. 338 | Axiom | df-clel 2813 df-cleq 2726 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2813 df-cleq 2726 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2712 |
| [Levy] p. 358 | Axiom | df-clab 2712 |
| [Levy58] p. 2 | Definition I | isfin1-3 10423 |
| [Levy58] p. 2 | Definition II | df-fin2 10323 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10322 |
| [Levy58] p. 2 | Definition III | df-fin3 10325 |
| [Levy58] p. 3 | Definition V | df-fin5 10326 |
| [Levy58] p. 3 | Definition IV | df-fin4 10324 |
| [Levy58] p. 4 | Definition VI | df-fin6 10327 |
| [Levy58] p. 4 | Definition VII | df-fin7 10328 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10452 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27745 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27756 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27788 nosupbnd1 27773 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27790 nosupbnd2 27775 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27794 noetasuplem4 27795 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27791 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1764 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1765 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1767 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32436 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32440 mdsymi 32439 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32434 mdsymlem6 32436 mdsymlem7 32437 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32438 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32341 ssdmd2 32342 ssmd1 32339 ssmd2 32340 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32337 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32309 df-md 32308 mdbr 32322 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32359 mdslj1i 32347 mdslj2i 32348 mdslle1i 32345 mdslle2i 32346 mdslmd1i 32357 mdslmd2i 32358 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32349 mdsl2bi 32351 mdsl2i 32350 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32363 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32360 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32361 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32338 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32343 mdsl3 32344 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32362 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32457 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 39302 hlrelat1 39382 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 39020 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32364 cvmdi 32352 cvnbtwn4 32317 cvrnbtwn4 39260 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32365 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 39321 cvp 32403 cvrp 39398 lcvp 39021 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32427 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32426 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 39314 hlexch4N 39374 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32429 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 39425 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 39731 atpsubN 39735 df-pointsN 39484 pointpsubN 39733 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 39486 pmap11 39744 pmaple 39743 pmapsub 39750 pmapval 39739 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 39747 pmap1N 39749 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 39752 pmapglb2N 39753 pmapglb2xN 39754 pmapglbx 39751 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 39834 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 39459 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 39778 paddclN 39824 paddidm 39823 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 39460 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 39820 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 39459 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 39460 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19707 lsmmod2 19708 lssats 38993 shatomici 32386 shatomistici 32389 shmodi 31418 shmodsi 31417 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32328 mdsymlem7 32437 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 31617 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31521 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32443 |
| [Margaris] p. 40 | Rule C | exlimiv 1927 |
| [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 1776 df-or 848 dfbi2 474 |
| [Margaris] p. 51 | Theorem 1 | idALT 23 |
| [Margaris] p. 56 | Theorem 3 | conventions 30428 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 44912 |
| [Margaris] p. 60 | Theorem 8 | jcn 162 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 44913 |
| [Margaris] p. 79 | Rule C | exinst01 44622 exinst11 44623 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1973 19.2g 2185 r19.2z 4500 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2199 rr19.3v 3666 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2156 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1822 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1777 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2178 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2202 19.9h 2284 exlimd 2215 exlimdh 2288 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2159 excomim 2160 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2325 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30429 conventions-labels 30429 conventions-labels 30429 conventions-labels 30429 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1823 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 44373 albi 1814 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2222 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2223 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 44375 exbi 1843 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2226 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 44372 2alimdv 1915 alimd 2209 alimdh 1813 alimdv 1913 ax-4 1805 ralimdaa 3257 ralimdv 3166 ralimdva 3164 ralimdvva 3203 sbcimdv 3864 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2204 19.21h 2285 19.21t 2203 19.21vv 44371 alrimd 2212 alrimdd 2211 alrimdh 1860 alrimdv 1926 alrimi 2210 alrimih 1820 alrimiv 1924 alrimivv 1925 hbralrimi 3141 r19.21be 3249 r19.21bi 3248 ralrimd 3261 ralrimdv 3149 ralrimdva 3151 ralrimdvv 3200 ralrimdvva 3208 ralrimi 3254 ralrimia 3255 ralrimiv 3142 ralrimiva 3143 ralrimivv 3197 ralrimivva 3199 ralrimivvva 3202 ralrimivw 3147 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 44374 2eximdv 1916 exim 1830 eximd 2213 eximdh 1861 eximdv 1914 rexim 3084 reximd2a 3266 reximdai 3258 reximdd 45090 reximddv 3168 reximddv2 3212 reximddv3 3169 reximdv 3167 reximdv2 3161 reximdva 3165 reximdvai 3162 reximdvva 3204 reximi2 3076 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2208 19.23bi 2188 19.23h 2286 19.23t 2207 exlimdv 1930 exlimdvv 1931 exlimexi 44521 exlimiv 1927 exlimivv 1929 rexlimd3 45083 rexlimdv 3150 rexlimdv3a 3156 rexlimdva 3152 rexlimdva2 3154 rexlimdvaa 3153 rexlimdvv 3209 rexlimdvva 3210 rexlimdvvva 3211 rexlimdvw 3157 rexlimiv 3145 rexlimiva 3144 rexlimivv 3198 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 1982 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1877 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1867 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2224 r19.27z 4510 r19.27zv 4511 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2225 19.28vv 44381 r19.28z 4503 r19.28zf 45101 r19.28zv 4506 rr19.28v 3667 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1870 r19.29d2r 3137 r19.29imd 3115 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1878 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2231 19.31vv 44379 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2230 r19.32 47047 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 44377 19.33 1881 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 1983 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1874 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2227 19.36vv 44378 r19.36zv 4512 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2229 19.37vv 44380 r19.37zv 4507 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1835 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 1981 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1884 19.40 1883 r19.40 3116 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2232 19.41rg 44547 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2233 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1879 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2234 r19.44zv 4509 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2235 r19.45zv 4508 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2607 |
| [Mayet] p. 370 | Remark | jpi 32298 largei 32295 stri 32285 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32240 ishst 32242 |
| [Mayet3] p. 10 | Theorem | hstrbi 32294 hstri 32293 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 31756 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 31757 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32306 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31360 chsupcl 31368 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32388 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32382 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32409 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 39965 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18544 latj32 18542 latjass 18540 |
| [Megill] p. 444 | Axiom C5 | ax-5 1907 ax5ALT 38888 |
| [Megill] p. 444 | Section 7 | conventions 30428 |
| [Megill] p. 445 | Lemma L12 | aecom-o 38882 ax-c11n 38869 axc11n 2428 |
| [Megill] p. 446 | Lemma L17 | equtrr 2018 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 38877 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 38909 hbnae 2434 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2483 sbid 2252 sbidd-misc 48949 sbidd 48948 |
| [Megill] p. 448 | Remark 9.6 | axc14 2465 |
| [Megill] p. 448 | Scheme C4' | ax-c4 38865 |
| [Megill] p. 448 | Scheme C5' | ax-c5 38864 sp 2180 |
| [Megill] p. 448 | Scheme C6' | ax-11 2154 |
| [Megill] p. 448 | Scheme C7' | ax-c7 38866 |
| [Megill] p. 448 | Scheme C8' | ax-7 2004 |
| [Megill] p. 448 | Scheme C9' | ax-c9 38871 |
| [Megill] p. 448 | Scheme C10' | ax-6 1964 ax-c10 38867 |
| [Megill] p. 448 | Scheme C11' | ax-c11 38868 |
| [Megill] p. 448 | Scheme C12' | ax-8 2107 |
| [Megill] p. 448 | Scheme C13' | ax-9 2115 |
| [Megill] p. 448 | Scheme C14' | ax-c14 38872 |
| [Megill] p. 448 | Scheme C15' | ax-c15 38870 |
| [Megill] p. 448 | Scheme C16' | ax-c16 38873 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 38885 dral1 2441 dral2-o 38911 dral2 2440 drex1 2443 drex2 2444 drsb1 2497 drsb2 2263 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2170 sbequ 2080 sbid2v 2511 |
