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 17616 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17616 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18030 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17637 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 47770 prsthinc 47761 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 47791 df-mndtc 47791 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17660 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17732 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17720 invisoinvl 17741 |
| [Adamek] p. 28 | Example 3.13 | idinv 17740 idiso 17739 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17725 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17699 df-iso 17700 dfiso2 17723 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17706 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17757 |
| [Adamek] p. 29 | Definition 3.15 | cic 17750 df-cic 17747 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17812 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17721 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17722 isoco 17728 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17812 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17835 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17828 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 47727 prsthinc 47761 thincciso 47756 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 47791 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17842 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18065 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18123 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17860 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17859 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18123 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17884 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17890 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17889 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18108 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18108 |
| [Adamek] p. 39 | Definition 3.41 | funcoppc 17829 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18053 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17878 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17877 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18062 |
| [Adamek] p. 40 | Definition 3.47 | df-catc 18053 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17792 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17793 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17804 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17763 |
| [Adamek] p. 49 | Remark 4.4(2) | ressffth 17893 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 17898 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 17921 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 17925 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 17899 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 17927 |
| [Adamek] p. 101 | Definition 7.1 | df-inito 17938 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 47055 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 17939 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 17966 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 17970 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 17940 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 47058 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 17973 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17698 |
| [Adamek] p. 185 | Section 10.67 | updjud 9931 |
| [Adamek] p. 478 | Item Rng | df-ringc 46991 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 47321 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 47343 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14525 df-pfx 14625 df-substr 14595 df-word 14469 lencl 14487 wrd0 14493 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24445 df-nmoo 30265 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 31673 hmopidmchi 31671 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 31721 pjcmul2i 31722 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 31438 unoplin 31440 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 31439 unopadj2 31458 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 31533 lnopunii 31532 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 31606 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 27652 |
| [Alling] p. 184 | Axiom B | bdayfo 27416 |
| [Alling] p. 184 | Axiom O | sltso 27415 |
| [Alling] p. 184 | Axiom SD | nodense 27431 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27516 |
| [Alling] p. 185 | Theorem | conway 27537 |
| [Alling] p. 185 | Axiom FE | noeta 27482 |
| [Alling] p. 186 | Theorem 4 | slerec 27557 |
| [Alling], p. 2 | Definition | rp-brsslt 42476 |
| [Alling], p. 3 | Note | nla0001 42479 nla0002 42477 nla0003 42478 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11402 addcan2d 11422 addcan2i 11412 addcand 11421 addcani 11411 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11454 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11512 negsubd 11581 negsubi 11542 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11514 negnegd 11566 negnegi 11534 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11651 subdid 11674 subdii 11667 subdir 11652 subdird 11675 subdiri 11668 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11397 mul01d 11417 mul01i 11408 mul02 11396 mul02d 11416 mul02i 11407 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11855 mulcan2d 11852 mulcand 11851 mulcani 11857 |
| [Apostol] p. 18 | Theorem I.8 | receu 11863 xreceu 32355 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11892 divrecd 11997 divreci 11963 divreczi 11956 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11915 recreci 11950 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11858 mul0ord 11868 mul0ori 11866 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11657 mul2negd 11673 mul2negi 11666 mulneg1 11654 mulneg1d 11671 mulneg1i 11664 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11933 divadddivd 12038 divadddivi 11980 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11918 divmuldivd 12035 divmuldivi 11978 rdivmuldivd 20304 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11919 divdivdivd 12041 divdivdivi 11981 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 13000 rpaddcld 13035 rpmulcl 13001 rpmulcld 13036 |
| [Apostol] p. 20 | Axiom 8 | rpneg 13010 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 13013 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11344 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11811 ltadd1dd 11829 ltadd1i 11772 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12068 ltmul1a 12067 ltmul1i 12136 ltmul1ii 12146 ltmul2 12069 ltmul2d 13062 ltmul2dd 13076 ltmul2i 12139 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11738 msqgt0d 11785 msqgt0i 11755 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11740 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11724 lt0neg1d 11787 ltneg 11718 ltnegd 11796 ltnegi 11762 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11703 lt2addd 11841 lt2addi 11780 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 12979 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12064 recgt0d 12152 recgt0i 12123 recgt0ii 12124 |
| [Apostol] p. 22 | Definition of integers | df-z 12563 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12230 |
| [Apostol] p. 22 | Definition of rationals | df-q 12937 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9451 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12472 |
| [Apostol] p. 26 | Theorem I.29 | arch 12473 archd 44157 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12669 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12474 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12935 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12934 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13182 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16286 zneo 12649 zneoALTV 46635 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26474 msqsqrtd 15391 resqrtth 15206 sqrtth 15315 sqrtthi 15321 sqsqrtd 15390 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12219 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12901 |
| [Apostol] p. 361 | Remark | crreczi 14195 |
| [Apostol] p. 363 | Remark | absgt0i 15350 |
| [Apostol] p. 363 | Example | abssubd 15404 abssubi 15354 |
| [ApostolNT] p. 7 | Remark | fmtno0 46506 fmtno1 46507 fmtno2 46516 fmtno3 46517 fmtno4 46518 fmtno5fac 46548 fmtnofz04prm 46543 |
| [ApostolNT] p. 7 | Definition | df-fmtno 46494 |
| [ApostolNT] p. 8 | Definition | df-ppi 26840 |
| [ApostolNT] p. 14 | Definition | df-dvds 16202 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16217 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16241 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16236 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16230 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16232 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16218 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16219 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16224 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16258 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16260 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16262 |
| [ApostolNT] p. 15 | Definition | df-gcd 16440 dfgcd2 16492 |
| [ApostolNT] p. 16 | Definition | isprm2 16623 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16594 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16852 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16458 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16493 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16495 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16473 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16465 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16652 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16654 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16865 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16859 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16350 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16528 |
| [ApostolNT] p. 24 | Definition | df-mu 26841 |
| [ApostolNT] p. 25 | Definition | df-phi 16703 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 26931 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16727 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16713 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16717 |
| [ApostolNT] p. 32 | Definition | df-vma 26838 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 26933 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 26955 |
| [ApostolNT] p. 38 | Remark | df-sgm 26842 |
| [ApostolNT] p. 38 | Definition | df-sgm 26842 |
| [ApostolNT] p. 75 | Definition | df-chp 26839 df-cht 26837 |
| [ApostolNT] p. 104 | Definition | congr 16605 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16205 |
| [ApostolNT] p. 106 | Definition | moddvds 16212 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16293 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16294 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13857 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13894 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14205 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16235 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16608 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17011 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16610 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16720 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16738 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16721 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 26812 |
| [ApostolNT] p. 179 | Definition | df-lgs 27034 lgsprme0 27078 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27079 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27055 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27070 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27127 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27146 2lgsoddprm 27155 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27113 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27122 |
