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 17711 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17711 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18121 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17732 df-termc 49120 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 49152 prsthinc 49111 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 49175 df-mndtc 49175 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17755 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 49170 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 49188 oppgoppchom 49187 oppgoppcid 49189 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17825 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17813 invisoinvl 17834 |
| [Adamek] p. 28 | Example 3.13 | idinv 17833 idiso 17832 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17818 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17792 df-iso 17793 dfiso2 17816 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17799 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17850 |
| [Adamek] p. 29 | Definition 3.15 | cic 17843 df-cic 17840 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17903 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17814 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17815 isoco 17821 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17903 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17926 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17919 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 49068 prsthinc 49111 thincciso 49102 thincciso2 49104 thincciso3 49105 thinccisod 49103 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 49175 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17933 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18156 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18212 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17952 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17951 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18212 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17976 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17982 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17981 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18197 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18197 |
| [Adamek] p. 39 | Definition 3.41 | funcoppc 17920 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18144 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17970 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17969 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18153 |
| [Adamek] p. 40 | Definition 3.47 | df-catc 18144 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17883 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17884 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17895 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17856 |
| [Adamek] p. 49 | Remark 4.4(2) | ressffth 17985 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 17991 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 18012 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 18016 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 17992 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 18018 |
| [Adamek] p. 101 | Definition 7.1 | df-inito 18029 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21490 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 18030 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 18057 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 18061 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 18031 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21491 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 18064 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17791 |
| [Adamek] p. 185 | Section 10.67 | updjud 9974 |
| [Adamek] p. 478 | Item Rng | df-ringc 20646 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 48469 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 48491 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14609 df-pfx 14709 df-substr 14679 df-word 14553 lencl 14571 wrd0 14577 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24729 df-nmoo 30764 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32172 hmopidmchi 32170 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32220 pjcmul2i 32221 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 31937 unoplin 31939 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 31938 unopadj2 31957 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 32032 lnopunii 32031 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32105 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 27961 |
| [Alling] p. 184 | Axiom B | bdayfo 27722 |
| [Alling] p. 184 | Axiom O | sltso 27721 |
| [Alling] p. 184 | Axiom SD | nodense 27737 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27823 |
| [Alling] p. 185 | Theorem | conway 27844 |
| [Alling] p. 185 | Axiom FE | noeta 27788 |
| [Alling] p. 186 | Theorem 4 | slerec 27864 |
| [Alling], p. 2 | Definition | rp-brsslt 43436 |
| [Alling], p. 3 | Note | nla0001 43439 nla0002 43437 nla0003 43438 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11445 addcan2d 11465 addcan2i 11455 addcand 11464 addcani 11454 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11498 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11557 negsubd 11626 negsubi 11587 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11559 negnegd 11611 negnegi 11579 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11696 subdid 11719 subdii 11712 subdir 11697 subdird 11720 subdiri 11713 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11440 mul01d 11460 mul01i 11451 mul02 11439 mul02d 11459 mul02i 11450 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11900 mulcan2d 11897 mulcand 11896 mulcani 11902 |
| [Apostol] p. 18 | Theorem I.8 | receu 11908 xreceu 32904 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11938 divrecd 12046 divreci 12012 divreczi 12005 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11964 recreci 11999 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11903 mul0ord 11913 mul0ori 11911 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11702 mul2negd 11718 mul2negi 11711 mulneg1 11699 mulneg1d 11716 mulneg1i 11709 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11982 divadddivd 12087 divadddivi 12029 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11967 divmuldivd 12084 divmuldivi 12027 rdivmuldivd 20413 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11968 divdivdivd 12090 divdivdivi 12030 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 13057 rpaddcld 13092 rpmulcl 13058 rpmulcld 13093 |
| [Apostol] p. 20 | Axiom 8 | rpneg 13067 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 13070 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11387 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11856 ltadd1dd 11874 ltadd1i 11817 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12117 ltmul1a 12116 ltmul1i 12186 ltmul1ii 12196 ltmul2 12118 ltmul2d 13119 ltmul2dd 13133 ltmul2i 12189 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11783 msqgt0d 11830 msqgt0i 11800 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11785 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11769 lt0neg1d 11832 ltneg 11763 ltnegd 11841 ltnegi 11807 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11748 lt2addd 11886 lt2addi 11825 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 13035 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12113 recgt0d 12202 recgt0i 12173 recgt0ii 12174 |
| [Apostol] p. 22 | Definition of integers | df-z 12614 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12280 |
| [Apostol] p. 22 | Definition of rationals | df-q 12991 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9494 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12522 |
| [Apostol] p. 26 | Theorem I.29 | arch 12523 archd 45167 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12721 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12524 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12989 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12988 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13241 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16376 zneo 12701 zneoALTV 47656 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26772 msqsqrtd 15479 resqrtth 15294 sqrtth 15403 sqrtthi 15409 sqsqrtd 15478 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12269 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12955 |
| [Apostol] p. 361 | Remark | crreczi 14267 |
| [Apostol] p. 363 | Remark | absgt0i 15438 |
| [Apostol] p. 363 | Example | abssubd 15492 abssubi 15442 |
| [ApostolNT] p. 7 | Remark | fmtno0 47527 fmtno1 47528 fmtno2 47537 fmtno3 47538 fmtno4 47539 fmtno5fac 47569 fmtnofz04prm 47564 |
| [ApostolNT] p. 7 | Definition | df-fmtno 47515 |
| [ApostolNT] p. 8 | Definition | df-ppi 27143 |
| [ApostolNT] p. 14 | Definition | df-dvds 16291 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16307 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16331 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16326 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16320 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16322 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16308 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16309 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16314 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16348 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16350 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16352 |
| [ApostolNT] p. 15 | Definition | df-gcd 16532 dfgcd2 16583 |
| [ApostolNT] p. 16 | Definition | isprm2 16719 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16690 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16953 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16550 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16584 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16586 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16565 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16557 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16748 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16750 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16966 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16960 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16440 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16624 |
| [ApostolNT] p. 24 | Definition | df-mu 27144 |
| [ApostolNT] p. 25 | Definition | df-phi 16803 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27234 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16828 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16813 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16817 |
| [ApostolNT] p. 32 | Definition | df-vma 27141 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27236 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27260 |
| [ApostolNT] p. 38 | Remark | df-sgm 27145 |
| [ApostolNT] p. 38 | Definition | df-sgm 27145 |
| [ApostolNT] p. 75 | Definition | df-chp 27142 df-cht 27140 |
| [ApostolNT] p. 104 | Definition | congr 16701 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16294 |
| [ApostolNT] p. 106 | Definition | moddvds 16301 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16383 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16384 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13928 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13966 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14277 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16325 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16704 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17112 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16706 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16820 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16839 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16821 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27115 |
| [ApostolNT] p. 179 | Definition | df-lgs 27339 lgsprme0 27383 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27384 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27360 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27375 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27432 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27451 2lgsoddprm 27460 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27418 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27427 |
| [ApostolNT] p. 188 | Definition | df-lgs 27339 lgs1 27385 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27376 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27378 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27386 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27387 |
| [Baer] p. 40 | Property (b) | mapdord 41640 |
| [Baer] p. 40 | Property (c) | mapd11 41641 |
| [Baer] p. 40 | Property (e) | mapdin 41664 mapdlsm 41666 |
| [Baer] p. 40 | Property (f) | mapd0 41667 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 41627 mapd1o 41650 |
| [Baer] p. 41 | Property (g) | mapdat 41669 |
| [Baer] p. 44 | Part (1) | mapdpg 41708 |
| [Baer] p. 45 | Part (2) | hdmap1eq 41803 mapdheq 41730 mapdheq2 41731 mapdheq2biN 41732 |
| [Baer] p. 45 | Part (3) | baerlem3 41715 |
| [Baer] p. 46 | Part (4) | mapdheq4 41734 mapdheq4lem 41733 |
| [Baer] p. 46 | Part (5) | baerlem5a 41716 baerlem5abmN 41720 baerlem5amN 41718 baerlem5b 41717 baerlem5bmN 41719 |
| [Baer] p. 47 | Part (6) | hdmap1l6 41823 hdmap1l6a 41811 hdmap1l6e 41816 hdmap1l6f 41817 hdmap1l6g 41818 hdmap1l6lem1 41809 hdmap1l6lem2 41810 mapdh6N 41749 mapdh6aN 41737 mapdh6eN 41742 mapdh6fN 41743 mapdh6gN 41744 mapdh6lem1N 41735 mapdh6lem2N 41736 |
| [Baer] p. 48 | Part 9 | hdmapval 41830 |
| [Baer] p. 48 | Part 10 | hdmap10 41842 |
| [Baer] p. 48 | Part 11 | hdmapadd 41845 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 41819 mapdh6hN 41745 |
| [Baer] p. 48 | Part (7) | mapdh75cN 41755 mapdh75d 41756 mapdh75e 41754 mapdh75fN 41757 mapdh7cN 41751 mapdh7dN 41752 mapdh7eN 41750 mapdh7fN 41753 |
| [Baer] p. 48 | Part (8) | mapdh8 41790 mapdh8a 41777 mapdh8aa 41778 mapdh8ab 41779 mapdh8ac 41780 mapdh8ad 41781 mapdh8b 41782 mapdh8c 41783 mapdh8d 41785 mapdh8d0N 41784 mapdh8e 41786 mapdh8g 41787 mapdh8i 41788 mapdh8j 41789 |
| [Baer] p. 48 | Part (9) | mapdh9a 41791 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 41771 |
| [Baer] p. 49 | Part 12 | hdmap11 41850 hdmapeq0 41846 hdmapf1oN 41867 hdmapneg 41848 hdmaprnN 41866 hdmaprnlem1N 41851 hdmaprnlem3N 41852 hdmaprnlem3uN 41853 hdmaprnlem4N 41855 hdmaprnlem6N 41856 hdmaprnlem7N 41857 hdmaprnlem8N 41858 hdmaprnlem9N 41859 hdmapsub 41849 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 41870 hdmap14lem10 41879 hdmap14lem1a 41868 hdmap14lem2N 41871 hdmap14lem2a 41869 hdmap14lem3 41872 hdmap14lem8 41877 hdmap14lem9 41878 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 41880 hdmap14lem12 41881 hdmap14lem13 41882 hdmap14lem14 41883 hdmap14lem15 41884 hgmapval 41889 |
| [Baer] p. 50 | Part 15 | hgmapadd 41896 hgmapmul 41897 hgmaprnlem2N 41899 hgmapvs 41893 |
| [Baer] p. 50 | Part 16 | hgmaprnN 41903 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 41919 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 41920 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 41921 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 41922 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 41924 hgmapvv 41928 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 41923 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 41925 |
| [Baer] p. 111 | Line 15 | hdmapg 41932 hdmapglem7 41931 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26773 2irrexpqALT 26843 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 23 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2569 |
| [BellMachover] p. 460 | Notation | df-mo 2540 |
| [BellMachover] p. 460 | Definition | mo3 2564 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2708 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2712 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5287 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5296 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37065 sepex 5300 |
| [BellMachover] p. 466 | Problem | axpow2 5367 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5368 |
| [BellMachover] p. 466 | Axiom Union | axun2 7757 |
| [BellMachover] p. 468 | Definition | df-ord 6387 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6402 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6409 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6404 |
| [BellMachover] p. 471 | Definition of N | df-om 7888 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7821 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6389 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9682 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7903 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9804 |
| [BellMachover] p. 478 | Definition | rankval2 9858 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9822 r1ord3g 9819 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9635 |
| [BellMachover] p. 488 | Axiom AC | ac5 10517 dfac4 10162 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10150 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 39320 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32372 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32414 chirredi 32413 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32402 |
| [Beran] p. 3 | Definition of join | sshjval3 31373 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 31635 cmcm2i 31612 cmcm2ii 31617 cmt2N 39251 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 31636 lecmi 31621 lecmii 31622 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 31610 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 31639 cm2ji 31644 cm2mi 31645 |
| [Beran] p. 95 | Definition | df-sh 31226 issh2 31228 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31105 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31118 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31109 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 31847 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 31849 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 31848 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 31850 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31101 his1i 31119 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31102 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31103 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31104 |
| [Beran] p. 96 | Definition of norm | df-hnorm 30987 dfhnorm2 31141 normval 31143 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31203 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 30992 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31260 |
| [Beran] p. 96 | Definition of converge | df-hlim 30991 hlimi 31207 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31152 norm-i 31148 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31156 norm-ii 31157 normlem0 31128 normlem1 31129 normlem2 31130 normlem3 31131 normlem4 31132 normlem5 31133 normlem6 31134 normlem7 31135 normlem7tALT 31138 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31158 norm-iii 31159 |
| [Beran] p. 98 | Remark 3.4 | bcs 31200 bcsiALT 31198 bcsiHIL 31199 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31140 normpar 31174 normpari 31173 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31165 normpyth 31164 normpythi 31161 |
| [Beran] p. 99 | Remark | lnfn0 32066 lnfn0i 32061 lnop0 31985 lnop0i 31989 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32045 nmcfnex 32072 nmcfnexi 32070 nmcopex 32048 nmcopexi 32046 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32073 nmcfnlbi 32071 nmcoplb 32049 nmcoplbi 32047 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32075 lnfnconi 32074 lnopcon 32054 lnopconi 32053 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31175 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31172 norm3adifii 31167 norm3dif 31169 norm3difi 31166 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31320 pjhth 31412 pjhtheu 31413 pjpjhth 31444 pjpjhthi 31445 pjth 25473 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31425 ococi 31424 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32080 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32081 riesz4 32083 riesz4i 32082 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32098 cnlnadjeu 32097 cnlnadjeui 32096 cnlnadji 32095 cnlnadjlem1 32086 nmopadjlei 32107 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32110 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32109 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32111 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 31955 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32121 nmopcoadji 32120 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32112 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32122 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32119 pjadj2coi 32223 pjadjcoi 32180 |
| [Beran] p. 107 | Definition | df-ch 31240 isch2 31242 |
| [Beran] p. 107 | Remark 3.12 | choccl 31325 isch3 31260 occl 31323 ocsh 31302 shoccl 31324 shocsh 31303 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31427 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31351 |
| [Beran] p. 109 | Property (i) | pjadj2 32206 pjadj3 32207 pjadji 31704 pjadjii 31693 |
| [Beran] p. 109 | Property (ii) | pjidmco 32200 pjidmcoi 32196 pjidmi 31692 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32192 |
| [Beran] p. 111 | Remark | ho0val 31769 pjch1 31689 |
| [Beran] p. 111 | Definition | df-hfmul 31753 df-hfsum 31752 df-hodif 31751 df-homul 31750 df-hosum 31749 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 31690 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 31713 pjchi 31451 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31458 pjoc2i 31457 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 31699 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32184 pjssmii 31700 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32183 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32182 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32187 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32185 pjssge0ii 31701 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32186 pjdifnormii 31702 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1776 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1774 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1777 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1772 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34294 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34302 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34300 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34304 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34324 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34355 df-sitm 34333 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34355 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34332 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29065 isuhgrop 29087 isusgrop 29179 isuspgrop 29178 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 47847 df-subgr 29285 uhgrspan1 29320 uhgrspansubgr 29308 |
| [Bollobas] p. 3 | Definition | df-gric 47867 gricuspgr 47887 isuspgrim 47875 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29472 df-clnbgr 47806 df-cusgr 29429 df-nbgr 29350 fusgrmaxsize 29482 |
| [Bollobas] p. 4 | Definition | df-upwlks 48050 df-wlks 29617 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 29568 finsumvtxdgeven 29570 fusgr1th 29569 fusgrvtxdgonume 29572 vtxdgoddnumeven 29571 |
| [Bollobas] p. 5 | Notation | df-pths 29734 |