| [Megill] p. 450 | Example in Appendix | hba1-o 38878 hba1 2291 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 46841 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 23 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3887 rspsbca 3888 stdpc4 2065 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 38865 ra4 3894 stdpc5 2205 |
| [Mendelson] p. 81 | Rule C | exlimiv 1927 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2024 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2247 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3788 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5523 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4403 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4404 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4282 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4339 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4283 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4150 |
| [Mendelson] p. 231 | Definition of union | dfun3 4281 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5461 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4908 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5578 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4622 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5579 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4935 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5838 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6289 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7793 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6391 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8631 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9178 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 9093 xpsneng 9094 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9101 xpcomeng 9102 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9104 |
| [Mendelson] p. 255 | Definition | brsdom 9013 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9096 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8868 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 9075 mapsnend 9074 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9184 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9183 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8920 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 9078 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9097 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10216 djucomen 10215 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10220 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10214 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8567 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8594 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10596 |
| [Mendelson] p. 281 | Definition | df-r1 9801 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9850 |
| [Mendelson] p. 287 | Axiom system MK | ru 3788 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30287 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30322 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30324 vdgn1frgrv3 30325 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30326 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30319 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30312 2pthfrgrrn 30310 2pthfrgrrn2 30311 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31280 |
| [Monk1] p. 22 | Remark | conventions 30428 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30428 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4246 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5794 ssrelf 32634 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5796 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5210 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6283 coi2 6284 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5933 rn0 5938 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 6163 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5706 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5941 rnxp 6191 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5786 xp0 6179 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6096 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6093 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7936 imaexALTV 38311 imaexg 7935 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6090 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7094 funfvop 7069 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6962 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6973 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6613 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7274 dff13f 7275 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7238 funrnex 7976 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7266 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6248 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4968 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 8029 df-1st 8012 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 8030 df-2nd 8013 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9891 ranksnb 9864 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9892 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9893 rankunb 9887 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9875 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9801 r1val2 9874 |
| [Monk1] p. 117 | Lemma | zorn2 10543 zorn2g 10540 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 10023 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10598 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 10018 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1805 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2004 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2174 ax-c15 38870 ax12v2 2176 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 38865 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2154 |
| [Monk2] p. 109 | Lemma 15 | equvini 2457 equvinv 2025 eqvinop 5497 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1907 ax5ALT 38888 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2138 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2154 |
| [Monk2] p. 114 | Lemma 21 | sp 2180 |
| [Monk2] p. 114 | Lemma 22 | axc4 2319 hba1-o 38878 hba1 2291 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2150 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2173 nfra2 3373 nfra2w 3296 |
| [Moore] p. 53 | Part I | df-mre 17630 |
| [Munkres] p. 77 | Example 2 | distop 23017 indistop 23024 indistopon 23023 |
| [Munkres] p. 77 | Example 3 | fctop 23026 fctop2 23027 |
| [Munkres] p. 77 | Example 4 | cctop 23028 |
| [Munkres] p. 78 | Definition of basis | df-bases 22968 isbasis3g 22971 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17489 tgval2 22978 |
| [Munkres] p. 79 | Remark | tgcl 22991 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 22985 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 23009 tgss3 23008 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 23010 basgen2 23011 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 37331 topdifinfeq 37332 topdifinffin 37330 topdifinfindis 37328 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23183 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 23061 topcld 23058 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 23062 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 23064 |
| [Munkres] p. 94 | Definition of closure | clsval 23060 |
| [Munkres] p. 94 | Definition of interior | ntrval 23059 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 23098 elcls 23096 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 23106 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23171 neindisj 23140 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23173 |
| [Munkres] p. 97 | Definition of limit point | islp2 23168 lpval 23162 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23338 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23250 iscn 23258 iscn2 23261 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23303 cncnp2 23304 cncnpi 23301 df-cnp 23251 iscnp 23260 iscnp2 23262 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24571 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25358 |
| [Nathanson] p. 123 | Remark | reprgt 34614 reprinfz1 34615 reprlt 34612 |
| [Nathanson] p. 123 | Definition | df-repr 34602 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 34634 |
| [Nathanson] p. 123 | Proposition | breprexp 34626 breprexpnat 34627 itgexpif 34599 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32132 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 47734 |
| [Pfenning] p. 17 | Definition XM | natded 30431 |
| [Pfenning] p. 17 | Definition NNC | natded 30431 notnotrd 133 |
| [Pfenning] p. 17 | Definition ` `C | natded 30431 |
| [Pfenning] p. 18 | Rule" | natded 30431 |
| [Pfenning] p. 18 | Definition /\I | natded 30431 |
| [Pfenning] p. 18 | Definition ` `E | natded 30431 natded 30431 natded 30431 natded 30431 natded 30431 |
| [Pfenning] p. 18 | Definition ` `I | natded 30431 natded 30431 natded 30431 natded 30431 natded 30431 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30431 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30431 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30431 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30431 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30431 |
| [Pfenning] p. 127 | Definition =E | natded 30431 |
| [Pfenning] p. 127 | Definition =I | natded 30431 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25249 df-dip 30729 dip0l 30746 ip0l 21671 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25290 ipval 30731 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 30742 ipcj 21669 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25252 dipdir 30870 ipdir 21674 ipdiri 30858 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 30738 nmsq 25241 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 30853 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 30855 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 30856 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25258 dipass 30873 ipass 21680 ipassi 30869 |
| [Prugovecki] p. 186 | Definition of bra | braval 31972 df-bra 31878 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 31879 kbval 31982 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32410 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 39870 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32424 atcvat4i 32425 cvrat3 39424 cvrat4 39425 lsatcvat3 39033 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32310 cvrval 39250 df-cv 32307 df-lcv 39000 lspsncv0 21165 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 39882 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 39883 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2712 rabid 3454 rabidd 45097 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2277 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2726 |