| [ApostolNT] p. 188 | Definition | df-lgs 27034 lgs1 27080 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27071 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27073 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27081 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27082 |
| [Baer] p. 40 | Property (b) | mapdord 40812 |
| [Baer] p. 40 | Property (c) | mapd11 40813 |
| [Baer] p. 40 | Property (e) | mapdin 40836 mapdlsm 40838 |
| [Baer] p. 40 | Property (f) | mapd0 40839 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 40799 mapd1o 40822 |
| [Baer] p. 41 | Property (g) | mapdat 40841 |
| [Baer] p. 44 | Part (1) | mapdpg 40880 |
| [Baer] p. 45 | Part (2) | hdmap1eq 40975 mapdheq 40902 mapdheq2 40903 mapdheq2biN 40904 |
| [Baer] p. 45 | Part (3) | baerlem3 40887 |
| [Baer] p. 46 | Part (4) | mapdheq4 40906 mapdheq4lem 40905 |
| [Baer] p. 46 | Part (5) | baerlem5a 40888 baerlem5abmN 40892 baerlem5amN 40890 baerlem5b 40889 baerlem5bmN 40891 |
| [Baer] p. 47 | Part (6) | hdmap1l6 40995 hdmap1l6a 40983 hdmap1l6e 40988 hdmap1l6f 40989 hdmap1l6g 40990 hdmap1l6lem1 40981 hdmap1l6lem2 40982 mapdh6N 40921 mapdh6aN 40909 mapdh6eN 40914 mapdh6fN 40915 mapdh6gN 40916 mapdh6lem1N 40907 mapdh6lem2N 40908 |
| [Baer] p. 48 | Part 9 | hdmapval 41002 |
| [Baer] p. 48 | Part 10 | hdmap10 41014 |
| [Baer] p. 48 | Part 11 | hdmapadd 41017 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 40991 mapdh6hN 40917 |
| [Baer] p. 48 | Part (7) | mapdh75cN 40927 mapdh75d 40928 mapdh75e 40926 mapdh75fN 40929 mapdh7cN 40923 mapdh7dN 40924 mapdh7eN 40922 mapdh7fN 40925 |
| [Baer] p. 48 | Part (8) | mapdh8 40962 mapdh8a 40949 mapdh8aa 40950 mapdh8ab 40951 mapdh8ac 40952 mapdh8ad 40953 mapdh8b 40954 mapdh8c 40955 mapdh8d 40957 mapdh8d0N 40956 mapdh8e 40958 mapdh8g 40959 mapdh8i 40960 mapdh8j 40961 |
| [Baer] p. 48 | Part (9) | mapdh9a 40963 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 40943 |
| [Baer] p. 49 | Part 12 | hdmap11 41022 hdmapeq0 41018 hdmapf1oN 41039 hdmapneg 41020 hdmaprnN 41038 hdmaprnlem1N 41023 hdmaprnlem3N 41024 hdmaprnlem3uN 41025 hdmaprnlem4N 41027 hdmaprnlem6N 41028 hdmaprnlem7N 41029 hdmaprnlem8N 41030 hdmaprnlem9N 41031 hdmapsub 41021 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 41042 hdmap14lem10 41051 hdmap14lem1a 41040 hdmap14lem2N 41043 hdmap14lem2a 41041 hdmap14lem3 41044 hdmap14lem8 41049 hdmap14lem9 41050 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 41052 hdmap14lem12 41053 hdmap14lem13 41054 hdmap14lem14 41055 hdmap14lem15 41056 hgmapval 41061 |
| [Baer] p. 50 | Part 15 | hgmapadd 41068 hgmapmul 41069 hgmaprnlem2N 41071 hgmapvs 41065 |
| [Baer] p. 50 | Part 16 | hgmaprnN 41075 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 41091 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 41092 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 41093 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 41094 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 41096 hgmapvv 41100 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 41095 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 41097 |
| [Baer] p. 111 | Line 15 | hdmapg 41104 hdmapglem7 41103 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26475 2irrexpqALT 26541 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 23 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2561 |
| [BellMachover] p. 460 | Notation | df-mo 2532 |
| [BellMachover] p. 460 | Definition | mo3 2556 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2701 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2705 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5290 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5298 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 36248 bm1.3ii 5301 |
| [BellMachover] p. 466 | Problem | axpow2 5364 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5365 |
| [BellMachover] p. 466 | Axiom Union | axun2 7729 |
| [BellMachover] p. 468 | Definition | df-ord 6366 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6381 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6388 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6383 |
| [BellMachover] p. 471 | Definition of N | df-om 7858 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7791 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6368 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9639 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7873 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9761 |
| [BellMachover] p. 478 | Definition | rankval2 9815 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9779 r1ord3g 9776 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9592 |
| [BellMachover] p. 488 | Axiom AC | ac5 10474 dfac4 10119 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10107 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 38492 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 31873 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 31915 chirredi 31914 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 31903 |
| [Beran] p. 3 | Definition of join | sshjval3 30874 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 31136 cmcm2i 31113 cmcm2ii 31118 cmt2N 38423 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 31137 lecmi 31122 lecmii 31123 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 31111 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 31140 cm2ji 31145 cm2mi 31146 |
| [Beran] p. 95 | Definition | df-sh 30727 issh2 30729 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 30606 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 30619 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 30610 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 31348 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 31350 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 31349 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 31351 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 30602 his1i 30620 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 30603 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 30604 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 30605 |
| [Beran] p. 96 | Definition of norm | df-hnorm 30488 dfhnorm2 30642 normval 30644 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 30704 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 30493 |
| [Beran] p. 96 | Definition of complete subspace | isch3 30761 |
| [Beran] p. 96 | Definition of converge | df-hlim 30492 hlimi 30708 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 30653 norm-i 30649 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 30657 norm-ii 30658 normlem0 30629 normlem1 30630 normlem2 30631 normlem3 30632 normlem4 30633 normlem5 30634 normlem6 30635 normlem7 30636 normlem7tALT 30639 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 30659 norm-iii 30660 |
| [Beran] p. 98 | Remark 3.4 | bcs 30701 bcsiALT 30699 bcsiHIL 30700 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 30641 normpar 30675 normpari 30674 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 30666 normpyth 30665 normpythi 30662 |
| [Beran] p. 99 | Remark | lnfn0 31567 lnfn0i 31562 lnop0 31486 lnop0i 31490 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 31546 nmcfnex 31573 nmcfnexi 31571 nmcopex 31549 nmcopexi 31547 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 31574 nmcfnlbi 31572 nmcoplb 31550 nmcoplbi 31548 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 31576 lnfnconi 31575 lnopcon 31555 lnopconi 31554 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 30676 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 30673 norm3adifii 30668 norm3dif 30670 norm3difi 30667 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 30821 pjhth 30913 pjhtheu 30914 pjpjhth 30945 pjpjhthi 30946 pjth 25187 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 30926 ococi 30925 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 31581 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 31582 riesz4 31584 riesz4i 31583 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 31599 cnlnadjeu 31598 cnlnadjeui 31597 cnlnadji 31596 cnlnadjlem1 31587 nmopadjlei 31608 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 31611 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 31610 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 31612 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 31456 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 31622 nmopcoadji 31621 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 31613 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 31623 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 31620 pjadj2coi 31724 pjadjcoi 31681 |
| [Beran] p. 107 | Definition | df-ch 30741 isch2 30743 |
| [Beran] p. 107 | Remark 3.12 | choccl 30826 isch3 30761 occl 30824 ocsh 30803 shoccl 30825 shocsh 30804 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 30928 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 30852 |
| [Beran] p. 109 | Property (i) | pjadj2 31707 pjadj3 31708 pjadji 31205 pjadjii 31194 |
| [Beran] p. 109 | Property (ii) | pjidmco 31701 pjidmcoi 31697 pjidmi 31193 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 31693 |
| [Beran] p. 111 | Remark | ho0val 31270 pjch1 31190 |
| [Beran] p. 111 | Definition | df-hfmul 31254 df-hfsum 31253 df-hodif 31252 df-homul 31251 df-hosum 31250 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 31191 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 31214 pjchi 30952 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 30959 pjoc2i 30958 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 31200 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 31685 pjssmii 31201 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 31684 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 31683 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 31688 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 31686 pjssge0ii 31202 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 31687 pjdifnormii 31203 |
| [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 33589 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 33597 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 33595 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 33599 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 33619 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 33650 df-sitm 33628 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 33650 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 33627 |
| [Bollobas] p. 1 | Section I.1 | df-edg 28575 isuhgrop 28597 isusgrop 28689 isuspgrop 28688 |
| [Bollobas] p. 2 | Section I.1 | df-subgr 28792 uhgrspan1 28827 uhgrspansubgr 28815 |
| [Bollobas] p. 3 | Definition | isomuspgr 46800 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 28978 df-cusgr 28936 df-nbgr 28857 fusgrmaxsize 28988 |
| [Bollobas] p. 4 | Definition | df-upwlks 46810 df-wlks 29123 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 29074 finsumvtxdgeven 29076 fusgr1th 29075 fusgrvtxdgonume 29078 vtxdgoddnumeven 29077 |
| [Bollobas] p. 5 | Notation | df-pths 29240 |
| [Bollobas] p. 5 | Definition | df-crcts 29310 df-cycls 29311 df-trls 29216 df-wlkson 29124 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 28586 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 46876 df-cllaw 46862 df-mgm 18565 df-mgm2 46895 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 46877 df-asslaw 46864 df-sgrp 18644 df-sgrp2 46897 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 46896 df-comlaw 46863 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18660 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20129 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20047 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7287 fcofo 7288 |
| [BourbakiTop1] p. | Remark | xnegmnf 13193 xnegpnf 13192 |
| [BourbakiTop1] p. | Remark | rexneg 13194 |
| [BourbakiTop1] p. | Remark 3 | ust0 23944 ustfilxp 23937 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 23814 |