| [Bollobas] p. 5 | Definition | df-crcts 29806 df-cycls 29807 df-trls 29710 df-wlkson 29618 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29076 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 48116 df-cllaw 48102 df-mgm 18653 df-mgm2 48135 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 48117 df-asslaw 48104 df-sgrp 18732 df-sgrp2 48137 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 48136 df-comlaw 48103 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18748 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33031 mndlactf1o 33035 mndractf1 33033 mndractf1o 33036 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20232 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20150 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 33684 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 33688 assarrginv 33687 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 33728 fldextrspunfld 33726 fldextrspunlem1 33725 fldextrspunlem2 33727 fldextrspunlsp 33724 fldextrspunlsplem 33723 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 33565 dfufd2 33578 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7307 fcofo 7308 |
| [BourbakiTop1] p. | Remark | xnegmnf 13252 xnegpnf 13251 |
| [BourbakiTop1] p. | Remark | rexneg 13253 |
| [BourbakiTop1] p. | Remark 3 | ust0 24228 ustfilxp 24221 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24098 |
| [BourbakiTop1] p. | Criterion | ishmeo 23767 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24293 iducn 24292 snfil 23872 |
| [BourbakiTop1] p. | Example 2 | neifil 23888 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 24075 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24313 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 33956 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23871 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24285 df-ust 24209 filintn0 23869 filn0 23870 istgp 24085 ucnprima 24291 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24296 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24307 df-usp 24266 df-utop 24240 trust 24238 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 33855 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23124 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23277 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24214 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24217 |
| [BourbakiTop1] p. | Property V_ii | innei 23133 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23141 neissex 23135 |
| [BourbakiTop1] p. | Proposition 1 | neips 23121 neiss 23117 ucncn 24294 ustund 24230 ustuqtop 24255 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23275 neiptopreu 23141 utop2nei 24259 utop3cls 24260 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24301 uspreg 24283 utopreg 24261 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23699 imasncls 23700 imasnopn 23698 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 24008 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24216 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24218 |
| [BourbakiTop1] p. | Property V_iii | elnei 23119 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24312 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24215 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24219 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23395 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23854 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 22900 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 33852 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 46077 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 46079 stoweid 46078 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 46016 stoweidlem10 46025 stoweidlem14 46029 stoweidlem15 46030 stoweidlem35 46050 stoweidlem36 46051 stoweidlem37 46052 stoweidlem38 46053 stoweidlem40 46055 stoweidlem41 46056 stoweidlem43 46058 stoweidlem44 46059 stoweidlem46 46061 stoweidlem5 46020 stoweidlem50 46065 stoweidlem52 46067 stoweidlem53 46068 stoweidlem55 46070 stoweidlem56 46071 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 46038 stoweidlem24 46039 stoweidlem27 46042 stoweidlem28 46043 stoweidlem30 46045 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 46049 stoweidlem59 46074 stoweidlem60 46075 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 46060 stoweidlem49 46064 stoweidlem7 46022 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 46046 stoweidlem39 46054 stoweidlem42 46057 stoweidlem48 46063 stoweidlem51 46066 stoweidlem54 46069 stoweidlem57 46072 stoweidlem58 46073 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 46040 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 46032 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 46026 stoweidlem13 46028 stoweidlem26 46041 stoweidlem61 46076 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 46033 |
| [Bruck] p. 1 | Section I.1 | df-clintop 48116 df-mgm 18653 df-mgm2 48135 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18732 df-sgrp2 48137 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 19057 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5226 |
| [Church] p. 129 | Section II.24 | df-ifp 1064 dfifp2 1065 |
| [Clemente] p. 10 | Definition IT | natded 30422 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30422 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30422 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30422 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30422 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30422 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30422 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30422 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30422 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30422 |
| [Clemente] p. 14 | Proof 5.11 | natded 30422 |
| [Clemente] p. 14 | Definition E` `n | natded 30422 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30424 ex-natded5.2 30423 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30427 ex-natded5.3 30426 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30429 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30431 ex-natded5.7 30430 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30433 ex-natded5.8 30432 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30435 ex-natded5.13 30434 |
| [Clemente] p. 32 | Definition I` `n | natded 30422 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30422 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30422 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30422 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30436 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30437 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30439 ex-natded9.26 30438 |
| [Cohen] p. 301 | Remark | relogoprlem 26633 |
| [Cohen] p. 301 | Property 2 | relogmul 26634 relogmuld 26667 |
| [Cohen] p. 301 | Property 3 | relogdiv 26635 relogdivd 26668 |
| [Cohen] p. 301 | Property 4 | relogexp 26638 |
| [Cohen] p. 301 | Property 1a | log1 26627 |
| [Cohen] p. 301 | Property 1b | loge 26628 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26830 |
| [Cohen4] p. 349 | Property | relogbf 26834 |
| [Cohen4] p. 352 | Definition | elogb 26813 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26820 |
| [Cohen4] p. 361 | Property 3 | logbrec 26825 relogbdiv 26822 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26818 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26823 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26811 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26812 |
| [Cohen4] p. 367 | Property | logbchbase 26814 |
| [Cohen4] p. 377 | Property 2 | logblt 26827 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34287 sxbrsigalem4 34289 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18602 acsinfd 18601 acsinfdimd 18603 acsmap2d 18600 acsmapd 18599 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34292 |
| [Connell] p. 57 | Definition | df-scmat 22497 df-scmatalt 48316 |
| [Conway] p. 4 | Definition | slerec 27864 |
| [Conway] p. 5 | Definition | addsval 27995 addsval2 27996 df-adds 27993 df-muls 28133 df-negs 28053 |
| [Conway] p. 7 | Theorem | 0slt1s 27874 |
| [Conway] p. 16 | Theorem 0(i) | ssltright 27910 |
| [Conway] p. 16 | Theorem 0(ii) | ssltleft 27909 |
| [Conway] p. 16 | Theorem 0(iii) | slerflex 27808 |
| [Conway] p. 17 | Theorem 3 | addsass 28038 addsassd 28039 addscom 27999 addscomd 28000 addsrid 27997 addsridd 27998 |
| [Conway] p. 17 | Definition | df-0s 27869 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 28076 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 28073 negsidd 28074 |
| [Conway] p. 18 | Theorem 5 | sleadd1 28022 sleadd1d 28028 |
| [Conway] p. 18 | Definition | df-1s 27870 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 28068 negscld 28069 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 28013 |
| [Conway] p. 19 | Note | mulsunif2 28196 |
| [Conway] p. 19 | Theorem 7 | addsdi 28181 addsdid 28182 addsdird 28183 mulnegs1d 28186 mulnegs2d 28187 mulsass 28192 mulsassd 28193 mulscom 28165 mulscomd 28166 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28160 mulscld 28161 |
| [Conway] p. 19 | Theorem 8(iii) | slemuld 28164 sltmul 28162 sltmuld 28163 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28170 mulsgt0d 28171 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28242 |
| [Conway] p. 24 | Definition | df-reno 28426 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28431 remulscl 28434 renegscl 28430 |
| [Conway] p. 27 | Definition | df-ons 28275 elons2 28281 |
| [Conway] p. 27 | Theorem 14 | sltonex 28284 |
| [Conway] p. 29 | Remark | madebday 27938 newbday 27940 oldbday 27939 |
| [Conway] p. 29 | Definition | df-made 27886 df-new 27888 df-old 27887 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13901 |
| [Crawley] p. 1 | Definition of poset | df-poset 18359 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 39388 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 40192 dalaw 39888 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 41967 |
| [Crawley] p. 111 | Definition of set W | df-watsN 39992 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 40108 df-ldil 40106 isldil 40112 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 40107 df-trnN 40109 isltrn 40121 ltrnu 40123 |
| [Crawley] p. 112 | Lemma A | cdlema1N 39793 cdlema2N 39794 exatleN 39406 |
| [Crawley] p. 112 | Lemma B | 1cvrat 39478 cdlemb 39796 cdlemb2 40043 cdlemb3 40608 idltrn 40152 l1cvat 39056 lhpat 40045 lhpat2 40047 lshpat 39057 ltrnel 40141 ltrnmw 40153 |
| [Crawley] p. 112 | Lemma C | cdlemc1 40193 cdlemc2 40194 ltrnnidn 40176 trlat 40171 trljat1 40168 trljat2 40169 trljat3 40170 trlne 40187 trlnidat 40175 trlnle 40188 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 39993 |
| [Crawley] p. 113 | Lemma C | cdlemc 40199 cdlemc3 40195 cdlemc4 40196 |
| [Crawley] p. 113 | Lemma D | cdlemd 40209 cdlemd1 40200 cdlemd2 40201 cdlemd3 40202 cdlemd4 40203 cdlemd5 40204 cdlemd6 40205 cdlemd7 40206 cdlemd8 40207 cdlemd9 40208 cdleme31sde 40387 cdleme31se 40384 cdleme31se2 40385 cdleme31snd 40388 cdleme32a 40443 cdleme32b 40444 cdleme32c 40445 cdleme32d 40446 cdleme32e 40447 cdleme32f 40448 cdleme32fva 40439 cdleme32fva1 40440 cdleme32fvcl 40442 cdleme32le 40449 cdleme48fv 40501 cdleme4gfv 40509 cdleme50eq 40543 cdleme50f 40544 cdleme50f1 40545 cdleme50f1o 40548 cdleme50laut 40549 cdleme50ldil 40550 cdleme50lebi 40542 cdleme50rn 40547 cdleme50rnlem 40546 cdlemeg49le 40513 cdlemeg49lebilem 40541 |
| [Crawley] p. 113 | Lemma E | cdleme 40562 cdleme00a 40211 cdleme01N 40223 cdleme02N 40224 cdleme0a 40213 cdleme0aa 40212 cdleme0b 40214 cdleme0c 40215 cdleme0cp 40216 cdleme0cq 40217 cdleme0dN 40218 cdleme0e 40219 cdleme0ex1N 40225 cdleme0ex2N 40226 cdleme0fN 40220 cdleme0gN 40221 cdleme0moN 40227 cdleme1 40229 cdleme10 40256 cdleme10tN 40260 cdleme11 40272 cdleme11a 40262 cdleme11c 40263 cdleme11dN 40264 cdleme11e 40265 cdleme11fN 40266 cdleme11g 40267 cdleme11h 40268 cdleme11j 40269 cdleme11k 40270 cdleme11l 40271 cdleme12 40273 cdleme13 40274 cdleme14 40275 cdleme15 40280 cdleme15a 40276 cdleme15b 40277 cdleme15c 40278 cdleme15d 40279 cdleme16 40287 cdleme16aN 40261 cdleme16b 40281 cdleme16c 40282 cdleme16d 40283 cdleme16e 40284 cdleme16f 40285 cdleme16g 40286 cdleme19a 40305 cdleme19b 40306 cdleme19c 40307 cdleme19d 40308 cdleme19e 40309 cdleme19f 40310 cdleme1b 40228 cdleme2 40230 cdleme20aN 40311 cdleme20bN 40312 cdleme20c 40313 cdleme20d 40314 cdleme20e 40315 cdleme20f 40316 cdleme20g 40317 cdleme20h 40318 cdleme20i 40319 cdleme20j 40320 cdleme20k 40321 cdleme20l 40324 cdleme20l1 40322 cdleme20l2 40323 cdleme20m 40325 cdleme20y 40304 cdleme20zN 40303 cdleme21 40339 cdleme21d 40332 cdleme21e 40333 cdleme22a 40342 cdleme22aa 40341 cdleme22b 40343 cdleme22cN 40344 cdleme22d 40345 cdleme22e 40346 cdleme22eALTN 40347 cdleme22f 40348 cdleme22f2 40349 cdleme22g 40350 cdleme23a 40351 cdleme23b 40352 cdleme23c 40353 cdleme26e 40361 cdleme26eALTN 40363 cdleme26ee 40362 cdleme26f 40365 cdleme26f2 40367 cdleme26f2ALTN 40366 cdleme26fALTN 40364 cdleme27N 40371 cdleme27a 40369 cdleme27cl 40368 cdleme28c 40374 cdleme3 40239 cdleme30a 40380 cdleme31fv 40392 cdleme31fv1 40393 cdleme31fv1s 40394 cdleme31fv2 40395 cdleme31id 40396 cdleme31sc 40386 cdleme31sdnN 40389 cdleme31sn 40382 cdleme31sn1 40383 cdleme31sn1c 40390 cdleme31sn2 40391 cdleme31so 40381 cdleme35a 40450 cdleme35b 40452 cdleme35c 40453 cdleme35d 40454 cdleme35e 40455 cdleme35f 40456 cdleme35fnpq 40451 cdleme35g 40457 cdleme35h 40458 cdleme35h2 40459 cdleme35sn2aw 40460 cdleme35sn3a 40461 cdleme36a 40462 cdleme36m 40463 cdleme37m 40464 cdleme38m 40465 cdleme38n 40466 cdleme39a 40467 cdleme39n 40468 cdleme3b 40231 cdleme3c 40232 cdleme3d 40233 cdleme3e 40234 cdleme3fN 40235 cdleme3fa 40238 cdleme3g 40236 cdleme3h 40237 cdleme4 40240 cdleme40m 40469 cdleme40n 40470 cdleme40v 40471 cdleme40w 40472 cdleme41fva11 40479 cdleme41sn3aw 40476 cdleme41sn4aw 40477 cdleme41snaw 40478 cdleme42a 40473 cdleme42b 40480 cdleme42c 40474 cdleme42d 40475 cdleme42e 40481 cdleme42f 40482 cdleme42g 40483 cdleme42h 40484 cdleme42i 40485 cdleme42k 40486 cdleme42ke 40487 cdleme42keg 40488 cdleme42mN 40489 cdleme42mgN 40490 cdleme43aN 40491 cdleme43bN 40492 cdleme43cN 40493 cdleme43dN 40494 cdleme5 40242 cdleme50ex 40561 cdleme50ltrn 40559 cdleme51finvN 40558 cdleme51finvfvN 40557 cdleme51finvtrN 40560 cdleme6 40243 cdleme7 40251 cdleme7a 40245 cdleme7aa 40244 cdleme7b 40246 cdleme7c 40247 cdleme7d 40248 cdleme7e 40249 cdleme7ga 40250 cdleme8 40252 cdleme8tN 40257 cdleme9 40255 cdleme9a 40253 cdleme9b 40254 cdleme9tN 40259 cdleme9taN 40258 cdlemeda 40300 cdlemedb 40299 cdlemednpq 40301 cdlemednuN 40302 cdlemefr27cl 40405 cdlemefr32fva1 40412 cdlemefr32fvaN 40411 cdlemefrs32fva 40402 cdlemefrs32fva1 40403 cdlemefs27cl 40415 cdlemefs32fva1 40425 cdlemefs32fvaN 40424 cdlemesner 40298 cdlemeulpq 40222 |
| [Crawley] p. 114 | Lemma E | 4atex 40078 4atexlem7 40077 cdleme0nex 40292 cdleme17a 40288 cdleme17c 40290 cdleme17d 40500 cdleme17d1 40291 cdleme17d2 40497 cdleme18a 40293 cdleme18b 40294 cdleme18c 40295 cdleme18d 40297 cdleme4a 40241 |
| [Crawley] p. 115 | Lemma E | cdleme21a 40327 cdleme21at 40330 cdleme21b 40328 cdleme21c 40329 cdleme21ct 40331 cdleme21f 40334 cdleme21g 40335 cdleme21h 40336 cdleme21i 40337 cdleme22gb 40296 |
| [Crawley] p. 116 | Lemma F | cdlemf 40565 cdlemf1 40563 cdlemf2 40564 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 40569 cdlemg16 40659 cdlemg28 40706 cdlemg28a 40695 cdlemg28b 40705 cdlemg3a 40599 cdlemg42 40731 cdlemg43 40732 cdlemg44 40735 cdlemg44a 40733 cdlemg46 40737 cdlemg47 40738 cdlemg9 40636 ltrnco 40721 ltrncom 40740 tgrpabl 40753 trlco 40729 |
| [Crawley] p. 116 | Definition of G | df-tgrp 40745 |
| [Crawley] p. 117 | Lemma G | cdlemg17 40679 cdlemg17b 40664 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 40758 df-edring 40759 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 40762 |
| [Crawley] p. 118 | Remark | tendopltp 40782 |
| [Crawley] p. 118 | Lemma H | cdlemh 40819 cdlemh1 40817 cdlemh2 40818 |
| [Crawley] p. 118 | Lemma I | cdlemi 40822 cdlemi1 40820 cdlemi2 40821 |
| [Crawley] p. 118 | Lemma J | cdlemj1 40823 cdlemj2 40824 cdlemj3 40825 tendocan 40826 |
| [Crawley] p. 118 | Lemma K | cdlemk 40976 cdlemk1 40833 cdlemk10 40845 cdlemk11 40851 cdlemk11t 40948 cdlemk11ta 40931 cdlemk11tb 40933 cdlemk11tc 40947 cdlemk11u-2N 40891 cdlemk11u 40873 cdlemk12 40852 cdlemk12u-2N 40892 cdlemk12u 40874 cdlemk13-2N 40878 cdlemk13 40854 cdlemk14-2N 40880 cdlemk14 40856 cdlemk15-2N 40881 cdlemk15 40857 cdlemk16-2N 40882 cdlemk16 40859 cdlemk16a 40858 cdlemk17-2N 40883 cdlemk17 40860 cdlemk18-2N 40888 cdlemk18-3N 40902 cdlemk18 40870 cdlemk19-2N 40889 cdlemk19 40871 cdlemk19u 40972 cdlemk1u 40861 cdlemk2 40834 cdlemk20-2N 40894 cdlemk20 40876 cdlemk21-2N 40893 cdlemk21N 40875 cdlemk22-3 40903 cdlemk22 40895 cdlemk23-3 40904 cdlemk24-3 40905 cdlemk25-3 40906 cdlemk26-3 40908 cdlemk26b-3 40907 cdlemk27-3 40909 cdlemk28-3 40910 cdlemk29-3 40913 cdlemk3 40835 cdlemk30 40896 cdlemk31 40898 cdlemk32 40899 cdlemk33N 40911 cdlemk34 40912 cdlemk35 40914 cdlemk36 40915 cdlemk37 40916 cdlemk38 40917 cdlemk39 40918 cdlemk39u 40970 cdlemk4 40836 cdlemk41 40922 cdlemk42 40943 cdlemk42yN 40946 cdlemk43N 40965 cdlemk45 40949 cdlemk46 40950 cdlemk47 40951 cdlemk48 40952 cdlemk49 40953 cdlemk5 40838 cdlemk50 40954 cdlemk51 40955 cdlemk52 40956 cdlemk53 40959 cdlemk54 40960 cdlemk55 40963 cdlemk55u 40968 cdlemk56 40973 cdlemk5a 40837 cdlemk5auN 40862 cdlemk5u 40863 cdlemk6 40839 cdlemk6u 40864 cdlemk7 40850 cdlemk7u-2N 40890 cdlemk7u 40872 cdlemk8 40840 cdlemk9 40841 cdlemk9bN 40842 cdlemki 40843 cdlemkid 40938 cdlemkj-2N 40884 cdlemkj 40865 cdlemksat 40848 cdlemksel 40847 cdlemksv 40846 cdlemksv2 40849 cdlemkuat 40868 cdlemkuel-2N 40886 cdlemkuel-3 40900 cdlemkuel 40867 cdlemkuv-2N 40885 cdlemkuv2-2 40887 cdlemkuv2-3N 40901 cdlemkuv2 40869 cdlemkuvN 40866 cdlemkvcl 40844 cdlemky 40928 cdlemkyyN 40964 tendoex 40977 |
| [Crawley] p. 120 | Remark | dva1dim 40987 |
| [Crawley] p. 120 | Lemma L | cdleml1N 40978 cdleml2N 40979 cdleml3N 40980 cdleml4N 40981 cdleml5N 40982 cdleml6 40983 cdleml7 40984 cdleml8 40985 cdleml9 40986 dia1dim 41063 |
| [Crawley] p. 120 | Lemma M | dia11N 41050 diaf11N 41051 dialss 41048 diaord 41049 dibf11N 41163 djajN 41139 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 41034 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 41120 dia2dimlem1 41066 dia2dimlem2 41067 dia2dimlem3 41068 dia2dimlem4 41069 dia2dimlem5 41070 diaf1oN 41132 diarnN 41131 dvheveccl 41114 dvhopN 41118 |
| [Crawley] p. 121 | Lemma N | cdlemn 41214 cdlemn10 41208 cdlemn11 41213 cdlemn11a 41209 cdlemn11b 41210 cdlemn11c 41211 cdlemn11pre 41212 cdlemn2 41197 cdlemn2a 41198 cdlemn3 41199 cdlemn4 41200 cdlemn4a 41201 cdlemn5 41203 cdlemn5pre 41202 cdlemn6 41204 cdlemn7 41205 cdlemn8 41206 cdlemn9 41207 diclspsn 41196 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 41175 |
| [Crawley] p. 122 | Lemma N | dih11 41267 dihf11 41269 dihjust 41219 dihjustlem 41218 dihord 41266 dihord1 41220 dihord10 41225 dihord11b 41224 dihord11c 41226 dihord2 41229 dihord2a 41221 dihord2b 41222 dihord2cN 41223 dihord2pre 41227 dihord2pre2 41228 dihordlem6 41215 dihordlem7 41216 dihordlem7b 41217 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 41232 dihfval 41233 dihval 41234 |
| [Diestel] p. 3 | Definition | df-gric 47867 df-grim 47864 isuspgrim 47875 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29429 df-nbgr 29350 |
| [Diestel] p. 3 | Definition by | df-grisom 47863 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 47847 df-subgr 29285 uhgrspan1 29320 uhgrspansubgr 29308 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 29572 vtxdgoddnumeven 29571 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29076 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 33863 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 33875 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 33867 zarcls1 33868 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 33878 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 33881 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 33884 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3954 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9687 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8868 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9695 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 10020 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10595 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5305 |
| [Enderton] p. 19 | Definition | df-tp 4631 |
| [Enderton] p. 26 | Exercise 5 | unissb 4939 |
| [Enderton] p. 26 | Exercise 10 | pwel 5381 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5576 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5079 iinin2 5078 iinun2 5073 iunin1 5072 iunin1f 32570 iunin2 5071 uniin1 32564 uniin2 32565 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5077 iundif2 5074 |
| [Enderton] p. 32 | Exercise 20 | unineq 4288 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5098 |
| [Enderton] p. 33 | Exercise 25 | iununi 5099 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5106 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7791 iunpwss 5107 |
| [Enderton] p. 36 | Definition | opthwiener 5519 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5455 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4945 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5475 rnex 7932 rnexg 7924 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5925 rnuni 6168 |
| [Enderton] p. 42 | Definition of a function | dffun7 6593 dffun8 6594 |
| [Enderton] p. 43 | Definition of function value | funfv2 6997 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6635 |
| [Enderton] p. 44 | Definition (d) | dfima2 6080 dfima3 6081 |
| [Enderton] p. 47 | Theorem 3H | fvco2 7006 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10513 ac7g 10514 df-ac 10156 dfac2 10172 dfac2a 10170 dfac2b 10171 dfac3 10161 dfac7 10173 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7266 |
| [Enderton] p. 52 | Definition | df-map 8868 |
| [Enderton] p. 53 | Exercise 21 | coass 6285 |
| [Enderton] p. 53 | Exercise 27 | dmco 6274 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6642 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6120 |
| [Enderton] p. 54 | Remark | ixpf 8960 ixpssmap 8972 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8938 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10523 ac9s 10533 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 38611 erref 8765 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 38614 erthi 8798 |
| [Enderton] p. 57 | Definition | df-ec 8747 |
| [Enderton] p. 58 | Definition | df-qs 8751 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8747 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5921 |
| [Enderton] p. 68 | Definition of successor | df-suc 6390 |
| [Enderton] p. 71 | Definition | df-tr 5260 dftr4 5266 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6463 unisucg 6462 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6463 unisucg 6462 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5275 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5277 trintALT 44901 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8642 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8644 onasuc 8566 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7434 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8643 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8645 onmsuc 8567 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8660 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8647 nnacom 8655 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8661 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8662 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8664 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8648 nnmsucr 8663 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8676 |
| [Enderton] p. 129 | Definition | df-en 8986 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7385 |