| [Quine] p. 19 | Definition 2.9 | conventions 30428 df-v 3479 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2878 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2875 abid2f 2933 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2273 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2082 sbalex 2239 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2813 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2734 eqid1 30495 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2741 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3791 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3792 dfsbcq2 3793 |
| [Quine] p. 43 | Theorem 6.8 | vex 3481 |
| [Quine] p. 43 | Theorem 6.9 | isset 3491 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3590 spcgv 3595 spcimgf 3549 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3803 spsbcd 3804 |
| [Quine] p. 44 | Theorem 6.12 | elex 3498 |
| [Quine] p. 44 | Theorem 6.13 | elab 3680 elabg 3676 elabgf 3674 |
| [Quine] p. 44 | Theorem 6.14 | noel 4343 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4721 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4633 df-sn 4631 |
| [Quine] p. 49 | Theorem 7.4 | snss 4789 snssg 4787 |
| [Quine] p. 49 | Theorem 7.5 | prss 4824 prssg 4823 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4766 prid1g 4764 prid2 4767 prid2g 4765 snid 4666 snidg 4664 |
| [Quine] p. 51 | Theorem 7.12 | snex 5441 |
| [Quine] p. 51 | Theorem 7.13 | prex 5442 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4930 unisnALT 44923 unisng 4929 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4934 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4941 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4939 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6529 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 47035 dfiota2 6516 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 47044 iotaval 6533 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6540 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6535 |
| [Quine] p. 58 | Definition 9.1 | df-op 4637 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5534 opabidw 5533 opelopab 5551 opelopaba 5545 opelopabaf 5553 opelopabf 5554 opelopabg 5547 opelopabga 5542 opelopabgf 5549 oprabid 7462 oprabidw 7461 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5694 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5696 |
| [Quine] p. 64 | Definition 9.15 | df-id 5582 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6632 |
| [Quine] p. 65 | Theorem 10.4 | funi 6599 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6620 funsng 6618 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6564 |
| [Quine] p. 65 | Definition 10.2 | args 6112 dffv4 6903 |
| [Quine] p. 68 | Definition 10.11 | conventions 30428 df-fv 6570 fv2 6901 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14307 nn0opth2i 14306 nn0opthi 14305 omopthi 8697 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8448 |
| [Quine] p. 232 | Equation i | carddom 10591 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6655 funimaexg 6653 |
| [Quine] p. 331 | Axiom system NF | ru 3788 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31112 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 30729 polid 31187 polid2i 31185 polidi 31186 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 30841 |
| [ReedSimon] p. 195 | Remark | lnophm 32047 lnophmi 32046 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32160 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32162 leopmuli 32161 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32165 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 31880 leoppos 32154 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32164 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32153 |
| [Roman] p. 4 | Definition | df-dmat 22511 df-dmatalt 48243 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20170 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20252 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 48330 |
| [Roman] p. 112 | Note | isldepslvec2 48330 ldepsnlinc 48353 zlmodzxznm 48342 |
| [Roman] p. 112 | Example | zlmodzxzequa 48341 zlmodzxzequap 48344 zlmodzxzldep 48349 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 22911 |
| [Rosenlicht] p. 80 | Theorem | heicant 37641 |
| [Rosser] p. 281 | Definition | df-op 4637 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 34638 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 34639 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 48210 pmtr3ncom 19507 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19503 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19446 cayleyth 19447 |
| [Rudin] p. 164 | Equation 27 | efcan 16128 |
| [Rudin] p. 164 | Equation 30 | efzval 16134 |
| [Rudin] p. 167 | Equation 48 | absefi 16228 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 197 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1767 |
| [Sanford] p. 39 | Rule 4 | mptxor 1765 |
| [Sanford] p. 40 | Rule 1 | mptnan 1764 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6137 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6140 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6134 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6132 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17630 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17631 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17631 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17633 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10174 |
| [Schechter] p. 141 | Definition (MC) | dfac11 43050 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10483 axdc3 10491 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20254 isrngo 37883 |
| [Schechter] p. 276 | Remark 11.6.e | span0 31570 |
| [Schechter] p. 276 | Definition of span | df-span 31337 spanval 31361 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 23015 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6410 onelord 43239 ordelon 6409 ordelord 6407 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 43240 sucidg 6466 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6439 onsuc 7830 ord0 6438 ordsuci 7827 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 43241 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5268 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 43016 elon2 6396 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6391 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5591 epelg 5589 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9634 epirron 43242 ordirr 6403 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 43244 oneptr 43243 ontr1 6431 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 43246 oneptri 43245 ordtri3or 6417 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8537 ord0eln0 6440 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6452 onsucss 43255 trsucss 6473 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7837 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6479 ordnbtwn 6478 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 43257 ordnexbtwnsuc 43256 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10438 onsucf1lem 43258 onsucf1o 43261 onsucf1olem 43259 onsucrn 43260 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 43262 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7865 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 43251 ordne0gt0 43250 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 43253 limnsuc 43254 onsucelab 43252 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9680 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7880 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9683 ordom 7896 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9684 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8676 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7798 ssorduni 7797 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8567 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9687 limom 7902 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8504 df1o2 8511 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8552 oa0suclim 43264 oalim 8568 oasuc 8560 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8553 om0suclim 43265 omlim 8569 omsuc 8562 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8558 oe0m1 8557 oe0suclim 43266 oelim 8570 oesuc 8563 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 43217 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 43268 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 43269 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 43270 limexissupab 43272 limiun 43271 limuni 6446 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8574 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8578 om1om1r 43273 om1r 8579 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8571 oaomoecl 43267 oecl 8573 omcl 8572 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 43219 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8580 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8581 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 43274 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 43275 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8647 nnamecl 43276 nnecl 8649 nnmcl 8648 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 43277 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8588 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8589 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8596 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 43279 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 43280 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 43282 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8595 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 43286 omword1 8609 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 43285 oaordnrex 43284 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 43281 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 43287 omword2 8610 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 43288 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 43289 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 43290 omordi 8602 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8604 omord2com 43291 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 43292 df-2o 8505 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 43295 oewordi 8627 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 