| [BourbakiTop1] p. | Criterion | ishmeo 23483 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24009 iducn 24008 snfil 23588 |
| [BourbakiTop1] p. | Example 2 | neifil 23604 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 23791 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24029 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 33235 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23587 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24001 df-ust 23925 filintn0 23585 filn0 23586 istgp 23801 ucnprima 24007 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24012 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24023 df-usp 23982 df-utop 23956 trust 23954 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 33134 |
| [BourbakiTop1] p. | Property V_i | ssnei2 22840 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 22993 |
| [BourbakiTop1] p. | Condition F_I | ustssel 23930 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 23933 |
| [BourbakiTop1] p. | Property V_ii | innei 22849 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 22857 neissex 22851 |
| [BourbakiTop1] p. | Proposition 1 | neips 22837 neiss 22833 ucncn 24010 ustund 23946 ustuqtop 23971 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 22991 neiptopreu 22857 utop2nei 23975 utop3cls 23976 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24017 uspreg 23999 utopreg 23977 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23415 imasncls 23416 imasnopn 23414 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 23724 |
| [BourbakiTop1] p. | Condition F_II | ustincl 23932 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 23934 |
| [BourbakiTop1] p. | Property V_iii | elnei 22835 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24028 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 23931 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 23935 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23111 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23570 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 22616 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 33131 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 45076 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 45078 stoweid 45077 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 45015 stoweidlem10 45024 stoweidlem14 45028 stoweidlem15 45029 stoweidlem35 45049 stoweidlem36 45050 stoweidlem37 45051 stoweidlem38 45052 stoweidlem40 45054 stoweidlem41 45055 stoweidlem43 45057 stoweidlem44 45058 stoweidlem46 45060 stoweidlem5 45019 stoweidlem50 45064 stoweidlem52 45066 stoweidlem53 45067 stoweidlem55 45069 stoweidlem56 45070 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 45037 stoweidlem24 45038 stoweidlem27 45041 stoweidlem28 45042 stoweidlem30 45044 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 45048 stoweidlem59 45073 stoweidlem60 45074 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 45059 stoweidlem49 45063 stoweidlem7 45021 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 45045 stoweidlem39 45053 stoweidlem42 45056 stoweidlem48 45062 stoweidlem51 45065 stoweidlem54 45068 stoweidlem57 45071 stoweidlem58 45072 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 45039 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 45031 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 45025 stoweidlem13 45027 stoweidlem26 45040 stoweidlem61 45075 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 45032 |
| [Bruck] p. 1 | Section I.1 | df-clintop 46876 df-mgm 18565 df-mgm2 46895 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18644 df-sgrp2 46897 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 18958 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5231 |
| [Church] p. 129 | Section II.24 | df-ifp 1060 dfifp2 1061 |
| [Clemente] p. 10 | Definition IT | natded 29923 |
| [Clemente] p. 10 | Definition I` `m,n | natded 29923 |
| [Clemente] p. 11 | Definition E=>m,n | natded 29923 |
| [Clemente] p. 11 | Definition I=>m,n | natded 29923 |
| [Clemente] p. 11 | Definition E` `(1) | natded 29923 |
| [Clemente] p. 11 | Definition E` `(2) | natded 29923 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 29923 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 29923 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 29923 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 29923 |
| [Clemente] p. 14 | Proof 5.11 | natded 29923 |
| [Clemente] p. 14 | Definition E` `n | natded 29923 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 29925 ex-natded5.2 29924 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 29928 ex-natded5.3 29927 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 29930 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 29932 ex-natded5.7 29931 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 29934 ex-natded5.8 29933 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 29936 ex-natded5.13 29935 |
| [Clemente] p. 32 | Definition I` `n | natded 29923 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 29923 |
| [Clemente] p. 32 | Definition E` `n,t | natded 29923 |
| [Clemente] p. 32 | Definition I` `n,t | natded 29923 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 29937 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 29938 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 29940 ex-natded9.26 29939 |
| [Cohen] p. 301 | Remark | relogoprlem 26335 |
| [Cohen] p. 301 | Property 2 | relogmul 26336 relogmuld 26369 |
| [Cohen] p. 301 | Property 3 | relogdiv 26337 relogdivd 26370 |
| [Cohen] p. 301 | Property 4 | relogexp 26340 |
| [Cohen] p. 301 | Property 1a | log1 26330 |
| [Cohen] p. 301 | Property 1b | loge 26331 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26528 |
| [Cohen4] p. 349 | Property | relogbf 26532 |
| [Cohen4] p. 352 | Definition | elogb 26511 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26518 |
| [Cohen4] p. 361 | Property 3 | logbrec 26523 relogbdiv 26520 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26516 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26521 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26509 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26510 |
| [Cohen4] p. 367 | Property | logbchbase 26512 |
| [Cohen4] p. 377 | Property 2 | logblt 26525 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 33582 sxbrsigalem4 33584 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18514 acsinfd 18513 acsinfdimd 18515 acsmap2d 18512 acsmapd 18511 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 33587 |
| [Connell] p. 57 | Definition | df-scmat 22213 df-scmatalt 47167 |
| [Conway] p. 4 | Definition | slerec 27557 |
| [Conway] p. 5 | Definition | addsval 27684 addsval2 27685 df-adds 27682 df-muls 27802 df-negs 27735 |
| [Conway] p. 7 | Theorem | 0slt1s 27567 |
| [Conway] p. 16 | Theorem 0(i) | ssltright 27603 |
| [Conway] p. 16 | Theorem 0(ii) | ssltleft 27602 |
| [Conway] p. 16 | Theorem 0(iii) | slerflex 27502 |
| [Conway] p. 17 | Theorem 3 | addsass 27727 addsassd 27728 addscom 27688 addscomd 27689 addsrid 27686 addsridd 27687 |
| [Conway] p. 17 | Definition | df-0s 27562 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 27757 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 27754 negsidd 27755 |
| [Conway] p. 18 | Theorem 5 | sleadd1 27711 sleadd1d 27717 |
| [Conway] p. 18 | Definition | df-1s 27563 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 27749 negscld 27750 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 27702 |
| [Conway] p. 19 | Theorem 7 | addsdi 27849 addsdid 27850 addsdird 27851 mulnegs1d 27854 mulnegs2d 27855 mulsass 27860 mulsassd 27861 mulscom 27834 mulscomd 27835 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 27829 mulscld 27830 |
| [Conway] p. 19 | Theorem 8(iii) | slemuld 27833 sltmul 27831 sltmuld 27832 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 27839 mulsgt0d 27840 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 27903 |
| [Conway] p. 27 | Definition | df-ons 27918 elons2 27924 |
| [Conway] p. 27 | Theorem 14 | sltonex 27927 |
| [Conway] p. 29 | Remark | madebday 27631 newbday 27633 oldbday 27632 |
| [Conway] p. 29 | Definition | df-made 27579 df-new 27581 df-old 27580 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13830 |
| [Crawley] p. 1 | Definition of poset | df-poset 18270 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 38560 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 39364 dalaw 39060 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 41139 |
| [Crawley] p. 111 | Definition of set W | df-watsN 39164 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 39280 df-ldil 39278 isldil 39284 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 39279 df-trnN 39281 isltrn 39293 ltrnu 39295 |
| [Crawley] p. 112 | Lemma A | cdlema1N 38965 cdlema2N 38966 exatleN 38578 |
| [Crawley] p. 112 | Lemma B | 1cvrat 38650 cdlemb 38968 cdlemb2 39215 cdlemb3 39780 idltrn 39324 l1cvat 38228 lhpat 39217 lhpat2 39219 lshpat 38229 ltrnel 39313 ltrnmw 39325 |
| [Crawley] p. 112 | Lemma C | cdlemc1 39365 cdlemc2 39366 ltrnnidn 39348 trlat 39343 trljat1 39340 trljat2 39341 trljat3 39342 trlne 39359 trlnidat 39347 trlnle 39360 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 39165 |
| [Crawley] p. 113 | Lemma C | cdlemc 39371 cdlemc3 39367 cdlemc4 39368 |
| [Crawley] p. 113 | Lemma D | cdlemd 39381 cdlemd1 39372 cdlemd2 39373 cdlemd3 39374 cdlemd4 39375 cdlemd5 39376 cdlemd6 39377 cdlemd7 39378 cdlemd8 39379 cdlemd9 39380 cdleme31sde 39559 cdleme31se 39556 cdleme31se2 39557 cdleme31snd 39560 cdleme32a 39615 cdleme32b 39616 cdleme32c 39617 cdleme32d 39618 cdleme32e 39619 cdleme32f 39620 cdleme32fva 39611 cdleme32fva1 39612 cdleme32fvcl 39614 cdleme32le 39621 cdleme48fv 39673 cdleme4gfv 39681 cdleme50eq 39715 cdleme50f 39716 cdleme50f1 39717 cdleme50f1o 39720 cdleme50laut 39721 cdleme50ldil 39722 cdleme50lebi 39714 cdleme50rn 39719 cdleme50rnlem 39718 cdlemeg49le 39685 cdlemeg49lebilem 39713 |
| [Crawley] p. 113 | Lemma E | cdleme 39734 cdleme00a 39383 cdleme01N 39395 cdleme02N 39396 cdleme0a 39385 cdleme0aa 39384 cdleme0b 39386 cdleme0c 39387 cdleme0cp 39388 cdleme0cq 39389 cdleme0dN 39390 cdleme0e 39391 cdleme0ex1N 39397 cdleme0ex2N 39398 cdleme0fN 39392 cdleme0gN 39393 cdleme0moN 39399 cdleme1 39401 cdleme10 39428 cdleme10tN 39432 cdleme11 39444 cdleme11a 39434 cdleme11c 39435 cdleme11dN 39436 cdleme11e 39437 cdleme11fN 39438 cdleme11g 39439 cdleme11h 39440 cdleme11j 39441 cdleme11k 39442 cdleme11l 39443 cdleme12 39445 cdleme13 39446 cdleme14 39447 cdleme15 39452 cdleme15a 39448 cdleme15b 39449 cdleme15c 39450 cdleme15d 39451 cdleme16 39459 cdleme16aN 39433 cdleme16b 39453 cdleme16c 39454 cdleme16d 39455 cdleme16e 39456 cdleme16f 39457 cdleme16g 39458 cdleme19a 39477 cdleme19b 39478 cdleme19c 39479 cdleme19d 39480 cdleme19e 39481 cdleme19f 39482 cdleme1b 39400 cdleme2 39402 cdleme20aN 39483 cdleme20bN 39484 cdleme20c 39485 cdleme20d 39486 cdleme20e 39487 cdleme20f 39488 cdleme20g 39489 cdleme20h 39490 cdleme20i 39491 cdleme20j 39492 cdleme20k 39493 cdleme20l 39496 cdleme20l1 39494 cdleme20l2 39495 cdleme20m 39497 cdleme20y 39476 cdleme20zN 39475 cdleme21 39511 cdleme21d 39504 cdleme21e 39505 cdleme22a 39514 cdleme22aa 39513 cdleme22b 39515 cdleme22cN 39516 cdleme22d 39517 cdleme22e 39518 cdleme22eALTN 39519 cdleme22f 39520 cdleme22f2 39521 cdleme22g 39522 cdleme23a 39523 cdleme23b 39524 cdleme23c 39525 cdleme26e 39533 cdleme26eALTN 39535 cdleme26ee 39534 cdleme26f 39537 cdleme26f2 39539 cdleme26f2ALTN 39538 cdleme26fALTN 39536 cdleme27N 39543 cdleme27a 39541 cdleme27cl 39540 cdleme28c 39546 cdleme3 39411 cdleme30a 39552 cdleme31fv 39564 cdleme31fv1 39565 cdleme31fv1s 39566 cdleme31fv2 39567 cdleme31id 39568 cdleme31sc 39558 cdleme31sdnN 39561 cdleme31sn 39554 cdleme31sn1 39555 cdleme31sn1c 39562 cdleme31sn2 39563 cdleme31so 39553 cdleme35a 39622 cdleme35b 39624 cdleme35c 39625 cdleme35d 39626 cdleme35e 39627 cdleme35f 39628 cdleme35fnpq 39623 cdleme35g 39629 cdleme35h 39630 cdleme35h2 39631 cdleme35sn2aw 39632 cdleme35sn3a 39633 cdleme36a 39634 cdleme36m 39635 cdleme37m 39636 cdleme38m 39637 cdleme38n 39638 cdleme39a 39639 cdleme39n 39640 cdleme3b 39403 cdleme3c 39404 cdleme3d 39405 cdleme3e 39406 cdleme3fN 39407 cdleme3fa 39410 cdleme3g 39408 cdleme3h 39409 cdleme4 39412 cdleme40m 39641 cdleme40n 39642 cdleme40v 39643 cdleme40w 39644 cdleme41fva11 39651 cdleme41sn3aw 39648 cdleme41sn4aw 39649 cdleme41snaw 39650 cdleme42a 39645 cdleme42b 39652 cdleme42c 39646 cdleme42d 39647 cdleme42e 39653 cdleme42f 39654 cdleme42g 39655 cdleme42h 39656 cdleme42i 39657 cdleme42k 39658 cdleme42ke 39659 cdleme42keg 39660 cdleme42mN 39661 cdleme42mgN 39662 cdleme43aN 39663 cdleme43bN 39664 cdleme43cN 39665 cdleme43dN 39666 cdleme5 39414 cdleme50ex 39733 cdleme50ltrn 39731 cdleme51finvN 39730 cdleme51finvfvN 39729 cdleme51finvtrN 39732 cdleme6 39415 cdleme7 39423 cdleme7a 39417 cdleme7aa 39416 cdleme7b 39418 cdleme7c 39419 cdleme7d 39420 cdleme7e 39421 cdleme7ga 39422 cdleme8 39424 cdleme8tN 39429 cdleme9 39427 cdleme9a 39425 cdleme9b 39426 cdleme9tN 39431 cdleme9taN 39430 cdlemeda 39472 cdlemedb 39471 cdlemednpq 39473 cdlemednuN 39474 cdlemefr27cl 39577 cdlemefr32fva1 39584 cdlemefr32fvaN 39583 cdlemefrs32fva 39574 cdlemefrs32fva1 39575 cdlemefs27cl 39587 cdlemefs32fva1 39597 cdlemefs32fvaN 39596 cdlemesner 39470 cdlemeulpq 39394 |