| [Enderton] p. 133 | Exercise 1 | xpomen 10055 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16249 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9247 |
| [Enderton] p. 135 | Corollary 6C | php3 9249 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9246 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9292 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9294 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9208 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9213 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9181 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10220 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10221 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10216 dju1en 10212 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9383 unifi 9384 unifi2 9385 |
| [Enderton] p. 144 | Corollary 6K | undif2 4477 unfi 9211 unfi2 9348 |
| [Enderton] p. 145 | Figure 38 | ffoss 7970 |
| [Enderton] p. 145 | Definition | df-dom 8987 |
| [Enderton] p. 146 | Example 1 | domen 9002 domeng 9003 |
| [Enderton] p. 146 | Example 3 | nndomo 9269 nnsdom 9694 nnsdomg 9335 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10224 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9182 xpdom1 9111 xpdom1g 9109 xpdom2g 9108 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9188 |
| [Enderton] p. 151 | Theorem 6M | zorn 10547 zorng 10544 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10532 dfac5 10169 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10615 |
| [Enderton] p. 164 | Example | infdif 10248 |
| [Enderton] p. 168 | Definition | df-po 5592 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6498 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6430 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6497 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6438 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7859 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7801 |
| [Enderton] p. 194 | Remark | onprc 7798 |
| [Enderton] p. 194 | Exercise 16 | suc11 6491 |
| [Enderton] p. 197 | Definition | df-card 9979 |
| [Enderton] p. 197 | Theorem 7P | carden 10591 |
| [Enderton] p. 200 | Exercise 25 | tfis 7876 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9816 |
| [Enderton] p. 202 | Definition | df-r1 9804 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9826 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9907 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9646 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9897 rankprb 9891 rankpw 9883 rankpwi 9863 rankuniss 9906 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9658 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9659 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10150 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 10116 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10130 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8381 |
| [Enderton] p. 222 | Definition of kard | karden 9935 kardex 9934 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8635 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8637 |
| [Enderton] p. 240 | Exercise 25 | oarec 8600 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10290 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17685 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17631 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18598 mrieqv2d 17682 mrieqvd 17681 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17686 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17691 mreexexlem2d 17688 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18604 mreexfidimd 17693 |
| [Frege1879] p. 11 | Statement | df3or2 43781 |
| [Frege1879] p. 12 | Statement | df3an2 43782 dfxor4 43779 dfxor5 43780 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 43803 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 43804 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 43808 |
| [Frege1879] p. 31 | Proposition 4 | frege4 43812 |
| [Frege1879] p. 32 | Proposition 5 | frege5 43813 |
| [Frege1879] p. 33 | Proposition 6 | frege6 43819 |
| [Frege1879] p. 34 | Proposition 7 | frege7 43821 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 43822 axfrege8 43820 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 90 wl-luk-pm2.04 37446 |
| [Frege1879] p. 35 | Proposition 9 | frege9 43825 |
| [Frege1879] p. 36 | Proposition 10 | frege10 43833 |
| [Frege1879] p. 36 | Proposition 11 | frege11 43827 |
| [Frege1879] p. 37 | Proposition 12 | frege12 43826 |
| [Frege1879] p. 37 | Proposition 13 | frege13 43835 |
| [Frege1879] p. 37 | Proposition 14 | frege14 43836 |
| [Frege1879] p. 38 | Proposition 15 | frege15 43839 |
| [Frege1879] p. 38 | Proposition 16 | frege16 43829 |
| [Frege1879] p. 39 | Proposition 17 | frege17 43834 |
| [Frege1879] p. 39 | Proposition 18 | frege18 43831 |
| [Frege1879] p. 39 | Proposition 19 | frege19 43837 |
| [Frege1879] p. 40 | Proposition 20 | frege20 43841 |
| [Frege1879] p. 40 | Proposition 21 | frege21 43840 |
| [Frege1879] p. 41 | Proposition 22 | frege22 43832 |
| [Frege1879] p. 42 | Proposition 23 | frege23 43838 |
| [Frege1879] p. 42 | Proposition 24 | frege24 43828 |
| [Frege1879] p. 42 | Proposition 25 | frege25 43830 rp-frege25 43818 |
| [Frege1879] p. 42 | Proposition 26 | frege26 43823 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 43843 |
| [Frege1879] p. 43 | Proposition 27 | frege27 43824 |
| [Frege1879] p. 43 | Proposition 28 | con3 153 |
| [Frege1879] p. 43 | Proposition 29 | frege29 43844 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 43847 axfrege31 43846 |
| [Frege1879] p. 44 | Proposition 30 | frege30 43845 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 130 |
| [Frege1879] p. 44 | Proposition 32 | frege32 43848 |
| [Frege1879] p. 44 | Proposition 33 | frege33 43849 |
| [Frege1879] p. 45 | Proposition 34 | frege34 43850 |
| [Frege1879] p. 45 | Proposition 35 | frege35 43851 |
| [Frege1879] p. 45 | Proposition 36 | frege36 43852 |
| [Frege1879] p. 46 | Proposition 37 | frege37 43853 |
| [Frege1879] p. 46 | Proposition 38 | frege38 43854 |
| [Frege1879] p. 46 | Proposition 39 | frege39 43855 |
| [Frege1879] p. 46 | Proposition 40 | frege40 43856 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 43858 axfrege41 43857 |
| [Frege1879] p. 47 | Proposition 41 | notnot 142 |
| [Frege1879] p. 47 | Proposition 42 | frege42 43859 |
| [Frege1879] p. 47 | Proposition 43 | frege43 43860 |
| [Frege1879] p. 47 | Proposition 44 | frege44 43861 |
| [Frege1879] p. 47 | Proposition 45 | frege45 43862 |
| [Frege1879] p. 48 | Proposition 46 | frege46 43863 |
| [Frege1879] p. 48 | Proposition 47 | frege47 43864 |
| [Frege1879] p. 49 | Proposition 48 | frege48 43865 |
| [Frege1879] p. 49 | Proposition 49 | frege49 43866 |
| [Frege1879] p. 49 | Proposition 50 | frege50 43867 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 43870 ax-frege52c 43901 frege52aid 43871 frege52b 43902 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 43875 ax-frege54c 43905 frege54b 43906 |
| [Frege1879] p. 50 | Proposition 51 | frege51 43868 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3790 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 43873 frege53aid 43872 frege53b 43903 frege53c 43927 |
| [Frege1879] p. 50 | Proposition 54 | biid 261 eqid 2737 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 43881 frege55aid 43878 frege55b 43910 frege55c 43931 frege55cor1a 43882 frege55lem2a 43880 frege55lem2b 43909 frege55lem2c 43930 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 43884 frege56aid 43883 frege56b 43911 frege56c 43932 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 43888 ax-frege58b 43914 frege58bid 43915 frege58c 43934 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 43886 frege57aid 43885 frege57b 43912 frege57c 43933 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3801 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 43890 frege59b 43917 frege59c 43935 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 43891 frege60b 43918 frege60c 43936 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 43892 frege61b 43919 frege61c 43937 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 43893 frege62b 43920 frege62c 43938 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 43894 frege63b 43921 frege63c 43939 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 43895 frege64b 43922 frege64c 43940 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 43896 frege65b 43923 frege65c 43941 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 43897 frege66b 43924 frege66c 43942 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 43898 frege67b 43925 frege67c 43943 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 43899 frege68b 43926 frege68c 43944 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 43945 |
| [Frege1879] p. 58 | Proposition 70 | frege70 43946 |
| [Frege1879] p. 59 | Proposition 71 | frege71 43947 |
| [Frege1879] p. 59 | Proposition 72 | frege72 43948 |
| [Frege1879] p. 59 | Proposition 73 | frege73 43949 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 43952 |
| [Frege1879] p. 60 | Proposition 74 | frege74 43950 |
| [Frege1879] p. 60 | Proposition 75 | frege75 43951 |
| [Frege1879] p. 62 | Proposition 77 | frege77 43953 frege77d 43759 |
| [Frege1879] p. 63 | Proposition 78 | frege78 43954 |
| [Frege1879] p. 63 | Proposition 79 | frege79 43955 |
| [Frege1879] p. 63 | Proposition 80 | frege80 43956 |
| [Frege1879] p. 63 | Proposition 81 | frege81 43957 frege81d 43760 |
| [Frege1879] p. 64 | Proposition 82 | frege82 43958 |
| [Frege1879] p. 65 | Proposition 83 | frege83 43959 frege83d 43761 |
| [Frege1879] p. 65 | Proposition 84 | frege84 43960 |
| [Frege1879] p. 66 | Proposition 85 | frege85 43961 |
| [Frege1879] p. 66 | Proposition 86 | frege86 43962 |
| [Frege1879] p. 66 | Proposition 87 | frege87 43963 frege87d 43763 |
| [Frege1879] p. 67 | Proposition 88 | frege88 43964 |
| [Frege1879] p. 68 | Proposition 89 | frege89 43965 |
| [Frege1879] p. 68 | Proposition 90 | frege90 43966 |
| [Frege1879] p. 68 | Proposition 91 | frege91 43967 frege91d 43764 |
| [Frege1879] p. 69 | Proposition 92 | frege92 43968 |
| [Frege1879] p. 70 | Proposition 93 | frege93 43969 |
| [Frege1879] p. 70 | Proposition 94 | frege94 43970 |
| [Frege1879] p. 70 | Proposition 95 | frege95 43971 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 43975 |
| [Frege1879] p. 71 | Proposition 96 | frege96 43972 frege96d 43762 |
| [Frege1879] p. 71 | Proposition 97 | frege97 43973 frege97d 43765 |
| [Frege1879] p. 71 | Proposition 98 | frege98 43974 frege98d 43766 |
| [Frege1879] p. 72 | Proposition 100 | frege100 43976 |
| [Frege1879] p. 72 | Proposition 101 | frege101 43977 |
| [Frege1879] p. 72 | Proposition 102 | frege102 43978 frege102d 43767 |
| [Frege1879] p. 73 | Proposition 103 | frege103 43979 |
| [Frege1879] p. 73 | Proposition 104 | frege104 43980 |
| [Frege1879] p. 73 | Proposition 105 | frege105 43981 |
| [Frege1879] p. 73 | Proposition 106 | frege106 43982 frege106d 43768 |
| [Frege1879] p. 74 | Proposition 107 | frege107 43983 |
| [Frege1879] p. 74 | Proposition 108 | frege108 43984 frege108d 43769 |
| [Frege1879] p. 74 | Proposition 109 | frege109 43985 frege109d 43770 |
| [Frege1879] p. 75 | Proposition 110 | frege110 43986 |
| [Frege1879] p. 75 | Proposition 111 | frege111 43987 frege111d 43772 |
| [Frege1879] p. 76 | Proposition 112 | frege112 43988 |
| [Frege1879] p. 76 | Proposition 113 | frege113 43989 |
| [Frege1879] p. 76 | Proposition 114 | frege114 43990 frege114d 43771 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 43991 |
| [Frege1879] p. 77 | Proposition 116 | frege116 43992 |
| [Frege1879] p. 78 | Proposition 117 | frege117 43993 |
| [Frege1879] p. 78 | Proposition 118 | frege118 43994 |
| [Frege1879] p. 78 | Proposition 119 | frege119 43995 |
| [Frege1879] p. 78 | Proposition 120 | frege120 43996 |
| [Frege1879] p. 79 | Proposition 121 | frege121 43997 |
| [Frege1879] p. 79 | Proposition 122 | frege122 43998 frege122d 43773 |
| [Frege1879] p. 79 | Proposition 123 | frege123 43999 |
| [Frege1879] p. 80 | Proposition 124 | frege124 44000 frege124d 43774 |
| [Frege1879] p. 81 | Proposition 125 | frege125 44001 |
| [Frege1879] p. 81 | Proposition 126 | frege126 44002 frege126d 43775 |
| [Frege1879] p. 82 | Proposition 127 | frege127 44003 |
| [Frege1879] p. 83 | Proposition 128 | frege128 44004 |
| [Frege1879] p. 83 | Proposition 129 | frege129 44005 frege129d 43776 |
| [Frege1879] p. 84 | Proposition 130 | frege130 44006 |
| [Frege1879] p. 85 | Proposition 131 | frege131 44007 frege131d 43777 |
| [Frege1879] p. 86 | Proposition 132 | frege132 44008 |
| [Frege1879] p. 86 | Proposition 133 | frege133 44009 frege133d 43778 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 46328 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 46651 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 46351 |
| [Fremlin1] p. 14 | Definition 112A | ismea 46466 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 46486 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 46477 meadjunre 46491 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 46478 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 46479 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 46475 meaiunle 46484 meaiunlelem 46483 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 46496 meaiuninc2 46497 meaiuninc3 46500 meaiuninc3v 46499 meaiunincf 46498 meaiuninclem 46495 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 46502 meaiininc2 46503 meaiininclem 46501 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 46521 caragendifcl 46529 caratheodory 46543 omelesplit 46533 |
| [Fremlin1] p. 19 | Definition 113A | isome 46509 isomennd 46546 isomenndlem 46545 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 46531 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 46550 voncmpl 46636 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 46513 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 46538 carageniuncllem1 46536 carageniuncllem2 46537 caragenuncl 46528 caragenuncllem 46527 caragenunicl 46539 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 46547 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 46541 caratheodorylem2 46542 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 46550 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 46609 hoidmv1lelem1 46606 hoidmv1lelem2 46607 hoidmv1lelem3 46608 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 46653 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 46609 hoidmvle 46615 hoidmvlelem1 46610 hoidmvlelem2 46611 hoidmvlelem3 46612 hoidmvlelem4 46613 hoidmvlelem5 46614 hsphoidmvle2 46600 hsphoif 46591 hsphoival 46594 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 46563 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 46571 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 46598 hoidmvn0val 46599 hoidmvval 46592 hoidmvval0 46602 hoidmvval0b 46605 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 46603 hsphoidmvle 46601 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 46552 df-voln 46554 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 46619 ovn0 46581 ovn0lem 46580 ovnf 46578 ovnome 46588 ovnssle 46576 ovnsslelem 46575 ovnsupge0 46572 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 46618 ovnhoilem1 46616 ovnhoilem2 46617 vonhoi 46682 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 46635 hoidifhspf 46633 hoidifhspval 46623 hoidifhspval2 46630 hoidifhspval3 46634 hspmbl 46644 hspmbllem1 46641 hspmbllem2 46642 hspmbllem3 46643 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 46636 vonmea 46589 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 46587 ovnsubadd2 46661 ovnsubadd2lem 46660 ovnsubaddlem1 46585 ovnsubaddlem2 46586 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 46646 hoimbl2 46680 hoimbllem 46645 hspdifhsp 46631 opnvonmbl 46649 opnvonmbllem2 46648 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 46651 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 46694 iccvonmbllem 46693 ioovonmbl 46692 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 46700 vonicclem2 46699 vonioo 46697 vonioolem2 46696 vonn0icc 46703 vonn0icc2 46707 vonn0ioo 46702 vonn0ioo2 46705 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 46704 snvonmbl 46701 vonct 46708 vonsn 46706 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 46374 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 46373 subsaliuncllem 46372 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 46740 salpreimalegt 46724 salpreimaltle 46741 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 46743 issmff 46749 issmflem 46742 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 46760 issmflelem 46759 smfpreimale 46769 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 46771 issmfgtlem 46770 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 46711 issmf 46743 issmff 46749 issmfge 46785 issmfgelem 46784 issmfgt 46771 issmfgtlem 46770 issmfle 46760 issmflelem 46759 issmflem 46742 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 46722 salpreimagtlt 46745 salpreimalelt 46744 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 46785 issmfgelem 46784 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 46768 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 46766 cnfsmf 46755 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 46782 decsmflem 46781 incsmf 46757 incsmflem 46756 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 46716 pimconstlt1 46717 smfconst 46764 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 46780 smfaddlem1 46778 smfaddlem2 46779 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 46811 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 46810 smfmullem1 46806 smfmullem2 46807 smfmullem3 46808 smfmullem4 46809 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 46812 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 46815 smfpimbor1lem2 46814 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 46817 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 46805 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 46804 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 46813 smfresal 46803 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 46792 smflim2 46821 smflimlem1 46786 smflimlem2 46787 smflimlem3 46788 smflimlem4 46789 smflimlem5 46790 smflimlem6 46791 smflimmpt 46825 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 46829 smfsuplem1 46826 smfsuplem2 46827 smfsuplem3 46828 smfsupmpt 46830 smfsupxr 46831 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 46833 smfinflem 46832 smfinfmpt 46834 |
| [Fremlin1] p. 39 | Remark 121G | smflim 46792 smflim2 46821 smflimmpt 46825 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 46823 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 46853 smfdivdmmbl2 46856 smfinfdmmbl 46864 smfinfdmmbllem 46863 smfsupdmmbl 46860 smfsupdmmbllem 46859 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 46843 smflimsuplem2 46836 smflimsuplem6 46840 smflimsuplem7 46841 smflimsuplem8 46842 smflimsupmpt 46844 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 46846 smfliminflem 46845 smfliminfmpt 46847 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 46711 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 46857 fsupdm2 46858 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 46848 adddmmbl2 46849 finfdm 46861 finfdm2 46862 fsupdm 46857 fsupdm2 46858 muldmmbl 46850 muldmmbl2 46851 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 46861 finfdm2 46862 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25571 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25614 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25624 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 37705 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 37708 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9678 inf1 9662 inf2 9663 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10951 enqer 10961 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10956 df-nq 10952 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10948 df-plq 10954 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7670 df-mpq 10949 df-mq 10955 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10957 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 11015 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 11016 ltbtwnnq 11018 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 11011 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 11012 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 11019 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 11021 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 11033 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 11035 |
| [Gleason] p. 122 | Definition | df-1p 11022 |
| [Gleason] p. 122 | Remark (1) | prub 11034 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 11073 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 11025 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 11072 psslinpr 11071 supexpr 11094 suplem1pr 11092 suplem2pr 11093 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 11058 addclprlem1 11056 addclprlem2 11057 df-plp 11023 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 11062 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 11061 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 11074 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 11083 ltexprlem1 11076 ltexprlem2 11077 ltexprlem3 11078 ltexprlem4 11079 ltexprlem5 11080 ltexprlem6 11081 ltexprlem7 11082 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 11085 ltaprlem 11084 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 11086 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 11087 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 11024 mulclpr 11060 mulclprlem 11059 reclem2pr 11088 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 11069 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 11064 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 11063 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 11068 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 11091 reclem3pr 11089 reclem4pr 11090 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 11095 enrer 11103 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 11100 df-1r 11101 df-nr 11096 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 11098 df-plr 11097 negexsr 11142 recexsr 11147 recexsrlem 11143 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 11099 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12261 creur 12260 cru 12258 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11228 axcnre 11204 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15154 crimd 15271 crimi 15232 crre 15153 crred 15270 crrei 15231 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15156 remimd 15237 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15323 absval2d 15484 absval2i 15436 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15180 cjaddd 15259 cjaddi 15227 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15181 cjmuld 15260 cjmuli 15228 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15179 cjcjd 15238 cjcji 15210 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15178 cjreb 15162 cjrebd 15241 cjrebi 15213 cjred 15265 rere 15161 rereb 15159 rerebd 15240 rerebi 15212 rered 15263 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15187 addcjd 15251 addcji 15222 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15277 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15318 abscjd 15489 abscji 15440 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15328 abs00d 15485 abs00i 15437 absne0d 15486 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15360 releabsd 15490 releabsi 15441 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15333 absmuld 15493 absmuli 15443 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15321 sqabsaddi 15444 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15369 abstrid 15495 abstrii 15447 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14103 exp0 14106 expp1 14109 expp1d 14187 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26721 cxpaddd 26759 expadd 14145 expaddd 14188 expaddz 14147 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26730 cxpmuld 26779 expmul 14148 expmuld 14189 expmulz 14149 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26727 mulcxpd 26770 mulexp 14142 mulexpd 14201 mulexpz 14143 |