43296 oeworde 8629 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 43297 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 43298 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 43294 omnord1ex 43293 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 43299 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 43301 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 43305 oenord1ex 43304 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 43306 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8597 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 43300 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8615 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8616 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 43308 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8633 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 43309 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 43310 cantnfub2 43311 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 43314 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 28943 axtgcgrrflx 28484 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 28944 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 28945 axtgcgrid 28485 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28470 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 28956 axtgsegcon 28486 df-trkgcb 28472 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 28967 axtg5seg 28487 df-trkgcb 28472 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 28968 axtgbtwnid 28488 df-trkgb 28471 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 28970 axtgpasch 28489 df-trkgb 28471 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 28989 df-trkg2d 34658 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28492 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28493 df-trkg2d 34658 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 28992 axtgeucl 28494 df-trkge 28473 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 29005 axtgcont 28491 axtgcont1 28490 df-trkgb 28471 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 35968 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 35970 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 35973 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 35977 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 35978 tgcgrcomimp 28499 tgcgrcoml 28501 tgcgrcomr 28500 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 35983 tgcgrtriv 28506 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 35987 tg5segofs 34666 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 34663 df-ofs 35964 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 35989 tgcgrextend 28507 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 35991 tgsegconeq 28508 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36003 btwntriv2 35993 tgbtwntriv2 28509 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 35994 tgbtwncom 28510 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 35997 tgbtwntriv1 28513 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 35998 tgbtwnswapid 28514 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36004 btwnintr 36000 tgbtwnexch2 28518 tgbtwnintr 28515 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36006 btwnexch3 36001 tgbtwnexch 28520 tgbtwnexch3 28516 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36005 tgbtwnouttr 28519 tgbtwnouttr2 28517 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 28988 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36008 tgbtwndiff 28528 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28521 trisegint 36009 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36025 tgifscgr 28530 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28580 colrot1 28581 colrot2 28582 lncom 28644 lnrot1 28645 lnrot2 28646 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36021 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36026 tgcgrsub 28531 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36036 tgcgrxfr 28540 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28539 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36022 df-cgrg 28533 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28533 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36037 tgbtwnxfr 28552 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36043 colinearperm2 36045 colinearperm3 36044 colinearperm4 36046 colinearperm5 36047 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28555 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36020 tgellng 28575 tglng 28568 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36048 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36056 lnxfr 28588 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36057 lnext 28589 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36061 tgfscgr 28590 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36062 lncgr 28591 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36023 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36064 lnid 28592 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36065 tgidinside 28593 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36082 tgbtwnconn1 28597 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36083 tgbtwnconn2 28598 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36084 tgbtwnconn3 28599 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36090 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36088 legov 28607 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28608 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28621 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36091 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36093 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36095 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36096 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36097 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36094 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36099 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28609 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28611 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28612 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28613 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28614 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36106 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36107 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36102 df-outsideof 36101 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36103 ishlg 28624 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28629 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28631 outsideofrflx 36108 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28625 hlcomd 28626 outsideofcom 36109 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28632 outsideoftr 36110 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 28640 outsideofeu 36112 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36119 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36120 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36113 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36128 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36129 tglineelsb2 28654 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36131 linerflx1 36130 linerflx2 36132 tglinecom 28657 tglinerflx1 28655 tglinerflx2 28656 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36134 tglinethru 28658 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36118 tglng 28568 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28616 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36137 tglinethrueu 28661 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36138 tglineineq 28665 tglineinteq 28667 tglineintmo 28664 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28671 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28672 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 28673 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 28688 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 28684 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 28676 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 28675 ismir 28681 mirbtwn 28680 mircgr 28679 mirfv 28678 mirval 28677 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 28686 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 28687 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 28688 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 28691 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 28692 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 28697 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 28694 mirbtwni 28693 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 28695 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 28707 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 28711 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 28708 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 28709 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 28710 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 28713 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 28714 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 28720 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 28716 israg 28719 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 28721 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 28722 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 28724 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 28725 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 28726 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 28727 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 28728 ragncol 28731 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 28729 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 28735 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 28739 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 28736 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 28718 isperp 28734 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 28737 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 28744 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 28752 colperpexlem2 28753 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 28755 colperpexlem3 28754 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 28760 midex 28759 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 28757 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 28766 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 28761 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 28770 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 28773 opphllem6 28774 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 28776 