| [Crawley] p. 114 | Lemma E | 4atex 39250 4atexlem7 39249 cdleme0nex 39464 cdleme17a 39460 cdleme17c 39462 cdleme17d 39672 cdleme17d1 39463 cdleme17d2 39669 cdleme18a 39465 cdleme18b 39466 cdleme18c 39467 cdleme18d 39469 cdleme4a 39413 |
| [Crawley] p. 115 | Lemma E | cdleme21a 39499 cdleme21at 39502 cdleme21b 39500 cdleme21c 39501 cdleme21ct 39503 cdleme21f 39506 cdleme21g 39507 cdleme21h 39508 cdleme21i 39509 cdleme22gb 39468 |
| [Crawley] p. 116 | Lemma F | cdlemf 39737 cdlemf1 39735 cdlemf2 39736 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 39741 cdlemg16 39831 cdlemg28 39878 cdlemg28a 39867 cdlemg28b 39877 cdlemg3a 39771 cdlemg42 39903 cdlemg43 39904 cdlemg44 39907 cdlemg44a 39905 cdlemg46 39909 cdlemg47 39910 cdlemg9 39808 ltrnco 39893 ltrncom 39912 tgrpabl 39925 trlco 39901 |
| [Crawley] p. 116 | Definition of G | df-tgrp 39917 |
| [Crawley] p. 117 | Lemma G | cdlemg17 39851 cdlemg17b 39836 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 39930 df-edring 39931 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 39934 |
| [Crawley] p. 118 | Remark | tendopltp 39954 |
| [Crawley] p. 118 | Lemma H | cdlemh 39991 cdlemh1 39989 cdlemh2 39990 |
| [Crawley] p. 118 | Lemma I | cdlemi 39994 cdlemi1 39992 cdlemi2 39993 |
| [Crawley] p. 118 | Lemma J | cdlemj1 39995 cdlemj2 39996 cdlemj3 39997 tendocan 39998 |
| [Crawley] p. 118 | Lemma K | cdlemk 40148 cdlemk1 40005 cdlemk10 40017 cdlemk11 40023 cdlemk11t 40120 cdlemk11ta 40103 cdlemk11tb 40105 cdlemk11tc 40119 cdlemk11u-2N 40063 cdlemk11u 40045 cdlemk12 40024 cdlemk12u-2N 40064 cdlemk12u 40046 cdlemk13-2N 40050 cdlemk13 40026 cdlemk14-2N 40052 cdlemk14 40028 cdlemk15-2N 40053 cdlemk15 40029 cdlemk16-2N 40054 cdlemk16 40031 cdlemk16a 40030 cdlemk17-2N 40055 cdlemk17 40032 cdlemk18-2N 40060 cdlemk18-3N 40074 cdlemk18 40042 cdlemk19-2N 40061 cdlemk19 40043 cdlemk19u 40144 cdlemk1u 40033 cdlemk2 40006 cdlemk20-2N 40066 cdlemk20 40048 cdlemk21-2N 40065 cdlemk21N 40047 cdlemk22-3 40075 cdlemk22 40067 cdlemk23-3 40076 cdlemk24-3 40077 cdlemk25-3 40078 cdlemk26-3 40080 cdlemk26b-3 40079 cdlemk27-3 40081 cdlemk28-3 40082 cdlemk29-3 40085 cdlemk3 40007 cdlemk30 40068 cdlemk31 40070 cdlemk32 40071 cdlemk33N 40083 cdlemk34 40084 cdlemk35 40086 cdlemk36 40087 cdlemk37 40088 cdlemk38 40089 cdlemk39 40090 cdlemk39u 40142 cdlemk4 40008 cdlemk41 40094 cdlemk42 40115 cdlemk42yN 40118 cdlemk43N 40137 cdlemk45 40121 cdlemk46 40122 cdlemk47 40123 cdlemk48 40124 cdlemk49 40125 cdlemk5 40010 cdlemk50 40126 cdlemk51 40127 cdlemk52 40128 cdlemk53 40131 cdlemk54 40132 cdlemk55 40135 cdlemk55u 40140 cdlemk56 40145 cdlemk5a 40009 cdlemk5auN 40034 cdlemk5u 40035 cdlemk6 40011 cdlemk6u 40036 cdlemk7 40022 cdlemk7u-2N 40062 cdlemk7u 40044 cdlemk8 40012 cdlemk9 40013 cdlemk9bN 40014 cdlemki 40015 cdlemkid 40110 cdlemkj-2N 40056 cdlemkj 40037 cdlemksat 40020 cdlemksel 40019 cdlemksv 40018 cdlemksv2 40021 cdlemkuat 40040 cdlemkuel-2N 40058 cdlemkuel-3 40072 cdlemkuel 40039 cdlemkuv-2N 40057 cdlemkuv2-2 40059 cdlemkuv2-3N 40073 cdlemkuv2 40041 cdlemkuvN 40038 cdlemkvcl 40016 cdlemky 40100 cdlemkyyN 40136 tendoex 40149 |
| [Crawley] p. 120 | Remark | dva1dim 40159 |
| [Crawley] p. 120 | Lemma L | cdleml1N 40150 cdleml2N 40151 cdleml3N 40152 cdleml4N 40153 cdleml5N 40154 cdleml6 40155 cdleml7 40156 cdleml8 40157 cdleml9 40158 dia1dim 40235 |
| [Crawley] p. 120 | Lemma M | dia11N 40222 diaf11N 40223 dialss 40220 diaord 40221 dibf11N 40335 djajN 40311 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 40206 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 40292 dia2dimlem1 40238 dia2dimlem2 40239 dia2dimlem3 40240 dia2dimlem4 40241 dia2dimlem5 40242 diaf1oN 40304 diarnN 40303 dvheveccl 40286 dvhopN 40290 |
| [Crawley] p. 121 | Lemma N | cdlemn 40386 cdlemn10 40380 cdlemn11 40385 cdlemn11a 40381 cdlemn11b 40382 cdlemn11c 40383 cdlemn11pre 40384 cdlemn2 40369 cdlemn2a 40370 cdlemn3 40371 cdlemn4 40372 cdlemn4a 40373 cdlemn5 40375 cdlemn5pre 40374 cdlemn6 40376 cdlemn7 40377 cdlemn8 40378 cdlemn9 40379 diclspsn 40368 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 40347 |
| [Crawley] p. 122 | Lemma N | dih11 40439 dihf11 40441 dihjust 40391 dihjustlem 40390 dihord 40438 dihord1 40392 dihord10 40397 dihord11b 40396 dihord11c 40398 dihord2 40401 dihord2a 40393 dihord2b 40394 dihord2cN 40395 dihord2pre 40399 dihord2pre2 40400 dihordlem6 40387 dihordlem7 40388 dihordlem7b 40389 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 40404 dihfval 40405 dihval 40406 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 28936 df-nbgr 28857 |
| [Diestel] p. 4 | Section 1.1 | df-subgr 28792 uhgrspan1 28827 uhgrspansubgr 28815 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 29078 vtxdgoddnumeven 29077 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 28586 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 33142 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 33154 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 33146 zarcls1 33147 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 33157 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 33160 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 33163 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3950 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9644 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8824 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9652 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9977 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10552 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5304 |
| [Enderton] p. 19 | Definition | df-tp 4632 |
| [Enderton] p. 26 | Exercise 5 | unissb 4942 |
| [Enderton] p. 26 | Exercise 10 | pwel 5378 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5571 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5081 iinin2 5080 iinun2 5075 iunin1 5074 iunin1f 32056 iunin2 5073 uniin1 32050 uniin2 32051 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5079 iundif2 5076 |
| [Enderton] p. 32 | Exercise 20 | unineq 4276 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5100 |
| [Enderton] p. 33 | Exercise 25 | iununi 5101 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5108 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7760 iunpwss 5109 |
| [Enderton] p. 36 | Definition | opthwiener 5513 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5449 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4948 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5469 rnex 7905 rnexg 7897 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5913 rnuni 6147 |
| [Enderton] p. 42 | Definition of a function | dffun7 6574 dffun8 6575 |
| [Enderton] p. 43 | Definition of function value | funfv2 6978 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6616 |
| [Enderton] p. 44 | Definition (d) | dfima2 6060 dfima3 6061 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6987 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10470 ac7g 10471 df-ac 10113 dfac2 10128 dfac2a 10126 dfac2b 10127 dfac3 10118 dfac7 10129 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7247 |
| [Enderton] p. 52 | Definition | df-map 8824 |
| [Enderton] p. 53 | Exercise 21 | coass 6263 |
| [Enderton] p. 53 | Exercise 27 | dmco 6252 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6623 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6100 |
| [Enderton] p. 54 | Remark | ixpf 8916 ixpssmap 8928 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8894 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10480 ac9s 10490 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 37783 erref 8725 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 37786 erthi 8756 |
| [Enderton] p. 57 | Definition | df-ec 8707 |
| [Enderton] p. 58 | Definition | df-qs 8711 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8707 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5909 |
| [Enderton] p. 68 | Definition of successor | df-suc 6369 |
| [Enderton] p. 71 | Definition | df-tr 5265 dftr4 5271 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6442 unisucg 6441 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6442 unisucg 6441 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5280 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5282 trintALT 43944 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8606 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8608 onasuc 8530 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7414 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8607 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8609 onmsuc 8531 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8624 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8611 nnacom 8619 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8625 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8626 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8628 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8612 nnmsucr 8627 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8640 |
| [Enderton] p. 129 | Definition | df-en 8942 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7364 |
| [Enderton] p. 133 | Exercise 1 | xpomen 10012 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16160 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9212 |
| [Enderton] p. 135 | Corollary 6C | php3 9214 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9211 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9258 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9260 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9170 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9175 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9143 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10176 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10177 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10172 dju1en 10168 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9342 unifi 9343 unifi2 9344 |
| [Enderton] p. 144 | Corollary 6K | undif2 4475 unfi 9174 unfi2 9317 |
| [Enderton] p. 145 | Figure 38 | ffoss 7934 |
| [Enderton] p. 145 | Definition | df-dom 8943 |
| [Enderton] p. 146 | Example 1 | domen 8959 domeng 8960 |
| [Enderton] p. 146 | Example 3 | nndomo 9235 nnsdom 9651 nnsdomg 9304 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10180 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9144 xpdom1 9073 xpdom1g 9071 xpdom2g 9070 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9150 |
| [Enderton] p. 151 | Theorem 6M | zorn 10504 zorng 10501 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10489 dfac5 10125 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10572 |
| [Enderton] p. 164 | Example | infdif 10206 |
| [Enderton] p. 168 | Definition | df-po 5587 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6477 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6409 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6476 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6417 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7829 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7770 |