| [Gleason] p. 140 | Exercise 1 | znnen 16248 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13549 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15668 rlimadd 15679 rlimdiv 15682 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15670 rlimsub 15680 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15669 rlimmul 15681 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15673 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15619 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15640 climcj 15641 climim 15643 climre 15642 rlimabs 15645 rlimcj 15646 rlimim 15648 rlimre 15647 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11300 df-xr 11299 ltxr 13157 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15507 limsupval 15510 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15706 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15715 caucvgb 15716 caucvgbf 45500 caucvgr 15712 climcau 15707 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15852 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15919 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15374 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13868 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21358 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24353 xmet0 24352 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24369 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24360 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24362 mstri 24479 xmettri 24361 xmstri 24478 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24392 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23656 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25344 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24553 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24887 addcn2 15630 mulcn 24889 mulcn2 15632 subcn 24888 subcn2 15631 |
| [Gleason] p. 295 | Remark | bcval3 14345 bcval4 14346 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14360 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14343 df-bc 14342 |
| [Gleason] p. 296 | Remark | bcn0 14349 bcnn 14351 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15866 |
| [Gleason] p. 308 | Equation 2 | ef0 16127 |
| [Gleason] p. 308 | Equation 3 | efcj 16128 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16133 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16137 |
| [Gleason] p. 310 | Equation 14 | sinadd 16200 |
| [Gleason] p. 310 | Equation 15 | cosadd 16201 |
| [Gleason] p. 311 | Equation 17 | sincossq 16212 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16217 sinbnd 16216 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14255 sqeqori 14253 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16108 |
| [Godowski] p. 730 | Equation SF | goeqi 32292 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 31687 |
| [Golan] p. 1 | Remark | srgisid 20206 |
| [Golan] p. 1 | Definition | df-srg 20184 |
| [Golan] p. 149 | Definition | df-slmd 33207 |
| [Gonshor] p. 7 | Definition | df-scut 27828 |
| [Gonshor] p. 9 | Theorem 2.5 | slerec 27864 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 27954 cofcut1d 27955 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 27956 cofcut2d 27957 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 27958 cofcutr1d 27959 cofcutr2d 27960 |
| [Gonshor] p. 13 | Definition | df-adds 27993 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 28009 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 28035 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28156 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28176 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28416 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28420 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28419 |
| [Gonshor] p. 95 | Theorem 6.1 | addsbday 28050 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36160 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17629 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17631 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 48104 df-cllaw 48102 df-comlaw 48103 |
| [Hall] p. 2 | Section 1.2 | df-clintop 48116 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 48137 |
| [Halmos] p. 28 | Partition ` ` | df-parts 38766 dfmembpart2 38771 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32084 riesz2 32085 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 31960 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32192 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32204 elpjidm 32203 pjnmopi 32167 |
| [Halmos] p. 44 | Remark | pjinormi 31706 pjinormii 31695 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32208 pjrn 31726 pjrni 31721 pjvec 31715 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 31746 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32173 hmopidmpji 32171 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32210 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32199 pjocvec 31716 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32188 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32191 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32194 pjssdif2i 32193 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 31874 |
| [Hamilton] p. 28 | Definition 2.1 | ax-1 6 |
| [Hamilton] p. 31 | Example 2.7(a) | idALT 23 |
| [Hamilton] p. 73 | Rule 1 | ax-mp 5 |
| [Hamilton] p. 74 | Rule 2 | ax-gen 1795 |
| [Hatcher] p. 25 | Definition | df-phtpc 25024 df-phtpy 25003 |
| [Hatcher] p. 26 | Definition | df-pco 25038 df-pi1 25041 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 25027 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 25083 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22496 df-dmatalt 48315 |
| [Helfgott] p. 2 | Theorem | tgoldbach 47804 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 47789 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 47801 bgoldbtbnd 47796 bgoldbtbnd 47796 tgblthelfgott 47802 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 34657 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 34658 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 34672 hgt750lemb 34671 hgt750leme 34673 hgt750lemf 34668 hgt750lemg 34669 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 47798 tgoldbachgt 34678 tgoldbachgtALTV 47799 tgoldbachgtd 34677 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 34659 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30512 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 18962 grpoideu 30528 mndideu 18758 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 18992 grpoinveu 30538 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 19023 grpo2inv 30550 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 19036 grpoinvop 30552 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 19058 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1768 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1769 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1771 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32439 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32452 cdj3i 32460 cdj3lem1 32453 cdjreui 32451 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32450 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 41967 |
| [Holland95] p. 14 | Line 15 | hgmapvs 41893 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 41915 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 41916 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 41913 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 41919 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 41838 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 41933 |
| [Holland95] p. 204 | Definition of involution | df-srng 20841 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 39505 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 41530 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 41483 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 39935 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 41379 poml4N 39955 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 41470 pexmidALTN 39980 pexmidN 39971 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 41535 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 39125 ldualset 39126 |
| [Holland95] p. 222 | Item 1 | df-lines 39503 df-pointsN 39504 |
| [Holland95] p. 222 | Item 2 | df-polarityN 39905 |
| [Holland95] p. 223 | Remark | ispsubcl2N 39949 omllaw4 39247 pol1N 39912 polcon3N 39919 |
| [Holland95] p. 223 | Definition | df-psubclN 39937 |
| [Holland95] p. 223 | Equation for polarity | polval2N 39908 |
| [Holmes] p. 40 | Definition | df-xrn 38372 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31103 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32201 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 31982 eigre 31854 eigrei 31853 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 31983 eigorth 31857 eigorthi 31856 |
| [Hughes] p. 137 | Remark (ii) | eigposi 31855 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30328 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30324 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30325 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30326 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30344 frgrregorufr0 30343 frgrregorufrg 30345 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30351 frrusgrord 30360 frrusgrord0 30359 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30107 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30334 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30337 frgrwopreg2 30338 frgrwopregasn 30335 frgrwopregbsn 30336 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30340 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30354 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30357 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30105 numclwlk1 30390 numclwlk1lem1 30388 numclwlk1lem2 30389 numclwwlk1 30380 numclwwlk8 30411 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30331 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 29791 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30366 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30392 numclwwlkovh0 30391 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30400 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 29997 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30404 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30407 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30410 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30422 natded 30422 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30422 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30422 natded 30422 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30422 |
| [Jech] p. 4 | Definition of class | cv 1539 cvjust 2731 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10619 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10617 alephmul 10618 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10616 infmap2 10257 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9854 |
| [Jech] p. 72 | Equation 9.3 | scott0 9926 scottex 9925 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9907 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9931 |
| [Jech] p. 78 | Note | opthprc 5749 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 42927 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 43015 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 43016 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 42939 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 42943 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 42944 rmyp1 42945 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 42946 rmym1 42947 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 42937 rmx1 42938 rmxluc 42948 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 42941 rmy1 42942 rmyluc 42949 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 42951 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 42952 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 42972 jm2.17b 42973 jm2.17c 42974 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 43005 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 43009 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 43000 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 42975 jm2.24nn 42971 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 43014 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 43020 rmygeid 42976 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 43032 |
| [Juillerat] p. 11 | Section *5 | etransc 46298 etransclem47 46296 etransclem48 46297 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 46293 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 46295 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 46281 |
| [Juillerat] p. 13 | Proof | etransclem35 46284 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 46287 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 46273 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 46290 |
| [Juillerat] p. 14 | Proof | etransclem23 46272 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1967 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2011 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2016 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2006 cbvaliw 2005 wl-cbvmotv 37514 wl-motae 37516 wl-moteq 37515 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 1995 spimw 1970 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2032 spw 2033 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31535 chabs1i 31537 chabs2 31536 chabs2i 31538 chjass 31552 chjassi 31505 latabs1 18520 latabs2 18521 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32357 ela 32358 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32302 cvrval2 39275 |
| [Kalmbach] p. 16 | Definition | df-ol 39179 df-oml 39180 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 31603 cmbri 31609 cmtvalN 39212 df-cm 31602 df-cmtN 39178 |
| [Kalmbach] p. 22 | Remark | omllaw5N 39248 pjoml5 31632 pjoml5i 31607 |
| [Kalmbach] p. 22 | Definition | pjoml2 31630 pjoml2i 31604 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 31633 cmcmi 31611 cmcmii 31616 cmtcomN 39250 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 39246 omlsi 31423 pjoml 31455 pjomli 31454 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 39245 |
| [Kalmbach] p. 23 | Remark | cmbr2i 31615 cmcm3 31634 cmcm3i 31613 cmcm3ii 31618 cmcm4i 31614 cmt3N 39252 cmt4N 39253 cmtbr2N 39254 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 31627 cmbr3i 31619 cmtbr3N 39255 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 31637 fh1i 31640 fh2 31638 fh2i 31641 omlfh1N 39259 |
| [Kalmbach] p. 65 | Remark | chjatom 32376 chslej 31517 chsleji 31477 shslej 31399 shsleji 31389 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31514 chocini 31473 chsupcl 31359 chsupval2 31429 h0elch 31274 helch 31262 hsupval2 31428 ocin 31315 ococss 31312 shococss 31313 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31331 |
| [Kalmbach] p. 66 | Remark | df-pjh 31414 pjssmi 32184 pjssmii 31700 |
| [Kalmbach] p. 67 | Lemma 3 | osum 31664 osumi 31661 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32219 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32419 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32329 |
| [Kalmbach] p. 140 | Remark | hatomic 32379 hatomici 32378 hatomistici 32381 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 39320 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32400 lsatexch 39044 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32374 cvlcvr1 39340 cvr1 39412 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32393 cvexchi 32388 cvrexch 39422 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32383 hlrelat 39404 hlrelat5N 39403 lrelat 39015 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21143 lsmsatcv 39011 spansncv 31672 spansncvi 31671 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 39030 spansncv2 32312 |
| [Kalmbach] p. 266 | Definition | df-st 32230 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 31868 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10686 fpwwe2 10683 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10687 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10694 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10689 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10691 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10704 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10708 gchxpidm 10709 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10720 gchhar 10719 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10255 unxpwdom 9629 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10710 |
| [Kreyszig] p. 3 | Property M1 | metcl 24342 xmetcl 24341 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24349 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24585 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11984 muleqadd 11907 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24448 |
| [Kreyszig] p. 19 | Remark | mopntopon 24449 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24511 mopnm 24454 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24509 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24514 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24555 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23266 lmmbr 25292 lmmbr2 25293 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23388 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25347 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25310 iscmet2 25328 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25350 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23469 metelcls 25339 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25340 metcld2 25341 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25132 lmodvneg1 20903 nvinv 30658 vcm 30595 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25128 lmod0vs 20893 slmd0vs 33230 vc0 30593 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20894 slmdvs0 33231 vcz 30594 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 30710 ngpmet 24616 nrmmetd 24587 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 30705 imsdval2 30706 ncvspds 25195 ngpds 24617 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24602 nvnd 30707 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24631 nmge0 24630 nvge0 30692 nvz 30688 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24637 nvabs 30691 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 30820 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 30764 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 30826 blocni 30824 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 30825 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25238 ipeq0 21656 ipz 30738 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25250 pythi 30869 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 30873 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25272 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15892 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25470 minveco 30903 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 30769 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25363 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 30892 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32142 leopg 32141 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32160 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 30937 |
| [Kulpa] p. 547 | Theorem | poimir 37660 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 37659 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 37658 |
| [Kulpa] p. 548 | Theorem | broucube 37661 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 37653 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 37654 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2388 axnul 5305 |
| [Kunen] p. 11 | Axiom 3 | axnul 5305 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 7979 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8878 mapvalg 8876 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10562 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7963 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9804 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9846 r1elssi 9845 |
| [Kunen] p. 107 | Exercise 4 | rankop 9898 rankopb 9892 rankuni 9903 rankxplim 9919 rankxpsuc 9922 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 44975 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 44979 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 44978 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 44980 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 44985 rexabso 44986 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 44992 n0abso 44993 ssabso 44991 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 44994 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 45004 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 44999 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 45002 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 45003 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 44998 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 45010 wfaxpr 45015 wfaxreg 45017 wfaxrep 45011 wfaxsep 45012 wfaxun 45016 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 45001 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 45014 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 45010 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 45009 omelaxinf2 45006 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 45019 wfaxinf2 45018 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 5004 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 33715 |
| [Lang] p. | Definition | df-rn 5696 |
| [Lang] p. 3 | Statement | lidrideqd 18682 mndbn0 18763 |
| [Lang] p. 3 | Definition | df-mnd 18748 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18700 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18854 |
| [Lang] p. 5 | Equation | gsumreidx 19935 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 48098 |
| [Lang] p. 6 | Example | nn0mnd 48095 |
| [Lang] p. 6 | Equation | gsumxp2 19998 |
| [Lang] p. 6 | Statement | cycsubm 19220 |
| [Lang] p. 6 | Definition | mulgnn0gsum 19098 |
| [Lang] p. 6 | Observation | mndlsmidm 19688 |
| [Lang] p. 7 | Definition | dfgrp2e 18981 |
| [Lang] p. 30 | Definition | df-tocyc 33127 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33172 |
| [Lang] p. 32 | Property (b) | cyc3conja 33177 cycpmconjv 33162 |
| [Lang] p. 53 | Definition | df-cat 17711 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18142 cat1lem 18141 |
| [Lang] p. 54 | Definition | df-iso 17793 |
| [Lang] p. 57 | Definition | df-inito 18029 df-termo 18030 |
| [Lang] p. 58 | Example | irinitoringc 21490 |
| [Lang] p. 58 | Statement | initoeu1 18056 termoeu1 18063 |
| [Lang] p. 62 | Definition | df-func 17903 |
| [Lang] p. 65 | Definition | df-nat 17991 |
| [Lang] p. 91 | Note | df-ringc 20646 |
| [Lang] p. 92 | Statement | mxidlprm 33498 |
| [Lang] p. 92 | Definition | isprmidlc 33475 |
| [Lang] p. 128 | Remark | dsmmlmod 21765 |
| [Lang] p. 129 | Proof | lincscm 48347 lincscmcl 48349 lincsum 48346 lincsumcl 48348 |
| [Lang] p. 129 | Statement | lincolss 48351 |
| [Lang] p. 129 | Observation | dsmmfi 21758 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 33678 qusdimsum 33679 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 33658 |
| [Lang] p. 147 | Definition | snlindsntor 48388 |