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28489 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 28777 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 28785 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 28780 hpgbr 28782 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 28787 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 28786 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 28788 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 28789 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 28790 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 28791 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 28792 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 28806 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 28796 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 28810 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 28811 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 28812 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 28813 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 28814 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 28817 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 28819 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 28797 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 28820 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 28823 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 28824 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 28825 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 28826 trgcopyeu 28828 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 28852 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 28831 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 28840 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 28838 cgrahl2 28839 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 28841 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 28842 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 28844 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 28845 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 28848 cgrahl 28849 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 28853 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 28854 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 28855 acopyeu 28856 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 28863 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 28867 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 28860 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 28875 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 28868 isleag 28869 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 28877 tgsas1 28876 tgsas2 28878 tgsas3 28879 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 28881 tgasa1 28880 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 28882 tgsss2 28883 tgsss3 28884 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27329 dchrsum 27327 dchrsum2 27326 sumdchr 27330 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27331 sum2dchr 27332 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 20100 ablfacrp2 20101 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27274 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27275 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27282 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27540 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27543 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27597 vmalogdivsum2 27596 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27587 dirith2 27586 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27585 rpvmasum 27584 rpvmasum2 27570 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27545 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27583 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27550 dchrisumlem1 27547 dchrisumlem2 27548 dchrisumlem3 27549 dchrisumlema 27546 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27553 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27582 dchrmusumlem 27580 dchrvmasumlem 27581 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27552 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27554 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27578 dchrisum0re 27571 dchrisumn0 27579 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27564 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27568 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27569 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27624 pntrsumbnd2 27625 pntrsumo1 27623 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27588 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27590 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27592 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27595 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27600 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27601 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27606 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27608 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27609 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27617 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27618 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27615 selberg3lem2 27616 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27619 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27613 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27626 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27627 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27628 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27642 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27654 pntlemb 27655 pntlemc 27653 pntlemd 27652 pntlemg 27656 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27654 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27646 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27651 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27654 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27667 pntleml 27669 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4311 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4410 dif0 4383 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4497 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4480 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4302 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4303 |
| [Stoll] p. 20 | Remark | invdif 4284 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4639 |
| [Stoll] p. 43 | Definition | uniiun 5062 |
| [Stoll] p. 44 | Definition | intiin 5063 |
| [Stoll] p. 45 | Definition | df-iin 4998 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4997 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 401 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4311 |
| [Strang] p. 242 | Section 6.3 | expgrowth 44330 |
| [Suppes] p. 22 | Theorem 2 | eq0 4355 eq0f 4352 |
| [Suppes] p. 22 | Theorem 4 | eqss 4010 eqssd 4012 eqssi 4011 |
| [Suppes] p. 23 | Theorem 5 | ss0 4407 ss0b 4406 |
| [Suppes] p. 23 | Theorem 6 | sstr 4003 sstrALT2 44832 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4112 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4113 |
| [Suppes] p. 23 | Theorem 9 | psstr 4116 |
| [Suppes] p. 23 | Theorem 10 | pssss 4107 |
| [Suppes] p. 25 | Theorem 12 | elin 3978 elun 4162 |
| [Suppes] p. 26 | Theorem 15 | inidm 4234 |
| [Suppes] p. 26 | Theorem 16 | in0 4400 |
| [Suppes] p. 27 | Theorem 23 | unidm 4166 |
| [Suppes] p. 27 | Theorem 24 | un0 4399 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4187 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4195 |
| [Suppes] p. 27 | Theorem 27 | unss 4199 |
| [Suppes] p. 27 | Theorem 28 | indir 4291 |
| [Suppes] p. 27 | Theorem 29 | undir 4292 |
| [Suppes] p. 28 | Theorem 32 | difid 4381 |
| [Suppes] p. 29 | Theorem 33 | difin 4277 |
| [Suppes] p. 29 | Theorem 34 | indif 4285 |
| [Suppes] p. 29 | Theorem 35 | undif1 4481 |
| [Suppes] p. 29 | Theorem 36 | difun2 4486 |
| [Suppes] p. 29 | Theorem 37 | difin0 4479 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4477 |
| [Suppes] p. 29 | Theorem 39 | difundi 4295 |
| [Suppes] p. 29 | Theorem 40 | difindi 4297 |
| [Suppes] p. 30 | Theorem 41 | nalset 5318 |
| [Suppes] p. 39 | Theorem 61 | uniss 4919 |
| [Suppes] p. 39 | Theorem 65 | uniop 5524 |
| [Suppes] p. 41 | Theorem 70 | intsn 4988 |
| [Suppes] p. 42 | Theorem 71 | intpr 4986 intprg 4985 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5481 |
| [Suppes] p. 42 | Theorem 78 | intun 4984 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 5037 dfiun2g 5034 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 5038 |
| [Suppes] p. 47 | Theorem 86 | elpw 4608 elpw2 5339 elpw2g 5338 elpwg 4607 elpwgdedVD 44914 |
| [Suppes] p. 47 | Theorem 87 | pwid 4626 |
| [Suppes] p. 47 | Theorem 89 | pw0 4816 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4817 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5703 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5846 xpindir 5847 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5756 xpundir 5757 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9633 |
| [Suppes] p. 58 | Theorem 2 | relss 5793 |
| [Suppes] p. 59 | Theorem 4 | eldm 5913 eldm2 5914 eldm2g 5912 eldmg 5911 |
| [Suppes] p. 59 | Definition 3 | df-dm 5698 |
| [Suppes] p. 60 | Theorem 6 | dmin 5924 |
| [Suppes] p. 60 | Theorem 8 | rnun 6167 |
| [Suppes] p. 60 | Theorem 9 | rnin 6168 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5901 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5895 brcnvg 5892 |
| [Suppes] p. 62 | Equation 5 | elcnv 5889 elcnv2 5890 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6124 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6166 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6164 |
| [Suppes] p. 63 | Definition | dftrrels2 38556 |
| [Suppes] p. 63 | Theorem 20 | co02 6281 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5987 |
| [Suppes] p. 63 | Definition 7 | df-co 5697 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5898 |
| [Suppes] p. 64 | Theorem 27 | coass 6286 |
| [Suppes] p. 65 | Theorem 31 | resundi 6013 |
| [Suppes] p. 65 | Theorem 34 | elima 6084 elima2 6085 elima3 6086 elimag 6083 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6171 |
| [Suppes] p. 66 | Theorem 40 | dminss 6174 |
| [Suppes] p. 66 | Theorem 41 | imainss 6175 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6178 |
| [Suppes] p. 81 | Definition 34 | dfec2 8746 |
| [Suppes] p. 82 | Theorem 72 | elec 8789 elecALTV 38247 elecg 8787 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 38592 erth 8794 erth2 8795 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 38595 erdisj 8797 |
| [Suppes] p. 83 | Definition 35, | df-parts 38746 dfmembpart2 38751 |
| [Suppes] p. 89 | Theorem 96 | map0b 8921 |