| [Enderton] p. 194 | Remark | onprc 7767 |
| [Enderton] p. 194 | Exercise 16 | suc11 6470 |
| [Enderton] p. 197 | Definition | df-card 9936 |
| [Enderton] p. 197 | Theorem 7P | carden 10548 |
| [Enderton] p. 200 | Exercise 25 | tfis 7846 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9773 |
| [Enderton] p. 202 | Definition | df-r1 9761 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9783 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9864 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9603 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9854 rankprb 9848 rankpw 9840 rankpwi 9820 rankuniss 9863 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9615 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9616 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10107 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 10073 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10087 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8343 |
| [Enderton] p. 222 | Definition of kard | karden 9892 kardex 9891 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8599 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8601 |
| [Enderton] p. 240 | Exercise 25 | oarec 8564 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10247 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17590 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17536 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18510 mrieqv2d 17587 mrieqvd 17586 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17591 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17596 mreexexlem2d 17593 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18516 mreexfidimd 17598 |
| [Frege1879] p. 11 | Statement | df3or2 42821 |
| [Frege1879] p. 12 | Statement | df3an2 42822 dfxor4 42819 dfxor5 42820 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 42843 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 42844 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 42848 |
| [Frege1879] p. 31 | Proposition 4 | frege4 42852 |
| [Frege1879] p. 32 | Proposition 5 | frege5 42853 |
| [Frege1879] p. 33 | Proposition 6 | frege6 42859 |
| [Frege1879] p. 34 | Proposition 7 | frege7 42861 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 42862 axfrege8 42860 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 90 wl-luk-pm2.04 36629 |
| [Frege1879] p. 35 | Proposition 9 | frege9 42865 |
| [Frege1879] p. 36 | Proposition 10 | frege10 42873 |
| [Frege1879] p. 36 | Proposition 11 | frege11 42867 |
| [Frege1879] p. 37 | Proposition 12 | frege12 42866 |
| [Frege1879] p. 37 | Proposition 13 | frege13 42875 |
| [Frege1879] p. 37 | Proposition 14 | frege14 42876 |
| [Frege1879] p. 38 | Proposition 15 | frege15 42879 |
| [Frege1879] p. 38 | Proposition 16 | frege16 42869 |
| [Frege1879] p. 39 | Proposition 17 | frege17 42874 |
| [Frege1879] p. 39 | Proposition 18 | frege18 42871 |
| [Frege1879] p. 39 | Proposition 19 | frege19 42877 |
| [Frege1879] p. 40 | Proposition 20 | frege20 42881 |
| [Frege1879] p. 40 | Proposition 21 | frege21 42880 |
| [Frege1879] p. 41 | Proposition 22 | frege22 42872 |
| [Frege1879] p. 42 | Proposition 23 | frege23 42878 |
| [Frege1879] p. 42 | Proposition 24 | frege24 42868 |
| [Frege1879] p. 42 | Proposition 25 | frege25 42870 rp-frege25 42858 |
| [Frege1879] p. 42 | Proposition 26 | frege26 42863 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 42883 |
| [Frege1879] p. 43 | Proposition 27 | frege27 42864 |
| [Frege1879] p. 43 | Proposition 28 | con3 153 |
| [Frege1879] p. 43 | Proposition 29 | frege29 42884 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 42887 axfrege31 42886 |
| [Frege1879] p. 44 | Proposition 30 | frege30 42885 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 130 |
| [Frege1879] p. 44 | Proposition 32 | frege32 42888 |
| [Frege1879] p. 44 | Proposition 33 | frege33 42889 |
| [Frege1879] p. 45 | Proposition 34 | frege34 42890 |
| [Frege1879] p. 45 | Proposition 35 | frege35 42891 |
| [Frege1879] p. 45 | Proposition 36 | frege36 42892 |
| [Frege1879] p. 46 | Proposition 37 | frege37 42893 |
| [Frege1879] p. 46 | Proposition 38 | frege38 42894 |
| [Frege1879] p. 46 | Proposition 39 | frege39 42895 |
| [Frege1879] p. 46 | Proposition 40 | frege40 42896 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 42898 axfrege41 42897 |
| [Frege1879] p. 47 | Proposition 41 | notnot 142 |
| [Frege1879] p. 47 | Proposition 42 | frege42 42899 |
| [Frege1879] p. 47 | Proposition 43 | frege43 42900 |
| [Frege1879] p. 47 | Proposition 44 | frege44 42901 |
| [Frege1879] p. 47 | Proposition 45 | frege45 42902 |
| [Frege1879] p. 48 | Proposition 46 | frege46 42903 |
| [Frege1879] p. 48 | Proposition 47 | frege47 42904 |
| [Frege1879] p. 49 | Proposition 48 | frege48 42905 |
| [Frege1879] p. 49 | Proposition 49 | frege49 42906 |
| [Frege1879] p. 49 | Proposition 50 | frege50 42907 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 42910 ax-frege52c 42941 frege52aid 42911 frege52b 42942 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 42915 ax-frege54c 42945 frege54b 42946 |
| [Frege1879] p. 50 | Proposition 51 | frege51 42908 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3778 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 42913 frege53aid 42912 frege53b 42943 frege53c 42967 |
| [Frege1879] p. 50 | Proposition 54 | biid 260 eqid 2730 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 42921 frege55aid 42918 frege55b 42950 frege55c 42971 frege55cor1a 42922 frege55lem2a 42920 frege55lem2b 42949 frege55lem2c 42970 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 42924 frege56aid 42923 frege56b 42951 frege56c 42972 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 42928 ax-frege58b 42954 frege58bid 42955 frege58c 42974 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 42926 frege57aid 42925 frege57b 42952 frege57c 42973 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3789 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 42930 frege59b 42957 frege59c 42975 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 42931 frege60b 42958 frege60c 42976 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 42932 frege61b 42959 frege61c 42977 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 42933 frege62b 42960 frege62c 42978 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 42934 frege63b 42961 frege63c 42979 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 42935 frege64b 42962 frege64c 42980 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 42936 frege65b 42963 frege65c 42981 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 42937 frege66b 42964 frege66c 42982 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 42938 frege67b 42965 frege67c 42983 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 42939 frege68b 42966 frege68c 42984 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 42985 |
| [Frege1879] p. 58 | Proposition 70 | frege70 42986 |
| [Frege1879] p. 59 | Proposition 71 | frege71 42987 |
| [Frege1879] p. 59 | Proposition 72 | frege72 42988 |
| [Frege1879] p. 59 | Proposition 73 | frege73 42989 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 42992 |
| [Frege1879] p. 60 | Proposition 74 | frege74 42990 |
| [Frege1879] p. 60 | Proposition 75 | frege75 42991 |
| [Frege1879] p. 62 | Proposition 77 | frege77 42993 frege77d 42799 |
| [Frege1879] p. 63 | Proposition 78 | frege78 42994 |
| [Frege1879] p. 63 | Proposition 79 | frege79 42995 |
| [Frege1879] p. 63 | Proposition 80 | frege80 42996 |
| [Frege1879] p. 63 | Proposition 81 | frege81 42997 frege81d 42800 |
| [Frege1879] p. 64 | Proposition 82 | frege82 42998 |
| [Frege1879] p. 65 | Proposition 83 | frege83 42999 frege83d 42801 |
| [Frege1879] p. 65 | Proposition 84 | frege84 43000 |
| [Frege1879] p. 66 | Proposition 85 | frege85 43001 |
| [Frege1879] p. 66 | Proposition 86 | frege86 43002 |
| [Frege1879] p. 66 | Proposition 87 | frege87 43003 frege87d 42803 |
| [Frege1879] p. 67 | Proposition 88 | frege88 43004 |
| [Frege1879] p. 68 | Proposition 89 | frege89 43005 |
| [Frege1879] p. 68 | Proposition 90 | frege90 43006 |
| [Frege1879] p. 68 | Proposition 91 | frege91 43007 frege91d 42804 |
| [Frege1879] p. 69 | Proposition 92 | frege92 43008 |
| [Frege1879] p. 70 | Proposition 93 | frege93 43009 |
| [Frege1879] p. 70 | Proposition 94 | frege94 43010 |
| [Frege1879] p. 70 | Proposition 95 | frege95 43011 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 43015 |
| [Frege1879] p. 71 | Proposition 96 | frege96 43012 frege96d 42802 |
| [Frege1879] p. 71 | Proposition 97 | frege97 43013 frege97d 42805 |
| [Frege1879] p. 71 | Proposition 98 | frege98 43014 frege98d 42806 |
| [Frege1879] p. 72 | Proposition 100 | frege100 43016 |
| [Frege1879] p. 72 | Proposition 101 | frege101 43017 |
| [Frege1879] p. 72 | Proposition 102 | frege102 43018 frege102d 42807 |
| [Frege1879] p. 73 | Proposition 103 | frege103 43019 |
| [Frege1879] p. 73 | Proposition 104 | frege104 43020 |
| [Frege1879] p. 73 | Proposition 105 | frege105 43021 |
| [Frege1879] p. 73 | Proposition 106 | frege106 43022 frege106d 42808 |
| [Frege1879] p. 74 | Proposition 107 | frege107 43023 |
| [Frege1879] p. 74 | Proposition 108 | frege108 43024 frege108d 42809 |
| [Frege1879] p. 74 | Proposition 109 | frege109 43025 frege109d 42810 |
| [Frege1879] p. 75 | Proposition 110 | frege110 43026 |
| [Frege1879] p. 75 | Proposition 111 | frege111 43027 frege111d 42812 |
| [Frege1879] p. 76 | Proposition 112 | frege112 43028 |
| [Frege1879] p. 76 | Proposition 113 | frege113 43029 |
| [Frege1879] p. 76 | Proposition 114 | frege114 43030 frege114d 42811 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 43031 |
| [Frege1879] p. 77 | Proposition 116 | frege116 43032 |
| [Frege1879] p. 78 | Proposition 117 | frege117 43033 |
| [Frege1879] p. 78 | Proposition 118 | frege118 43034 |
| [Frege1879] p. 78 | Proposition 119 | frege119 43035 |
| [Frege1879] p. 78 | Proposition 120 | frege120 43036 |
| [Frege1879] p. 79 | Proposition 121 | frege121 43037 |
| [Frege1879] p. 79 | Proposition 122 | frege122 43038 frege122d 42813 |
| [Frege1879] p. 79 | Proposition 123 | frege123 43039 |
| [Frege1879] p. 80 | Proposition 124 | frege124 43040 frege124d 42814 |
| [Frege1879] p. 81 | Proposition 125 | frege125 43041 |
| [Frege1879] p. 81 | Proposition 126 | frege126 43042 frege126d 42815 |
| [Frege1879] p. 82 | Proposition 127 | frege127 43043 |
| [Frege1879] p. 83 | Proposition 128 | frege128 43044 |
| [Frege1879] p. 83 | Proposition 129 | frege129 43045 frege129d 42816 |
| [Frege1879] p. 84 | Proposition 130 | frege130 43046 |
| [Frege1879] p. 85 | Proposition 131 | frege131 43047 frege131d 42817 |
| [Frege1879] p. 86 | Proposition 132 | frege132 43048 |
| [Frege1879] p. 86 | Proposition 133 | frege133 43049 frege133d 42818 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 45327 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 45650 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 45350 |
| [Fremlin1] p. 14 | Definition 112A | ismea 45465 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 45485 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 45476 meadjunre 45490 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 45477 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 45478 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 45474 meaiunle 45483 meaiunlelem 45482 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 45495 meaiuninc2 45496 meaiuninc3 45499 meaiuninc3v 45498 meaiunincf 45497 meaiuninclem 45494 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 45501 meaiininc2 45502 meaiininclem 45500 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 45520 caragendifcl 45528 caratheodory 45542 omelesplit 45532 |