| [Lang] p. 504 | Statement | mat1 22453 matring 22449 |
| [Lang] p. 504 | Definition | df-mamu 22395 |
| [Lang] p. 505 | Statement | mamuass 22406 mamutpos 22464 matassa 22450 mattposvs 22461 tposmap 22463 |
| [Lang] p. 513 | Definition | mdet1 22607 mdetf 22601 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22697 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22593 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22617 |
| [Lang] p. 515 | Definition | df-minmar1 22641 smadiadetr 22681 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22616 mdetralt 22614 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22629 |
| [Lang] p. 518 | Definition | df-madu 22640 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22651 madurid 22650 matinv 22683 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 22896 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 33714 fedgmul 33682 |
| [Lang], p. 561 | Remark | chpmatply1 22838 |
| [Lang], p. 561 | Definition | df-chpmat 22833 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 44353 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 44348 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 44354 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5305 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2715 |
| [Levy] p. 59 | Definition | df-ttrcl 9748 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9791 |
| [Levy] p. 338 | Axiom | df-clel 2816 df-cleq 2729 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2816 df-cleq 2729 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2715 |
| [Levy] p. 358 | Axiom | df-clab 2715 |
| [Levy58] p. 2 | Definition I | isfin1-3 10426 |
| [Levy58] p. 2 | Definition II | df-fin2 10326 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10325 |
| [Levy58] p. 2 | Definition III | df-fin3 10328 |
| [Levy58] p. 3 | Definition V | df-fin5 10329 |
| [Levy58] p. 3 | Definition IV | df-fin4 10327 |
| [Levy58] p. 4 | Definition VI | df-fin6 10330 |
| [Levy58] p. 4 | Definition VII | df-fin7 10331 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10455 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27731 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27742 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27774 nosupbnd1 27759 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27776 nosupbnd2 27761 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27780 noetasuplem4 27781 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27777 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1768 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1769 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1771 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32427 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32431 mdsymi 32430 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32425 mdsymlem6 32427 mdsymlem7 32428 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32429 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32332 ssdmd2 32333 ssmd1 32330 ssmd2 32331 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32328 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32300 df-md 32299 mdbr 32313 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32350 mdslj1i 32338 mdslj2i 32339 mdslle1i 32336 mdslle2i 32337 mdslmd1i 32348 mdslmd2i 32349 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32340 mdsl2bi 32342 mdsl2i 32341 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32354 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32351 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32352 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32329 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32334 mdsl3 32335 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32353 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32448 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 39322 hlrelat1 39402 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 39040 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32355 cvmdi 32343 cvnbtwn4 32308 cvrnbtwn4 39280 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32356 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 39341 cvp 32394 cvrp 39418 lcvp 39041 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32418 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32417 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 39334 hlexch4N 39394 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32420 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 39445 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 39751 atpsubN 39755 df-pointsN 39504 pointpsubN 39753 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 39506 pmap11 39764 pmaple 39763 pmapsub 39770 pmapval 39759 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 39767 pmap1N 39769 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 39772 pmapglb2N 39773 pmapglb2xN 39774 pmapglbx 39771 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 39854 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 39479 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 39798 paddclN 39844 paddidm 39843 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 39480 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 39840 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 39479 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 39480 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19693 lsmmod2 19694 lssats 39013 shatomici 32377 shatomistici 32380 shmodi 31409 shmodsi 31408 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32319 mdsymlem7 32428 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 31608 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31512 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32434 |
| [Margaris] p. 40 | Rule C | exlimiv 1930 |
| [Margaris] p. 49 | Axiom A1 | ax-1 6 |
| [Margaris] p. 49 | Axiom A2 | ax-2 7 |
| [Margaris] p. 49 | Axiom A3 | ax-3 8 |
| [Margaris] p. 49 | Definition | df-an 396 df-ex 1780 df-or 849 dfbi2 474 |
| [Margaris] p. 51 | Theorem 1 | idALT 23 |
| [Margaris] p. 56 | Theorem 3 | conventions 30419 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 44935 |
| [Margaris] p. 60 | Theorem 8 | jcn 162 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 44936 |
| [Margaris] p. 79 | Rule C | exinst01 44645 exinst11 44646 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1976 19.2g 2188 r19.2z 4495 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2202 rr19.3v 3667 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2159 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1826 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1781 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2181 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2205 19.9h 2286 exlimd 2218 exlimdh 2290 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2162 excomim 2163 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2327 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30420 conventions-labels 30420 conventions-labels 30420 conventions-labels 30420 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1827 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 44397 albi 1818 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2225 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2226 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 44399 exbi 1847 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2229 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 44396 2alimdv 1918 alimd 2212 alimdh 1817 alimdv 1916 ax-4 1809 ralimdaa 3260 ralimdv 3169 ralimdva 3167 ralimdvva 3206 sbcimdv 3859 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2207 19.21h 2287 19.21t 2206 19.21vv 44395 alrimd 2215 alrimdd 2214 alrimdh 1863 alrimdv 1929 alrimi 2213 alrimih 1824 alrimiv 1927 alrimivv 1928 hbralrimi 3144 r19.21be 3252 r19.21bi 3251 ralrimd 3264 ralrimdv 3152 ralrimdva 3154 ralrimdvv 3203 ralrimdvva 3211 ralrimi 3257 ralrimia 3258 ralrimiv 3145 ralrimiva 3146 ralrimivv 3200 ralrimivva 3202 ralrimivvva 3205 ralrimivw 3150 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 44398 2eximdv 1919 exim 1834 eximd 2216 eximdh 1864 eximdv 1917 rexim 3087 reximd2a 3269 reximdai 3261 reximdd 45153 reximddv 3171 reximddv2 3215 reximddv3 3172 reximdv 3170 reximdv2 3164 reximdva 3168 reximdvai 3165 reximdvva 3207 reximi2 3079 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2211 19.23bi 2191 19.23h 2288 19.23t 2210 exlimdv 1933 exlimdvv 1934 exlimexi 44544 exlimiv 1930 exlimivv 1932 rexlimd3 45149 rexlimdv 3153 rexlimdv3a 3159 rexlimdva 3155 rexlimdva2 3157 rexlimdvaa 3156 rexlimdvv 3212 rexlimdvva 3213 rexlimdvvva 3214 rexlimdvw 3160 rexlimiv 3148 rexlimiva 3147 rexlimivv 3201 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 1985 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1880 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1870 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2227 r19.27z 4505 r19.27zv 4506 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2228 19.28vv 44405 r19.28z 4498 r19.28zf 45164 r19.28zv 4501 rr19.28v 3668 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1873 r19.29d2r 3140 r19.29imd 3118 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1881 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2234 19.31vv 44403 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2233 r19.32 47110 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 44401 19.33 1884 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 1986 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1877 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2230 19.36vv 44402 r19.36zv 4507 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2232 19.37vv 44404 r19.37zv 4502 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1839 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 1984 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1887 19.40 1886 r19.40 3119 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2235 19.41rg 44570 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2236 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1882 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2237 r19.44zv 4504 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2238 r19.45zv 4503 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2610 |
| [Mayet] p. 370 | Remark | jpi 32289 largei 32286 stri 32276 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32231 ishst 32233 |
| [Mayet3] p. 10 | Theorem | hstrbi 32285 hstri 32284 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 31747 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 31748 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32297 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31351 chsupcl 31359 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32379 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32373 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32400 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 39985 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18532 latj32 18530 latjass 18528 |
| [Megill] p. 444 | Axiom C5 | ax-5 1910 ax5ALT 38908 |
| [Megill] p. 444 | Section 7 | conventions 30419 |
| [Megill] p. 445 | Lemma L12 | aecom-o 38902 ax-c11n 38889 axc11n 2431 |
| [Megill] p. 446 | Lemma L17 | equtrr 2021 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 38897 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 38929 hbnae 2437 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2486 sbid 2255 sbidd-misc 49238 sbidd 49237 |
| [Megill] p. 448 | Remark 9.6 | axc14 2468 |
| [Megill] p. 448 | Scheme C4' | ax-c4 38885 |
| [Megill] p. 448 | Scheme C5' | ax-c5 38884 sp 2183 |
| [Megill] p. 448 | Scheme C6' | ax-11 2157 |
| [Megill] p. 448 | Scheme C7' | ax-c7 38886 |
| [Megill] p. 448 | Scheme C8' | ax-7 2007 |
| [Megill] p. 448 | Scheme C9' | ax-c9 38891 |
| [Megill] p. 448 | Scheme C10' | ax-6 1967 ax-c10 38887 |
| [Megill] p. 448 | Scheme C11' | ax-c11 38888 |
| [Megill] p. 448 | Scheme C12' | ax-8 2110 |
| [Megill] p. 448 | Scheme C13' | ax-9 2118 |
| [Megill] p. 448 | Scheme C14' | ax-c14 38892 |
| [Megill] p. 448 | Scheme C15' | ax-c15 38890 |
| [Megill] p. 448 | Scheme C16' | ax-c16 38893 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 38905 dral1 2444 dral2-o 38931 dral2 2443 drex1 2446 drex2 2447 drsb1 2500 drsb2 2266 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2173 sbequ 2083 sbid2v 2514 |
| [Megill] p. 450 | Example in Appendix | hba1-o 38898 hba1 2293 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 46904 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 23 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3879 rspsbca 3880 stdpc4 2068 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 38885 ra4 3886 stdpc5 2208 |
| [Mendelson] p. 81 | Rule C | exlimiv 1930 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2027 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2250 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3786 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5519 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4398 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4399 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4277 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4334 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4278 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4141 |
| [Mendelson] p. 231 | Definition of union | dfun3 4276 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5456 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4904 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5574 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4618 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5575 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4931 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5836 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6288 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7795 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6390 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8633 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9180 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 9095 xpsneng 9096 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9103 xpcomeng 9104 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9106 |
| [Mendelson] p. 255 | Definition | brsdom 9015 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9098 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8870 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 9077 mapsnend 9076 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9186 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9185 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8922 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 9080 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9099 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10219 djucomen 10218 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10223 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10217 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8569 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8596 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10599 |
| [Mendelson] p. 281 | Definition | df-r1 9804 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9853 |
| [Mendelson] p. 287 | Axiom system MK | ru 3786 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30278 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30313 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30315 vdgn1frgrv3 30316 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30317 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30310 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30303 2pthfrgrrn 30301 2pthfrgrrn2 30302 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31271 |
| [Monk1] p. 22 | Remark | conventions 30419 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30419 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4239 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5792 ssrelf 32627 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5794 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5206 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6282 coi2 6283 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5931 rn0 5936 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 6161 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5703 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5939 rnxp 6190 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5784 xp0 6178 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6095 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6092 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7936 imaexALTV 38331 imaexg 7935 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6089 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7095 funfvop 7070 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6963 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6974 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6612 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7275 dff13f 7276 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7239 funrnex 7978 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7267 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6247 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4964 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 8031 df-1st 8014 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 8032 df-2nd 8015 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9894 ranksnb 9867 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9895 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9896 rankunb 9890 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9878 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9804 r1val2 9877 |
| [Monk1] p. 117 | Lemma | zorn2 10546 zorn2g 10543 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 10026 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10601 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 10021 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1809 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2007 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2177 ax-c15 38890 ax12v2 2179 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 38885 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2157 |
| [Monk2] p. 109 | Lemma 15 | equvini 2460 equvinv 2028 eqvinop 5492 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1910 ax5ALT 38908 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2141 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2157 |
| [Monk2] p. 114 | Lemma 21 | sp 2183 |
| [Monk2] p. 114 | Lemma 22 | axc4 2321 hba1-o 38898 hba1 2293 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2153 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2176 nfra2 3376 nfra2w 3299 |
| [Moore] p. 53 | Part I | df-mre 17629 |
| [Munkres] p. 77 | Example 2 | distop 23002 indistop 23009 indistopon 23008 |
| [Munkres] p. 77 | Example 3 | fctop 23011 fctop2 23012 |
| [Munkres] p. 77 | Example 4 | cctop 23013 |
| [Munkres] p. 78 | Definition of basis | df-bases 22953 isbasis3g 22956 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17488 tgval2 22963 |
| [Munkres] p. 79 | Remark | tgcl 22976 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 22970 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 22994 tgss3 22993 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 22995 basgen2 22996 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 37350 topdifinfeq 37351 topdifinffin 37349 topdifinfindis 37347 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23168 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 23046 topcld 23043 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 23047 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 23049 |
| [Munkres] p. 94 | Definition of closure | clsval 23045 |
| [Munkres] p. 94 | Definition of interior | ntrval 23044 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 23083 elcls 23081 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 23091 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23156 neindisj 23125 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23158 |
| [Munkres] p. 97 | Definition of limit point | islp2 23153 lpval 23147 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23323 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23235 iscn 23243 iscn2 23246 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23288 cncnp2 23289 cncnpi 23286 df-cnp 23236 iscnp 23245 iscnp2 23247 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24556 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25345 |
| [Nathanson] p. 123 | Remark | reprgt 34636 reprinfz1 34637 reprlt 34634 |
| [Nathanson] p. 123 | Definition | df-repr 34624 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 34656 |
| [Nathanson] p. 123 | Proposition | breprexp 34648 breprexpnat 34649 itgexpif 34621 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32123 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 47797 |
| [Pfenning] p. 17 | Definition XM | natded 30422 |
| [Pfenning] p. 17 | Definition NNC | natded 30422 notnotrd 133 |
| [Pfenning] p. 17 | Definition ` `C | natded 30422 |
| [Pfenning] p. 18 | Rule" | natded 30422 |
| [Pfenning] p. 18 | Definition /\I | natded 30422 |
| [Pfenning] p. 18 | Definition ` `E | natded 30422 natded 30422 natded 30422 natded 30422 natded 30422 |
| [Pfenning] p. 18 | Definition ` `I | natded 30422 natded 30422 natded 30422 natded 30422 natded 30422 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30422 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30422 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30422 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30422 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30422 |
| [Pfenning] p. 127 | Definition =E | natded 30422 |
| [Pfenning] p. 127 | Definition =I | natded 30422 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25236 df-dip 30720 dip0l 30737 ip0l 21654 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25277 ipval 30722 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 30733 ipcj 21652 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25239 dipdir 30861 ipdir 21657 ipdiri 30849 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 30729 nmsq 25228 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 30844 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 30846 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 30847 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25245 dipass 30864 ipass 21663 ipassi 30860 |
| [Prugovecki] p. 186 | Definition of bra | braval 31963 df-bra 31869 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 31870 kbval 31973 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32401 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 39890 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32415 atcvat4i 32416 cvrat3 39444 cvrat4 39445 lsatcvat3 39053 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32301 cvrval 39270 df-cv 32298 df-lcv 39020 lspsncv0 21148 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 39902 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 39903 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2715 rabid 3458 rabidd 45160 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2279 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2729 |
| [Quine] p. 19 | Definition 2.9 | conventions 30419 df-v 3482 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2881 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2878 abid2f 2936 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2276 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2085 sbalex 2242 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2816 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2737 eqid1 30486 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2744 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3789 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3790 dfsbcq2 3791 |