| [Suppes] p. 89 | Theorem 97 | map0 8925 map0g 8922 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8926 mapsnd 8924 |
| [Suppes] p. 89 | Theorem 99 | mapss 8927 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 10105 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 10104 |
| [Suppes] p. 92 | Theorem 1 | enref 9023 enrefg 9022 |
| [Suppes] p. 92 | Theorem 2 | ensym 9041 ensymb 9040 ensymi 9042 |
| [Suppes] p. 92 | Theorem 3 | entr 9044 |
| [Suppes] p. 92 | Theorem 4 | unen 9084 |
| [Suppes] p. 94 | Theorem 15 | endom 9017 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 9038 |
| [Suppes] p. 94 | Theorem 17 | domtr 9045 |
| [Suppes] p. 95 | Theorem 18 | sbth 9131 |
| [Suppes] p. 97 | Theorem 23 | canth2 9168 canth2g 9169 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9135 df-sdom 8986 dfsdom2 9134 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9152 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9137 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9136 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9150 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 9020 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9153 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9148 |
| [Suppes] p. 98 | Exercise 4 | fundmen 9069 fundmeng 9070 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9108 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9149 |
| [Suppes] p. 104 | Theorem 37 | fofi 9348 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9354 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9354 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10588 |
| [Suppes] p. 130 | Definition 3 | df-tr 5265 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7798 |
| [Suppes] p. 134 | Definition 6 | df-suc 6391 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7922 finds 7918 finds1 7921 finds2 7920 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9689 isfinite2 9331 isfiniteg 9334 unbnn 9329 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10955 df-ltpq 10947 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7883 tfinds 7880 tfinds2 7884 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8587 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8589 |
| [Suppes] p. 211 | Theorem 25 | oaass 8597 |
| [Suppes] p. 225 | Definition 8 | iscard2 10013 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10600 |
| [Suppes] p. 228 | Theorem 59 | harcard 10015 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 10103 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6436 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7812 onminsb 7813 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10609 |
| [Suppes] p. 229 | Theorem 65 | alephcard 10107 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 10114 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 10108 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9977 |
| [Suppes] p. 242 | Theorem 6 | weth 10532 |
| [Suppes] p. 242 | Theorem 8 | entric 10594 |
| [Suppes] p. 242 | Theorem 9 | carden 10588 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 35675 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 35679 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2705 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2726 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2813 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2728 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2757 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7434 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3788 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5426 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4654 elpr2 4656 elpr2g 4655 elprg 4652 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4645 elsn2 4669 elsn2g 4668 elsng 4644 velsn 4646 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5477 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4640 sneqr 4844 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4650 dfsn2 4643 dfsn2ALT 4651 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7759 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5486 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5474 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5458 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7762 unexg 7761 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4695 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4912 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3969 df-un 3967 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4928 uniprg 4927 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5382 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4693 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6455 elsucg 6453 sstr2 4001 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4167 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4216 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4181 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4235 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4289 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4290 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3982 df-ss 3979 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4606 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4196 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3980 sseqin2 4230 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 4017 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4244 inss2 4245 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 4059 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4922 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5459 sspwimp 44915 sspwimpALT 44922 sspwimpALT2 44925 sspwimpcf 44917 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5466 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5284 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3433 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5312 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3965 |
| [TakeutiZaring] p. 20 | Definition 5.14 | dfnul2 4341 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4381 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4358 n0f 4354 neq0 4357 neq0f 4353 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9632 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9769 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9771 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3479 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5320 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4405 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5326 ssexg 5328 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5322 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9639 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9634 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4371 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4144 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4305 undif3VD 44879 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4145 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4152 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3059 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3068 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7771 xpexg 7768 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5695 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6638 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6813 fun11 6641 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6578 svrelfun 6639 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5900 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5902 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5700 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5701 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5697 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6215 dfrel2 6210 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5704 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5823 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5830 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5844 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 6025 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 6005 opelresi 6007 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 6031 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 6021 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 6026 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6609 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6128 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6607 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6815 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2606 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30428 df-fv 6570 fv3 6924 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7947 cnvexg 7946 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7931 dmexg 7923 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7932 rnexg 7924 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 44449 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7942 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6919 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 47123 tz6.12-1-afv2 47190 tz6.12-1 6929 tz6.12-afv 47122 tz6.12-afv2 47189 tz6.12 6931 tz6.12c-afv2 47191 tz6.12c 6928 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 47186 tz6.12-2 6894 tz6.12i-afv2 47192 tz6.12i 6934 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6565 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6566 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6568 wfo 6560 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6567 wf1 6559 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6569 wf1o 6561 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 7050 eqfnfv2 7051 eqfnfv2f 7054 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 7006 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7236 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7234 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6655 funimaexg 6653 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5148 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5597 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5649 dffr3 6119 eliniseg 6114 iniseg 6117 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5588 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5665 fr3nr 7790 frirr 5664 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5640 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7792 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5652 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5674 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6369 tz6.26i 6371 wefrc 5682 wereu2 5685 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6372 wfii 6374 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6571 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7348 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7349 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7355 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7356 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7357 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7361 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7368 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7370 |