| [Fremlin1] p. 19 | Definition 113A | isome 45508 isomennd 45545 isomenndlem 45544 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 45530 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 45549 voncmpl 45635 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 45512 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 45537 carageniuncllem1 45535 carageniuncllem2 45536 caragenuncl 45527 caragenuncllem 45526 caragenunicl 45538 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 45546 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 45540 caratheodorylem2 45541 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 45549 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 45608 hoidmv1lelem1 45605 hoidmv1lelem2 45606 hoidmv1lelem3 45607 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 45652 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 45608 hoidmvle 45614 hoidmvlelem1 45609 hoidmvlelem2 45610 hoidmvlelem3 45611 hoidmvlelem4 45612 hoidmvlelem5 45613 hsphoidmvle2 45599 hsphoif 45590 hsphoival 45593 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 45562 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 45570 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 45597 hoidmvn0val 45598 hoidmvval 45591 hoidmvval0 45601 hoidmvval0b 45604 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 45602 hsphoidmvle 45600 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 45551 df-voln 45553 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 45618 ovn0 45580 ovn0lem 45579 ovnf 45577 ovnome 45587 ovnssle 45575 ovnsslelem 45574 ovnsupge0 45571 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 45617 ovnhoilem1 45615 ovnhoilem2 45616 vonhoi 45681 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 45634 hoidifhspf 45632 hoidifhspval 45622 hoidifhspval2 45629 hoidifhspval3 45633 hspmbl 45643 hspmbllem1 45640 hspmbllem2 45641 hspmbllem3 45642 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 45635 vonmea 45588 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 45586 ovnsubadd2 45660 ovnsubadd2lem 45659 ovnsubaddlem1 45584 ovnsubaddlem2 45585 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 45645 hoimbl2 45679 hoimbllem 45644 hspdifhsp 45630 opnvonmbl 45648 opnvonmbllem2 45647 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 45650 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 45693 iccvonmbllem 45692 ioovonmbl 45691 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 45699 vonicclem2 45698 vonioo 45696 vonioolem2 45695 vonn0icc 45702 vonn0icc2 45706 vonn0ioo 45701 vonn0ioo2 45704 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 45703 snvonmbl 45700 vonct 45707 vonsn 45705 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 45373 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 45372 subsaliuncllem 45371 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 45739 salpreimalegt 45723 salpreimaltle 45740 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 45742 issmff 45748 issmflem 45741 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 45759 issmflelem 45758 smfpreimale 45768 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 45770 issmfgtlem 45769 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 45710 issmf 45742 issmff 45748 issmfge 45784 issmfgelem 45783 issmfgt 45770 issmfgtlem 45769 issmfle 45759 issmflelem 45758 issmflem 45741 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 45721 salpreimagtlt 45744 salpreimalelt 45743 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 45784 issmfgelem 45783 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 45767 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 45765 cnfsmf 45754 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 45781 decsmflem 45780 incsmf 45756 incsmflem 45755 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 45715 pimconstlt1 45716 smfconst 45763 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 45779 smfaddlem1 45777 smfaddlem2 45778 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 45810 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 45809 smfmullem1 45805 smfmullem2 45806 smfmullem3 45807 smfmullem4 45808 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 45811 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 45814 smfpimbor1lem2 45813 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 45816 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 45804 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 45803 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 45812 smfresal 45802 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 45791 smflim2 45820 smflimlem1 45785 smflimlem2 45786 smflimlem3 45787 smflimlem4 45788 smflimlem5 45789 smflimlem6 45790 smflimmpt 45824 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 45828 smfsuplem1 45825 smfsuplem2 45826 smfsuplem3 45827 smfsupmpt 45829 smfsupxr 45830 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 45832 smfinflem 45831 smfinfmpt 45833 |
| [Fremlin1] p. 39 | Remark 121G | smflim 45791 smflim2 45820 smflimmpt 45824 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 45822 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 45852 smfdivdmmbl2 45855 smfinfdmmbl 45863 smfinfdmmbllem 45862 smfsupdmmbl 45859 smfsupdmmbllem 45858 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 45842 smflimsuplem2 45835 smflimsuplem6 45839 smflimsuplem7 45840 smflimsuplem8 45841 smflimsupmpt 45843 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 45845 smfliminflem 45844 smfliminfmpt 45846 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 45710 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 45856 fsupdm2 45857 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 45847 adddmmbl2 45848 finfdm 45860 finfdm2 45861 fsupdm 45856 fsupdm2 45857 muldmmbl 45849 muldmmbl2 45850 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 45860 finfdm2 45861 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25285 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25328 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25338 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 36869 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 36872 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9635 inf1 9619 inf2 9620 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10908 enqer 10918 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10913 df-nq 10909 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10905 df-plq 10911 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7646 df-mpq 10906 df-mq 10912 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10914 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10972 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10973 ltbtwnnq 10975 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10968 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10969 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10976 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10978 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 10990 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 10992 |
| [Gleason] p. 122 | Definition | df-1p 10979 |
| [Gleason] p. 122 | Remark (1) | prub 10991 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 11030 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10982 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 11029 psslinpr 11028 supexpr 11051 suplem1pr 11049 suplem2pr 11050 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 11015 addclprlem1 11013 addclprlem2 11014 df-plp 10980 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 11019 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 11018 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 11031 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 11040 ltexprlem1 11033 ltexprlem2 11034 ltexprlem3 11035 ltexprlem4 11036 ltexprlem5 11037 ltexprlem6 11038 ltexprlem7 11039 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 11042 ltaprlem 11041 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 11043 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 11044 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10981 mulclpr 11017 mulclprlem 11016 reclem2pr 11045 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 11026 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 11021 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 11020 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 11025 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 11048 reclem3pr 11046 reclem4pr 11047 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 11052 enrer 11060 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 11057 df-1r 11058 df-nr 11053 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 11055 df-plr 11054 negexsr 11099 recexsr 11104 recexsrlem 11100 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 11056 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12211 creur 12210 cru 12208 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11185 axcnre 11161 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15066 crimd 15183 crimi 15144 crre 15065 crred 15182 crrei 15143 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15068 remimd 15149 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15235 absval2d 15396 absval2i 15348 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15092 cjaddd 15171 cjaddi 15139 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15093 cjmuld 15172 cjmuli 15140 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15091 cjcjd 15150 cjcji 15122 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15090 cjreb 15074 cjrebd 15153 cjrebi 15125 cjred 15177 rere 15073 rereb 15071 rerebd 15152 rerebi 15124 rered 15175 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15099 addcjd 15163 addcji 15134 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15189 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15230 abscjd 15401 abscji 15352 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15240 abs00d 15397 abs00i 15349 absne0d 15398 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15272 releabsd 15402 releabsi 15353 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15245 absmuld 15405 absmuli 15355 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15233 sqabsaddi 15356 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15281 abstrid 15407 abstrii 15359 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14032 exp0 14035 expp1 14038 expp1d 14116 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26423 cxpaddd 26461 expadd 14074 expaddd 14117 expaddz 14076 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26432 cxpmuld 26481 expmul 14077 expmuld 14118 expmulz 14078 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26429 mulcxpd 26472 mulexp 14071 mulexpd 14130 mulexpz 14072 |
| [Gleason] p. 140 | Exercise 1 | znnen 16159 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13490 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15580 rlimadd 15591 rlimdiv 15596 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15582 rlimsub 15593 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15581 rlimmul 15594 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15585 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15531 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15552 climcj 15553 climim 15555 climre 15554 rlimabs 15557 rlimcj 15558 rlimim 15560 rlimre 15559 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11257 df-xr 11256 ltxr 13099 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15419 limsupval 15422 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15620 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15629 caucvgb 15630 caucvgbf 44498 caucvgr 15626 climcau 15621 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15766 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15833 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15286 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13797 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21138 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24069 xmet0 24068 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24085 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24076 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24078 mstri 24195 xmettri 24077 xmstri 24194 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24108 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23372 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25058 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24269 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24601 addcn2 15542 mulcn 24603 mulcn2 15544 subcn 24602 subcn2 15543 |