| [Quine] p. 43 | Theorem 6.8 | vex 3484 |
| [Quine] p. 43 | Theorem 6.9 | isset 3494 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3591 spcgv 3596 spcimgf 3550 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3801 spsbcd 3802 |
| [Quine] p. 44 | Theorem 6.12 | elex 3501 |
| [Quine] p. 44 | Theorem 6.13 | elab 3679 elabg 3676 elabgf 3674 |
| [Quine] p. 44 | Theorem 6.14 | noel 4338 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4717 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4629 df-sn 4627 |
| [Quine] p. 49 | Theorem 7.4 | snss 4785 snssg 4783 |
| [Quine] p. 49 | Theorem 7.5 | prss 4820 prssg 4819 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4762 prid1g 4760 prid2 4763 prid2g 4761 snid 4662 snidg 4660 |
| [Quine] p. 51 | Theorem 7.12 | snex 5436 |
| [Quine] p. 51 | Theorem 7.13 | prex 5437 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4926 unisnALT 44946 unisng 4925 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4930 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4937 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4935 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6528 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 47098 dfiota2 6515 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 47107 iotaval 6532 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6539 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6534 |
| [Quine] p. 58 | Definition 9.1 | df-op 4633 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5530 opabidw 5529 opelopab 5547 opelopaba 5541 opelopabaf 5549 opelopabf 5550 opelopabg 5543 opelopabga 5538 opelopabgf 5545 oprabid 7463 oprabidw 7462 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5691 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5693 |
| [Quine] p. 64 | Definition 9.15 | df-id 5578 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6631 |
| [Quine] p. 65 | Theorem 10.4 | funi 6598 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6619 funsng 6617 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6563 |
| [Quine] p. 65 | Definition 10.2 | args 6110 dffv4 6903 |
| [Quine] p. 68 | Definition 10.11 | conventions 30419 df-fv 6569 fv2 6901 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14311 nn0opth2i 14310 nn0opthi 14309 omopthi 8699 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8450 |
| [Quine] p. 232 | Equation i | carddom 10594 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6655 funimaexg 6653 |
| [Quine] p. 331 | Axiom system NF | ru 3786 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31103 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 30720 polid 31178 polid2i 31176 polidi 31177 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 30832 |
| [ReedSimon] p. 195 | Remark | lnophm 32038 lnophmi 32037 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32151 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32153 leopmuli 32152 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32156 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 31871 leoppos 32145 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32155 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32144 |
| [Roman] p. 4 | Definition | df-dmat 22496 df-dmatalt 48315 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20150 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20232 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 48402 |
| [Roman] p. 112 | Note | isldepslvec2 48402 ldepsnlinc 48425 zlmodzxznm 48414 |
| [Roman] p. 112 | Example | zlmodzxzequa 48413 zlmodzxzequap 48416 zlmodzxzldep 48421 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 22896 |
| [Rosenlicht] p. 80 | Theorem | heicant 37662 |
| [Rosser] p. 281 | Definition | df-op 4633 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 34660 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 34661 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 48282 pmtr3ncom 19493 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19489 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19432 cayleyth 19433 |
| [Rudin] p. 164 | Equation 27 | efcan 16132 |
| [Rudin] p. 164 | Equation 30 | efzval 16138 |
| [Rudin] p. 167 | Equation 48 | absefi 16232 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 197 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1771 |
| [Sanford] p. 39 | Rule 4 | mptxor 1769 |
| [Sanford] p. 40 | Rule 1 | mptnan 1768 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6135 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6138 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6132 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6130 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17629 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17630 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17630 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17632 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10177 |
| [Schechter] p. 141 | Definition (MC) | dfac11 43074 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10486 axdc3 10494 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20234 isrngo 37904 |
| [Schechter] p. 276 | Remark 11.6.e | span0 31561 |
| [Schechter] p. 276 | Definition of span | df-span 31328 spanval 31352 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 23000 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6409 onelord 43263 ordelon 6408 ordelord 6406 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 43264 sucidg 6465 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6438 onsuc 7831 ord0 6437 ordsuci 7828 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 43265 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5263 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 43040 elon2 6395 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6390 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5587 epelg 5585 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9637 epirron 43266 ordirr 6402 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 43268 oneptr 43267 ontr1 6430 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 43270 oneptri 43269 ordtri3or 6416 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8539 ord0eln0 6439 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6451 onsucss 43279 trsucss 6472 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7838 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6478 ordnbtwn 6477 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 43281 ordnexbtwnsuc 43280 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10441 onsucf1lem 43282 onsucf1o 43285 onsucf1olem 43283 onsucrn 43284 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 43286 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7866 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 43275 ordne0gt0 43274 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 43277 limnsuc 43278 onsucelab 43276 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9683 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7881 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9686 ordom 7897 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9687 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8678 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7800 ssorduni 7799 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8569 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9690 limom 7903 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8506 df1o2 8513 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8554 oa0suclim 43288 oalim 8570 oasuc 8562 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8555 om0suclim 43289 omlim 8571 omsuc 8564 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8560 oe0m1 8559 oe0suclim 43290 oelim 8572 oesuc 8565 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 43241 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 43292 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 43293 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 43294 limexissupab 43296 limiun 43295 limuni 6445 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8576 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8580 om1om1r 43297 om1r 8581 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8573 oaomoecl 43291 oecl 8575 omcl 8574 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 43243 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8582 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8583 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 43298 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 43299 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8649 nnamecl 43300 nnecl 8651 nnmcl 8650 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 43301 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8590 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8591 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8598 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 43303 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 43304 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 43306 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8597 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 43310 omword1 8611 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 43309 oaordnrex 43308 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 43305 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 43311 omword2 8612 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 43312 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 43313 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 43314 omordi 8604 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8606 omord2com 43315 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 43316 df-2o 8507 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 43319 oewordi 8629 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 43320 oeworde 8631 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 43321 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 43322 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 43318 omnord1ex 43317 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 43323 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 43325 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 43329 oenord1ex 43328 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 43330 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8599 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 43324 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8617 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8618 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 43332 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8635 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 43333 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 43334 cantnfub2 43335 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 43338 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 28929 axtgcgrrflx 28470 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 28930 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 28931 axtgcgrid 28471 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28456 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 28942 axtgsegcon 28472 df-trkgcb 28458 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 28953 axtg5seg 28473 df-trkgcb 28458 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 28954 axtgbtwnid 28474 df-trkgb 28457 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 28956 axtgpasch 28475 df-trkgb 28457 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 28975 df-trkg2d 34680 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28478 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28479 df-trkg2d 34680 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 28978 axtgeucl 28480 df-trkge 28459 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 28991 axtgcont 28477 axtgcont1 28476 df-trkgb 28457 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 35988 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 35990 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 35993 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 35997 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 35998 tgcgrcomimp 28485 tgcgrcoml 28487 tgcgrcomr 28486 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 36003 tgcgrtriv 28492 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 36007 tg5segofs 34688 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 34685 df-ofs 35984 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 36009 tgcgrextend 28493 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 36011 tgsegconeq 28494 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36023 btwntriv2 36013 tgbtwntriv2 28495 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 36014 tgbtwncom 28496 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36017 tgbtwntriv1 28499 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36018 tgbtwnswapid 28500 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36024 btwnintr 36020 tgbtwnexch2 28504 tgbtwnintr 28501 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36026 btwnexch3 36021 tgbtwnexch 28506 tgbtwnexch3 28502 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36025 tgbtwnouttr 28505 tgbtwnouttr2 28503 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 28974 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36028 tgbtwndiff 28514 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28507 trisegint 36029 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36045 tgifscgr 28516 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28566 colrot1 28567 colrot2 28568 lncom 28630 lnrot1 28631 lnrot2 28632 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36041 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36046 tgcgrsub 28517 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36056 tgcgrxfr 28526 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28525 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36042 df-cgrg 28519 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28519 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36057 tgbtwnxfr 28538 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36063 colinearperm2 36065 colinearperm3 36064 colinearperm4 36066 colinearperm5 36067 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28541 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36040 tgellng 28561 tglng 28554 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36068 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36076 lnxfr 28574 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36077 lnext 28575 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36081 tgfscgr 28576 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36082 lncgr 28577 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36043 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36084 lnid 28578 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36085 tgidinside 28579 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36102 tgbtwnconn1 28583 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36103 tgbtwnconn2 28584 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36104 tgbtwnconn3 28585 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36110 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36108 legov 28593 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28594 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28607 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36111 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36113 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36115 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36116 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36117 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36114 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36119 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28595 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28597 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28598 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28599 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28600 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36126 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36127 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36122 df-outsideof 36121 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36123 ishlg 28610 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28615 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28617 outsideofrflx 36128 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28611 hlcomd 28612 outsideofcom 36129 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28618 outsideoftr 36130 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 28626 outsideofeu 36132 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36139 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36140 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36133 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36148 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36149 tglineelsb2 28640 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36151 linerflx1 36150 linerflx2 36152 tglinecom 28643 tglinerflx1 28641 tglinerflx2 28642 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36154 tglinethru 28644 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36138 tglng 28554 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28602 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36157 tglinethrueu 28647 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36158 tglineineq 28651 tglineinteq 28653 tglineintmo 28650 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28657 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28658 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 28659 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 28674 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 28670 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 28662 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 28661 ismir 28667 mirbtwn 28666 mircgr 28665 mirfv 28664 mirval 28663 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 28672 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 28673 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 28674 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 28677 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 28678 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 28683 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 28680 mirbtwni 28679 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 28681 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 28693 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 28697 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 28694 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 28695 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 28696 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 28699 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 28700 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 28706 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 28702 israg 28705 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 28707 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 28708 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 28710 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 28711 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 28712 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 28713 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 28714 ragncol 28717 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 28715 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 28721 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 28725 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 28722 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 28704 isperp 28720 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 28723 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 28730 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 28738 colperpexlem2 28739 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 28741 colperpexlem3 28740 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 28746 midex 28745 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 28743 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 28752 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 28747 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 28756 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 28759 opphllem6 28760 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 28762 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28475 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 28763 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 28771 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 28766 hpgbr 28768 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 28773 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 28772 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 28774 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 28775 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 28776 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 28777 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 28778 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 28792 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 28782 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 28796 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 28797 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 28798 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 28799 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 28800 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 28803 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 28805 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 28783 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 28806 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 28809 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 28810 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 28811 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 28812 trgcopyeu 28814 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 28838 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 28817 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 28826 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 28824 cgrahl2 28825 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 28827 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 28828 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 28830 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 28831 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 28834 cgrahl 28835 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 28839 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 28840 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 28841 acopyeu 28842 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 28849 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 28853 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 28846 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 28861 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 28854 isleag 28855 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 28863 tgsas1 28862 tgsas2 28864 tgsas3 28865 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 28867 tgasa1 28866 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 28868 tgsss2 28869 tgsss3 28870 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27315 dchrsum 27313 dchrsum2 27312 sumdchr 27316 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27317 sum2dchr 27318 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 20086 ablfacrp2 20087 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27260 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27261 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27268 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27526 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27529 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27583 vmalogdivsum2 27582 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27573 dirith2 27572 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27571 rpvmasum 27570 rpvmasum2 27556 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27531 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27569 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27536 dchrisumlem1 27533 dchrisumlem2 27534 dchrisumlem3 27535 dchrisumlema 27532 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27539 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27568 dchrmusumlem 27566 dchrvmasumlem 27567 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27538 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27540 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27564 dchrisum0re 27557 dchrisumn0 27565 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27550 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27554 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27555 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27610 pntrsumbnd2 27611 pntrsumo1 27609 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27574 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27576 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27578 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27581 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27586 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27587 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27592 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27594 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27595 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27603 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27604 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27601 selberg3lem2 27602 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27605 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27599 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27612 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27613 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27614 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27628 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27640 pntlemb 27641 pntlemc 27639 pntlemd 27638 pntlemg 27642 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27640 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27632 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27637 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27640 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27653 pntleml 27655 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4306 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4405 dif0 4378 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4492 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4475 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4297 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4298 |