| [TakeutiZaring] p. 35 | Notation | wtr 5264 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 44450 tz7.2 5671 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5270 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6398 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6406 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6407 ordelordALT 44534 ordelordALTVD 44864 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6413 ordelssne 6412 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6411 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6415 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7800 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7801 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6389 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6417 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 44546 ordon 7795 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7796 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7873 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6432 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5266 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7811 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7850 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6489 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6488 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7797 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4941 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6391 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6465 sucidg 6466 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7830 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6479 ordnbtwn 6478 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7847 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6390 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7901 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7906 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7861 ordelsuc 7839 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7841 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7871 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7888 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7910 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7912 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7913 |
| [TakeutiZaring] p. 43 | Remark | omon 7898 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9672 omex 9680 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7896 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7917 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7914 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7915 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7891 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4966 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5283 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4967 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5349 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7814 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6435 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4951 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9697 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7809 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8414 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8435 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8436 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8437 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8444 tz7.44-2 8445 tz7.44-3 8446 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8405 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8400 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8384 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8483 tz7.49c 8484 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8481 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8480 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8482 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2653 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 10048 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 10049 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8568 oasuc 8560 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7881 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8571 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8552 oa0r 8574 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8572 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8584 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8655 nnaordi 8654 oaord 8583 oaordi 8582 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5053 uniss2 4945 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8586 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8591 oawordex 8593 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8647 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8684 |
| [TakeutiZaring] p. 60 | Remark | oancom 9688 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8596 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8652 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8588 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8555 omlim 8569 omsuc 8562 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8553 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8649 nnmcl 8648 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8668 nnmordi 8667 omord 8604 omordi 8602 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8605 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8672 omwordri 8608 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8575 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8578 om1r 8579 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8611 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8613 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8614 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8615 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8616 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8644 oe0 8558 oelim 8570 oesuc 8563 onesuc 8566 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8556 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8622 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8623 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8557 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8581 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8624 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8630 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8628 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8629 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8633 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8635 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9765 tz9.1 9766 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9801 r10 9805 r1lim 9809 r1limg 9808 r1suc 9807 r1sucg 9806 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9817 r1ord2 9818 r1ordg 9815 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9827 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9852 tz9.13 9828 tz9.13g 9829 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9802 rankval 9853 rankvalb 9834 rankvalg 9854 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9876 rankelb 9861 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9890 rankval3 9877 rankval3b 9863 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9866 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9832 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9871 rankr1c 9858 rankr1g 9869 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9872 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9886 rankssb 9885 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9879 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9878 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10512 dfac3 10158 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 10067 numth 10509 numth2 10508 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10583 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10584 cardid2 9990 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9997 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10588 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9996 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9981 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 10002 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9994 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9188 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 9056 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9193 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9112 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 10000 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10135 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9243 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9262 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10136 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9248 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10125 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 10103 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 10009 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10253 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9359 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8987 isfi 9014 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9264 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10571 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9105 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10563 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10223 unxpdom 9286 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 10011 cardsdomelir 10010 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9288 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 10051 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8866 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10599 infxpidm2 10054 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10244 infxp 10251 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9117 pw2f1o 9115 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9181 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10524 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10519 ac6s5 10528 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10580 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10581 uniimadomf 10582 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10311 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10306 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10291 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10288 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10294 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10301 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10310 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10619 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10289 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10313 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10134 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10133 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10145 alephfp2 10146 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10736 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10149 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10606 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10620 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10621 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 38864 |