| [Gleason] p. 295 | Remark | bcval3 14270 bcval4 14271 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14285 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14268 df-bc 14267 |
| [Gleason] p. 296 | Remark | bcn0 14274 bcnn 14276 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15780 |
| [Gleason] p. 308 | Equation 2 | ef0 16038 |
| [Gleason] p. 308 | Equation 3 | efcj 16039 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16044 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16048 |
| [Gleason] p. 310 | Equation 14 | sinadd 16111 |
| [Gleason] p. 310 | Equation 15 | cosadd 16112 |
| [Gleason] p. 311 | Equation 17 | sincossq 16123 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16128 sinbnd 16127 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14184 sqeqori 14182 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16020 |
| [Godowski] p. 730 | Equation SF | goeqi 31793 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 31188 |
| [Golan] p. 1 | Remark | srgisid 20103 |
| [Golan] p. 1 | Definition | df-srg 20081 |
| [Golan] p. 149 | Definition | df-slmd 32616 |
| [Gonshor] p. 7 | Definition | df-scut 27521 |
| [Gonshor] p. 9 | Theorem 2.5 | slerec 27557 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 27645 cofcut1d 27646 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 27647 cofcut2d 27648 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 27649 cofcutr1d 27650 cofcutr2d 27651 |
| [Gonshor] p. 13 | Definition | df-adds 27682 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 27698 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 27724 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 27825 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 27844 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 35435 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17534 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17536 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 46864 df-cllaw 46862 df-comlaw 46863 |
| [Hall] p. 2 | Section 1.2 | df-clintop 46876 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 46897 |
| [Halmos] p. 28 | Partition ` ` | df-parts 37938 dfmembpart2 37943 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 31585 riesz2 31586 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 31461 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 31693 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 31705 elpjidm 31704 pjnmopi 31668 |
| [Halmos] p. 44 | Remark | pjinormi 31207 pjinormii 31196 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 31709 pjrn 31227 pjrni 31222 pjvec 31216 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 31247 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 31674 hmopidmpji 31672 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 31711 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 31700 pjocvec 31217 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 31689 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 31692 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 31695 pjssdif2i 31694 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 31375 |
| [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 24738 df-phtpy 24717 |
| [Hatcher] p. 26 | Definition | df-pco 24752 df-pi1 24755 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 24741 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 24797 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22212 df-dmatalt 47166 |
| [Helfgott] p. 2 | Theorem | tgoldbach 46783 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 46768 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 46780 bgoldbtbnd 46775 bgoldbtbnd 46775 tgblthelfgott 46781 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 33952 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 33953 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 33967 hgt750lemb 33966 hgt750leme 33968 hgt750lemf 33963 hgt750lemg 33964 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 46777 tgoldbachgt 33973 tgoldbachgtALTV 46778 tgoldbachgtd 33972 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 33954 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30013 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 18866 grpoideu 30029 mndideu 18670 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 18895 grpoinveu 30039 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 18926 grpo2inv 30051 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 18937 grpoinvop 30053 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 18959 |
| [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 31940 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 31953 cdj3i 31961 cdj3lem1 31954 cdjreui 31952 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 31951 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 41139 |
| [Holland95] p. 14 | Line 15 | hgmapvs 41065 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 41087 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 41088 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 41085 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 41091 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 41010 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 41105 |
| [Holland95] p. 204 | Definition of involution | df-srng 20597 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 38677 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 40702 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 40655 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 39107 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 40551 poml4N 39127 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 40642 pexmidALTN 39152 pexmidN 39143 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 40707 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 38297 ldualset 38298 |
| [Holland95] p. 222 | Item 1 | df-lines 38675 df-pointsN 38676 |
| [Holland95] p. 222 | Item 2 | df-polarityN 39077 |
| [Holland95] p. 223 | Remark | ispsubcl2N 39121 omllaw4 38419 pol1N 39084 polcon3N 39091 |
| [Holland95] p. 223 | Definition | df-psubclN 39109 |
| [Holland95] p. 223 | Equation for polarity | polval2N 39080 |
| [Holmes] p. 40 | Definition | df-xrn 37544 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 30604 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 31702 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 31483 eigre 31355 eigrei 31354 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 31484 eigorth 31358 eigorthi 31357 |
| [Hughes] p. 137 | Remark (ii) | eigposi 31356 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 29829 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 29825 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 29826 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 29827 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 29845 frgrregorufr0 29844 frgrregorufrg 29846 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 29852 frrusgrord 29861 frrusgrord0 29860 |
| [Huneke] p. 2 | Statement | df-clwwlknon 29608 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 29835 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 29838 frgrwopreg2 29839 frgrwopregasn 29836 frgrwopregbsn 29837 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 29841 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 29855 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 29858 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 29606 numclwlk1 29891 numclwlk1lem1 29889 numclwlk1lem2 29890 numclwwlk1 29881 numclwwlk8 29912 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 29832 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 29295 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 29867 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 29893 numclwwlkovh0 29892 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 29901 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 29498 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 29905 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 29908 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 29911 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 29923 natded 29923 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 29923 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 29923 natded 29923 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 29923 |
| [Jech] p. 4 | Definition of class | cv 1538 cvjust 2724 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10576 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10574 alephmul 10575 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10573 infmap2 10215 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9811 |
| [Jech] p. 72 | Equation 9.3 | scott0 9883 scottex 9882 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9864 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9888 |
| [Jech] p. 78 | Note | opthprc 5739 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 41956 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 42044 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 42045 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 41968 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 41972 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 41973 rmyp1 41974 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 41975 rmym1 41976 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 41966 rmx1 41967 rmxluc 41977 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 41970 rmy1 41971 rmyluc 41978 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 41980 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 41981 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 42001 jm2.17b 42002 jm2.17c 42003 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 42034 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 42038 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 42029 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 42004 jm2.24nn 42000 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 42043 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 42049 rmygeid 42005 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 42061 |
| [Juillerat] p. 11 | Section *5 | etransc 45297 etransclem47 45295 etransclem48 45296 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 45292 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 45294 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 45280 |
| [Juillerat] p. 13 | Proof | etransclem35 45283 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 45286 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 45272 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 45289 |
| [Juillerat] p. 14 | Proof | etransclem23 45271 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1969 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2013 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2018 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2008 cbvaliw 2007 wl-cbvmotv 36685 wl-motae 36687 wl-moteq 36686 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 1997 spimw 1972 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2034 spw 2035 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31036 chabs1i 31038 chabs2 31037 chabs2i 31039 chjass 31053 chjassi 31006 latabs1 18432 latabs2 18433 |
| [Kalmbach] p. 15 | Definition of atom | df-at 31858 ela 31859 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 31803 cvrval2 38447 |
| [Kalmbach] p. 16 | Definition | df-ol 38351 df-oml 38352 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 31104 cmbri 31110 cmtvalN 38384 df-cm 31103 df-cmtN 38350 |
| [Kalmbach] p. 22 | Remark | omllaw5N 38420 pjoml5 31133 pjoml5i 31108 |
| [Kalmbach] p. 22 | Definition | pjoml2 31131 pjoml2i 31105 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 31134 cmcmi 31112 cmcmii 31117 cmtcomN 38422 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 38418 omlsi 30924 pjoml 30956 pjomli 30955 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 38417 |
| [Kalmbach] p. 23 | Remark | cmbr2i 31116 cmcm3 31135 cmcm3i 31114 cmcm3ii 31119 cmcm4i 31115 cmt3N 38424 cmt4N 38425 cmtbr2N 38426 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 31128 cmbr3i 31120 cmtbr3N 38427 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 31138 fh1i 31141 fh2 31139 fh2i 31142 omlfh1N 38431 |