| [Stoll] p. 20 | Remark | invdif 4279 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4635 |
| [Stoll] p. 43 | Definition | uniiun 5058 |
| [Stoll] p. 44 | Definition | intiin 5059 |
| [Stoll] p. 45 | Definition | df-iin 4994 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4993 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 401 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4306 |
| [Strang] p. 242 | Section 6.3 | expgrowth 44354 |
| [Suppes] p. 22 | Theorem 2 | eq0 4350 eq0f 4347 |
| [Suppes] p. 22 | Theorem 4 | eqss 3999 eqssd 4001 eqssi 4000 |
| [Suppes] p. 23 | Theorem 5 | ss0 4402 ss0b 4401 |
| [Suppes] p. 23 | Theorem 6 | sstr 3992 sstrALT2 44855 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4103 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4104 |
| [Suppes] p. 23 | Theorem 9 | psstr 4107 |
| [Suppes] p. 23 | Theorem 10 | pssss 4098 |
| [Suppes] p. 25 | Theorem 12 | elin 3967 elun 4153 |
| [Suppes] p. 26 | Theorem 15 | inidm 4227 |
| [Suppes] p. 26 | Theorem 16 | in0 4395 |
| [Suppes] p. 27 | Theorem 23 | unidm 4157 |
| [Suppes] p. 27 | Theorem 24 | un0 4394 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4178 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4186 |
| [Suppes] p. 27 | Theorem 27 | unss 4190 |
| [Suppes] p. 27 | Theorem 28 | indir 4286 |
| [Suppes] p. 27 | Theorem 29 | undir 4287 |
| [Suppes] p. 28 | Theorem 32 | difid 4376 |
| [Suppes] p. 29 | Theorem 33 | difin 4272 |
| [Suppes] p. 29 | Theorem 34 | indif 4280 |
| [Suppes] p. 29 | Theorem 35 | undif1 4476 |
| [Suppes] p. 29 | Theorem 36 | difun2 4481 |
| [Suppes] p. 29 | Theorem 37 | difin0 4474 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4472 |
| [Suppes] p. 29 | Theorem 39 | difundi 4290 |
| [Suppes] p. 29 | Theorem 40 | difindi 4292 |
| [Suppes] p. 30 | Theorem 41 | nalset 5313 |
| [Suppes] p. 39 | Theorem 61 | uniss 4915 |
| [Suppes] p. 39 | Theorem 65 | uniop 5520 |
| [Suppes] p. 41 | Theorem 70 | intsn 4984 |
| [Suppes] p. 42 | Theorem 71 | intpr 4982 intprg 4981 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5476 |
| [Suppes] p. 42 | Theorem 78 | intun 4980 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 5033 dfiun2g 5030 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 5034 |
| [Suppes] p. 47 | Theorem 86 | elpw 4604 elpw2 5334 elpw2g 5333 elpwg 4603 elpwgdedVD 44937 |
| [Suppes] p. 47 | Theorem 87 | pwid 4622 |
| [Suppes] p. 47 | Theorem 89 | pw0 4812 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4813 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5700 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5844 xpindir 5845 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5754 xpundir 5755 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9636 |
| [Suppes] p. 58 | Theorem 2 | relss 5791 |
| [Suppes] p. 59 | Theorem 4 | eldm 5911 eldm2 5912 eldm2g 5910 eldmg 5909 |
| [Suppes] p. 59 | Definition 3 | df-dm 5695 |
| [Suppes] p. 60 | Theorem 6 | dmin 5922 |
| [Suppes] p. 60 | Theorem 8 | rnun 6165 |
| [Suppes] p. 60 | Theorem 9 | rnin 6166 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5899 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5893 brcnvg 5890 |
| [Suppes] p. 62 | Equation 5 | elcnv 5887 elcnv2 5888 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6122 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6164 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6162 |
| [Suppes] p. 63 | Definition | dftrrels2 38576 |
| [Suppes] p. 63 | Theorem 20 | co02 6280 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5985 |
| [Suppes] p. 63 | Definition 7 | df-co 5694 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5896 |
| [Suppes] p. 64 | Theorem 27 | coass 6285 |
| [Suppes] p. 65 | Theorem 31 | resundi 6011 |
| [Suppes] p. 65 | Theorem 34 | elima 6083 elima2 6084 elima3 6085 elimag 6082 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6169 |
| [Suppes] p. 66 | Theorem 40 | dminss 6173 |
| [Suppes] p. 66 | Theorem 41 | imainss 6174 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6177 |
| [Suppes] p. 81 | Definition 34 | dfec2 8748 |
| [Suppes] p. 82 | Theorem 72 | elec 8791 elecALTV 38267 elecg 8789 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 38612 erth 8796 erth2 8797 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 38615 erdisj 8799 |
| [Suppes] p. 83 | Definition 35, | df-parts 38766 dfmembpart2 38771 |
| [Suppes] p. 89 | Theorem 96 | map0b 8923 |
| [Suppes] p. 89 | Theorem 97 | map0 8927 map0g 8924 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8928 mapsnd 8926 |
| [Suppes] p. 89 | Theorem 99 | mapss 8929 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 10108 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 10107 |
| [Suppes] p. 92 | Theorem 1 | enref 9025 enrefg 9024 |
| [Suppes] p. 92 | Theorem 2 | ensym 9043 ensymb 9042 ensymi 9044 |
| [Suppes] p. 92 | Theorem 3 | entr 9046 |
| [Suppes] p. 92 | Theorem 4 | unen 9086 |
| [Suppes] p. 94 | Theorem 15 | endom 9019 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 9040 |
| [Suppes] p. 94 | Theorem 17 | domtr 9047 |
| [Suppes] p. 95 | Theorem 18 | sbth 9133 |
| [Suppes] p. 97 | Theorem 23 | canth2 9170 canth2g 9171 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9137 df-sdom 8988 dfsdom2 9136 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9154 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9139 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9138 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9152 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 9022 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9155 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9150 |
| [Suppes] p. 98 | Exercise 4 | fundmen 9071 fundmeng 9072 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9110 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9151 |
| [Suppes] p. 104 | Theorem 37 | fofi 9351 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9357 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9357 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10591 |
| [Suppes] p. 130 | Definition 3 | df-tr 5260 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7800 |
| [Suppes] p. 134 | Definition 6 | df-suc 6390 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7922 finds 7918 finds1 7921 finds2 7920 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9692 isfinite2 9334 isfiniteg 9337 unbnn 9332 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10958 df-ltpq 10950 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7884 tfinds 7881 tfinds2 7885 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8589 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8591 |
| [Suppes] p. 211 | Theorem 25 | oaass 8599 |
| [Suppes] p. 225 | Definition 8 | iscard2 10016 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10603 |
| [Suppes] p. 228 | Theorem 59 | harcard 10018 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 10106 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6435 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7813 onminsb 7814 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10612 |
| [Suppes] p. 229 | Theorem 65 | alephcard 10110 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 10117 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 10111 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9980 |
| [Suppes] p. 242 | Theorem 6 | weth 10535 |
| [Suppes] p. 242 | Theorem 8 | entric 10597 |
| [Suppes] p. 242 | Theorem 9 | carden 10591 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 35696 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 35700 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2708 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2729 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2816 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2731 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2760 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7435 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3786 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5421 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4650 elpr2 4652 elpr2g 4651 elprg 4648 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4641 elsn2 4665 elsn2g 4664 elsng 4640 velsn 4642 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5472 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4636 sneqr 4840 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4646 dfsn2 4639 dfsn2ALT 4647 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7761 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5481 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5469 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5453 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7764 unexg 7763 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4691 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4908 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3958 df-un 3956 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4924 uniprg 4923 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5377 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4689 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6454 elsucg 6452 sstr2 3990 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4158 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4209 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4172 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4228 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4284 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4285 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3971 df-ss 3968 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4602 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4187 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3969 sseqin2 4223 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 4006 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4237 inss2 4238 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 4048 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4918 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5454 sspwimp 44938 sspwimpALT 44945 sspwimpALT2 44948 sspwimpcf 44940 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5461 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5279 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3437 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5307 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3954 |
| [TakeutiZaring] p. 20 | Definition 5.14 | dfnul2 4336 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4376 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4353 n0f 4349 neq0 4352 neq0f 4348 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9635 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9772 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9774 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3482 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5315 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4400 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5321 ssexg 5323 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5317 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9642 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9637 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4366 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4135 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4300 undif3VD 44902 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4136 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4143 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3062 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3071 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7773 xpexg 7770 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5692 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6637 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6813 fun11 6640 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6577 svrelfun 6638 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5898 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5900 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5697 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5698 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5694 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6214 dfrel2 6209 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5701 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5821 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5828 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5842 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 6023 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 6003 opelresi 6005 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 6030 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 6019 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 6024 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6608 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6126 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6606 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6815 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2609 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30419 df-fv 6569 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 44473 |
| [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 47186 tz6.12-1-afv2 47253 tz6.12-1 6929 tz6.12-afv 47185 tz6.12-afv2 47252 tz6.12 6931 tz6.12c-afv2 47254 tz6.12c 6928 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 47249 tz6.12-2 6894 tz6.12i-afv2 47255 tz6.12i 6934 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6564 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6565 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6567 wfo 6559 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6566 wf1 6558 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6568 wf1o 6560 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 7051 eqfnfv2 7052 eqfnfv2f 7055 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 7007 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7237 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7235 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6655 funimaexg 6653 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5144 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5593 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5646 dffr3 6117 eliniseg 6112 iniseg 6115 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5584 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5662 fr3nr 7792 frirr 5661 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5637 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7794 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5649 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5671 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6368 tz6.26i 6370 wefrc 5679 wereu2 5682 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6371 wfii 6373 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6570 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7349 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7350 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7356 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7357 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7358 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7362 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7369 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7371 |
| [TakeutiZaring] p. 35 | Notation | wtr 5259 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 44474 tz7.2 5668 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5265 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6397 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6405 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6406 ordelordALT 44557 ordelordALTVD 44887 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6412 ordelssne 6411 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6410 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6414 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7802 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7803 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6388 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6416 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 44569 ordon 7797 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7798 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7874 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6431 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5261 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7812 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7851 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6488 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6487 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7799 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4937 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6390 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6464 sucidg 6465 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7831 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6478 ordnbtwn 6477 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7848 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6389 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7902 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7907 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7862 ordelsuc 7840 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7842 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7872 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7889 |
| [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 7899 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9675 omex 9683 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7897 |
| [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 7892 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4962 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5278 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4963 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5344 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7815 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6434 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4947 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9700 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7810 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8416 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8437 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8438 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8439 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8446 tz7.44-2 8447 tz7.44-3 8448 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8407 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8402 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8386 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8485 tz7.49c 8486 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8483 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8482 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8484 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2656 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 10051 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 10052 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8570 oasuc 8562 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7882 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8573 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8554 oa0r 8576 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8574 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8586 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8657 nnaordi 8656 oaord 8585 oaordi 8584 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5049 uniss2 4941 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8588 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8593 oawordex 8595 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8649 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8686 |