| [Tarski] p. 67 | Scheme B5 | sp 2180 |
| [Tarski] p. 68 | Lemma 6 | avril1 30491 equid 2008 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2013 |
| [Tarski] p. 70 | Lemma 14 | spim 2389 spime 2391 spimew 1968 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2174 ax-c15 38870 ax12i 1963 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2082 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1965 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1907 ax5ALT 38888 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2004 ax-8 2107 ax-9 2115 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28486 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28487 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28489 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28489 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28490 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16275 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 37645 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 37647 |
| [Weierstrass] p. 272 | Definition | df-mdet 22606 mdetuni 22643 |
| [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 37427 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 43789 imim2 58 wl-luk-imim2 37422 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 46968 imim1 83 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 896 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2660 syl 17 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 902 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 22 wl-luk-id 37425 |
| [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 44924 wl-luk-notnotr 37426 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 146 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 43819 axfrege28 43818 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 37419 |
| [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 30429 pm2.27 42 wl-luk-pm2.27 37417 |
| [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 38344 |
| [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 | pm3.35 803 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 448 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 449 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 482 simplim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 484 simprim 166 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 765 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 766 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 808 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 622 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 810 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 492 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 493 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 962 pm3.44 961 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 809 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 473 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 965 |
| [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 | pm4.14 807 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 833 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 222 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 806 bitr 805 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 563 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 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 828 |
| [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 | pm5.1 824 |
| [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 | pm5.21 825 |
| [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 | pm5.31 831 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 573 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 836 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 826 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 834 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 389 pm5.41 390 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 543 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 542 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 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 44353 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 44354 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1867 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 44355 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 44356 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 44357 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1890 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 44358 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 44359 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 44360 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 44361 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 44362 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 44364 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 44365 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 44366 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 44363 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2087 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 44369 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 44370 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2067 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2157 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1825 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1826 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 44371 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 44372 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 44373 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 44374 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 44376 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 44375 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1884 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 44378 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 44379 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 44377 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1824 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 44380 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 44381 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1842 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 44382 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2346 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1857 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 44387 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 44383 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 44384 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 44385 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 44386 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 44391 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 44388 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 44389 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 44390 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 44392 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2566 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 44402 pm13.13b 44403 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 44404 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3019 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3020 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3665 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 44410 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 44411 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 44405 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 44549 pm13.193 44406 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 44407 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 44408 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 44409 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 44416 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 44415 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 44414 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3858 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 44417 pm14.122b 44418 pm14.122c 44419 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 44420 pm14.123b 44421 pm14.123c 44422 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 44424 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 44423 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 44425 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6543 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 44426 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6544 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 44427 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 44429 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2630 eupickbi 2633 sbaniota 44430 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 44428 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2581 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 44432 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30428 df-fv 6570 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 10038 pm54.43lem 10037 |
| [Young] p. 141 | Definition of operator ordering | leop2 32152 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32158 idleop 32159 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 42815 |
| [vandenDries] p. 43 | Theorem 62 | pellex 42822 pellexlem1 42816 |