| [TakeutiZaring] p. 60 | Remark | oancom 9691 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8598 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8654 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8590 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8557 omlim 8571 omsuc 8564 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8555 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8651 nnmcl 8650 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8670 nnmordi 8669 omord 8606 omordi 8604 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8607 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8674 omwordri 8610 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8577 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8580 om1r 8581 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8613 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8615 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8616 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8617 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8618 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8646 oe0 8560 oelim 8572 oesuc 8565 onesuc 8568 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8558 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8624 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8625 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8559 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8583 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8626 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8632 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8630 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8631 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8635 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8637 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9768 tz9.1 9769 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9804 r10 9808 r1lim 9812 r1limg 9811 r1suc 9810 r1sucg 9809 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9820 r1ord2 9821 r1ordg 9818 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9830 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9855 tz9.13 9831 tz9.13g 9832 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9805 rankval 9856 rankvalb 9837 rankvalg 9857 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9879 rankelb 9864 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9893 rankval3 9880 rankval3b 9866 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9869 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9835 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9874 rankr1c 9861 rankr1g 9872 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9875 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9889 rankssb 9888 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9882 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9881 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10515 dfac3 10161 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 10070 numth 10512 numth2 10511 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10586 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10587 cardid2 9993 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 10000 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10591 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9999 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9984 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 10005 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9997 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9190 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 9058 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9195 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9114 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 10003 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10138 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9246 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9265 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10139 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9251 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10128 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 10106 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 10012 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10256 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9362 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8989 isfi 9016 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9267 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10574 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9107 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10566 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10226 unxpdom 9289 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 10014 cardsdomelir 10013 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9291 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 10054 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8868 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10602 infxpidm2 10057 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10247 infxp 10254 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9119 pw2f1o 9117 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9183 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10527 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10522 ac6s5 10531 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10583 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10584 uniimadomf 10585 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10314 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10309 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10294 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10291 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10297 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10304 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10313 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10622 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10292 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10316 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10137 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10136 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10148 alephfp2 10149 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10739 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10152 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10609 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10623 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10624 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 38884 |
| [Tarski] p. 67 | Scheme B5 | sp 2183 |
| [Tarski] p. 68 | Lemma 6 | avril1 30482 equid 2011 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2016 |
| [Tarski] p. 70 | Lemma 14 | spim 2392 spime 2394 spimew 1971 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2177 ax-c15 38890 ax12i 1966 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2085 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1968 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1910 ax5ALT 38908 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2007 ax-8 2110 ax-9 2118 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28472 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28473 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28475 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28475 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28476 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16279 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 37666 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 37668 |
| [Weierstrass] p. 272 | Definition | df-mdet 22591 mdetuni 22628 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 904 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 869 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 870 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 920 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 970 |
| [WhiteheadRussell] p. 100 | Theorem *2.01 | pm2.01 188 |
| [WhiteheadRussell] p. 100 | Theorem *2.02 | ax-1 6 |
| [WhiteheadRussell] p. 100 | Theorem *2.03 | con2 135 |
| [WhiteheadRussell] p. 100 | Theorem *2.04 | pm2.04 90 wl-luk-pm2.04 37446 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 43813 imim2 58 wl-luk-imim2 37441 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 47031 imim1 83 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 897 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2663 syl 17 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 903 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 22 wl-luk-id 37444 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 895 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 142 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 898 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 130 notnotrALT2 44947 wl-luk-notnotr 37445 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 146 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 43843 axfrege28 43842 con3 153 |
| [WhiteheadRussell] p. 103 | Theorem *2.17 | ax-3 8 |
| [WhiteheadRussell] p. 103 | Theorem *2.18 | pm2.18 128 |
| [WhiteheadRussell] p. 104 | Theorem *2.2 | orc 868 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 925 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 123 wl-luk-pm2.21 37438 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 124 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 890 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 942 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 30420 pm2.27 42 wl-luk-pm2.27 37436 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 923 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 38364 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 924 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 972 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 973 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 971 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1088 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 907 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 908 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 945 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 56 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 882 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 883 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5 169 pm2.5g 168 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6 191 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 884 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 885 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 886 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 172 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 852 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 853 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 889 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 891 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 192 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 900 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 943 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 944 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 193 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 892 pm2.67 893 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 176 pm2.521g 174 pm2.521g2 175 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 899 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 975 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 901 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 203 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 976 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 977 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 934 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 932 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 974 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 978 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 84 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 933 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 109 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 994 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 469 pm3.2im 160 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 995 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 996 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 997 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 998 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 471 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 459 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 402 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 803 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 448 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 449 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 482 simplim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 484 simprim 166 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 765 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 766 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 808 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 622 |
| [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 963 pm3.44 962 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 809 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 473 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 966 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34b 316 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 261 |
| [WhiteheadRussell] p. 117 | Theorem *4.11 | notbi 319 |
| [WhiteheadRussell] p. 117 | Theorem *4.12 | con2bi 353 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotb 315 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14 807 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 833 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 222 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 806 bitr 805 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 563 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 905 pm4.25 906 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 460 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1010 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 871 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 468 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 922 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 633 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 918 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 637 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 979 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1089 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1008 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1054 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1025 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 999 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 1001 pm4.45 1000 pm4.45im 828 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 985 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 854 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 545 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 984 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 987 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 988 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 989 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 990 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 986 pm4.56 991 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 992 pm4.57 993 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 404 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 857 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 397 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 850 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 405 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 851 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67 398 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 557 pm4.71d 561 pm4.71i 559 pm4.71r 558 pm4.71rd 562 pm4.71ri 560 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 952 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 527 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 937 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 517 pm4.76 518 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 964 pm4.77 965 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 935 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1006 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 392 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81 393 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 1026 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1027 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 347 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 348 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 351 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 387 impexp 450 pm4.87 844 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 824 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 947 pm5.11g 946 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 948 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 950 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 949 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1015 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1016 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1014 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbn 383 pm5.18 381 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 386 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 825 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1017 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1050 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1051 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 902 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 572 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 388 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 361 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6 1004 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 956 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 831 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 573 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 836 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 826 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 834 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 389 pm5.41 390 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 543 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 542 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 1007 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1020 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 951 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1003 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1021 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1022 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1030 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 366 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 270 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 1031 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 44377 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 44378 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1870 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 44379 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 44380 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 44381 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1893 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 44382 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 44383 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 44384 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 44385 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 44386 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 44388 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 44389 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 44390 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 44387 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2090 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 44393 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 44394 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2070 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2160 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1829 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1830 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 44395 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 44396 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 44397 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 44398 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 44400 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 44399 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1887 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 44402 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 44403 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 44401 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1828 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 44404 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 44405 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1846 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 44406 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2348 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1860 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 44411 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 44407 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 44408 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 44409 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 44410 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 44415 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 44412 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 44413 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 44414 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 44416 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2569 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 44426 pm13.13b 44427 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 44428 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3022 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3023 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3666 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 44434 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 44435 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 44429 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 44572 pm13.193 44430 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 44431 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 44432 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 44433 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 44440 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 44439 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 44438 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3853 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 44441 pm14.122b 44442 pm14.122c 44443 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 44444 pm14.123b 44445 pm14.123c 44446 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 44448 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 44447 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 44449 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6542 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 44450 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6543 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 44451 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 44453 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2633 eupickbi 2636 sbaniota 44454 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 44452 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2584 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 44456 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30419 df-fv 6569 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 10041 pm54.43lem 10040 |
| [Young] p. 141 | Definition of operator ordering | leop2 32143 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32149 idleop 32150 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 42839 |
| [vandenDries] p. 43 | Theorem 62 | pellex 42846 pellexlem1 42840 |