| [Kalmbach] p. 65 | Remark | chjatom 31877 chslej 31018 chsleji 30978 shslej 30900 shsleji 30890 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31015 chocini 30974 chsupcl 30860 chsupval2 30930 h0elch 30775 helch 30763 hsupval2 30929 ocin 30816 ococss 30813 shococss 30814 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 30832 |
| [Kalmbach] p. 66 | Remark | df-pjh 30915 pjssmi 31685 pjssmii 31201 |
| [Kalmbach] p. 67 | Lemma 3 | osum 31165 osumi 31162 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 31720 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 31920 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 31830 |
| [Kalmbach] p. 140 | Remark | hatomic 31880 hatomici 31879 hatomistici 31882 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 38492 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 31901 lsatexch 38216 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 31875 cvlcvr1 38512 cvr1 38584 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 31894 cvexchi 31889 cvrexch 38594 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 31884 hlrelat 38576 hlrelat5N 38575 lrelat 38187 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 20899 lsmsatcv 38183 spansncv 31173 spansncvi 31172 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 38202 spansncv2 31813 |
| [Kalmbach] p. 266 | Definition | df-st 31731 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 31369 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10643 fpwwe2 10640 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10644 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10651 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10646 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10648 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10661 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10665 gchxpidm 10666 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10677 gchhar 10676 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10213 unxpwdom 9586 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10667 |
| [Kreyszig] p. 3 | Property M1 | metcl 24058 xmetcl 24057 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24065 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24301 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11935 muleqadd 11862 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24164 |
| [Kreyszig] p. 19 | Remark | mopntopon 24165 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24227 mopnm 24170 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24225 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24230 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24271 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 22982 lmmbr 25006 lmmbr2 25007 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23104 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25061 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25024 iscmet2 25042 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25064 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23185 metelcls 25053 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25054 metcld2 25055 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 24846 lmodvneg1 20659 nvinv 30159 vcm 30096 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 24842 lmod0vs 20649 slmd0vs 32639 vc0 30094 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20650 slmdvs0 32640 vcz 30095 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 30211 ngpmet 24332 nrmmetd 24303 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 30206 imsdval2 30207 ncvspds 24909 ngpds 24333 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24318 nvnd 30208 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24347 nmge0 24346 nvge0 30193 nvz 30189 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24353 nvabs 30192 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 30321 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 30265 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 30327 blocni 30325 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 30326 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 24952 ipeq0 21410 ipz 30239 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 24964 pythi 30370 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 30374 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 24986 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15806 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25184 minveco 30404 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 30270 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25077 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 30393 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 31643 leopg 31642 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 31661 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 30438 |
| [Kulpa] p. 547 | Theorem | poimir 36824 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 36823 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 36822 |
| [Kulpa] p. 548 | Theorem | broucube 36825 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 36817 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 36818 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2380 axnul 5304 |
| [Kunen] p. 11 | Axiom 3 | axnul 5304 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 7943 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8834 mapvalg 8832 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10519 |
| [Kunen] p. 31 | Definition 10.24 | mapex 8828 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9761 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9803 r1elssi 9802 |
| [Kunen] p. 107 | Exercise 4 | rankop 9855 rankopb 9849 rankuni 9860 rankxplim 9876 rankxpsuc 9879 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 5008 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 33029 |
| [Lang] p. | Definition | df-rn 5686 |
| [Lang] p. 3 | Statement | lidrideqd 18594 mndbn0 18675 |
| [Lang] p. 3 | Definition | df-mnd 18660 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18612 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18758 |
| [Lang] p. 5 | Equation | gsumreidx 19826 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 46858 |
| [Lang] p. 6 | Example | nn0mnd 46855 |
| [Lang] p. 6 | Equation | gsumxp2 19889 |
| [Lang] p. 6 | Statement | cycsubm 19117 |
| [Lang] p. 6 | Definition | mulgnn0gsum 18996 |
| [Lang] p. 6 | Observation | mndlsmidm 19579 |
| [Lang] p. 7 | Definition | dfgrp2e 18884 |
| [Lang] p. 30 | Definition | df-tocyc 32536 |
| [Lang] p. 32 | Property (a) | cyc3genpm 32581 |
| [Lang] p. 32 | Property (b) | cyc3conja 32586 cycpmconjv 32571 |
| [Lang] p. 53 | Definition | df-cat 17616 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18051 cat1lem 18050 |
| [Lang] p. 54 | Definition | df-iso 17700 |
| [Lang] p. 57 | Definition | df-inito 17938 df-termo 17939 |
| [Lang] p. 58 | Example | irinitoringc 47055 |
| [Lang] p. 58 | Statement | initoeu1 17965 termoeu1 17972 |
| [Lang] p. 62 | Definition | df-func 17812 |
| [Lang] p. 65 | Definition | df-nat 17898 |
| [Lang] p. 91 | Note | df-ringc 46991 |
| [Lang] p. 92 | Statement | mxidlprm 32860 |
| [Lang] p. 92 | Definition | isprmidlc 32840 |
| [Lang] p. 128 | Remark | dsmmlmod 21519 |
| [Lang] p. 129 | Proof | lincscm 47198 lincscmcl 47200 lincsum 47197 lincsumcl 47199 |
| [Lang] p. 129 | Statement | lincolss 47202 |
| [Lang] p. 129 | Observation | dsmmfi 21512 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 33000 qusdimsum 33001 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 32980 |
| [Lang] p. 147 | Definition | snlindsntor 47239 |
| [Lang] p. 504 | Statement | mat1 22169 matring 22165 |
| [Lang] p. 504 | Definition | df-mamu 22106 |
| [Lang] p. 505 | Statement | mamuass 22122 mamutpos 22180 matassa 22166 mattposvs 22177 tposmap 22179 |
| [Lang] p. 513 | Definition | mdet1 22323 mdetf 22317 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22413 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22309 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22333 |
| [Lang] p. 515 | Definition | df-minmar1 22357 smadiadetr 22397 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22332 mdetralt 22330 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22345 |
| [Lang] p. 518 | Definition | df-madu 22356 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22367 madurid 22366 matinv 22399 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 22612 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 33028 fedgmul 33004 |
| [Lang], p. 561 | Remark | chpmatply1 22554 |
| [Lang], p. 561 | Definition | df-chpmat 22549 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 43395 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 43390 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 43396 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5304 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2708 |
| [Levy] p. 59 | Definition | df-ttrcl 9705 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9748 |
| [Levy] p. 338 | Axiom | df-clel 2808 df-cleq 2722 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2808 df-cleq 2722 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2708 |
| [Levy] p. 358 | Axiom | df-clab 2708 |
| [Levy58] p. 2 | Definition I | isfin1-3 10383 |
| [Levy58] p. 2 | Definition II | df-fin2 10283 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10282 |
| [Levy58] p. 2 | Definition III | df-fin3 10285 |
| [Levy58] p. 3 | Definition V | df-fin5 10286 |
| [Levy58] p. 3 | Definition IV | df-fin4 10284 |
| [Levy58] p. 4 | Definition VI | df-fin6 10287 |
| [Levy58] p. 4 | Definition VII | df-fin7 10288 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10412 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27425 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27436 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27468 nosupbnd1 27453 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27470 nosupbnd2 27455 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27474 noetasuplem4 27475 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27471 |
| [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 31928 |
| [Maeda] p. 168 | Lemma 5 | mdsym 31932 mdsymi 31931 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 31926 mdsymlem6 31928 mdsymlem7 31929 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 31930 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 31833 ssdmd2 31834 ssmd1 31831 ssmd2 31832 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 31829 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 31801 df-md 31800 mdbr 31814 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 31851 mdslj1i 31839 mdslj2i 31840 mdslle1i 31837 mdslle2i 31838 mdslmd1i 31849 mdslmd2i 31850 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 31841 mdsl2bi 31843 mdsl2i 31842 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 31855 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 31852 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 31853 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 31830 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 31835 mdsl3 31836 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 31854 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 31949 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 38494 hlrelat1 38574 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 38212 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 31856 cvmdi 31844 cvnbtwn4 31809 cvrnbtwn4 38452 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 31857 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 38513 cvp 31895 cvrp 38590 lcvp 38213 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 31919 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 31918 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 38506 hlexch4N 38566 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 31921 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 38617 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 38923 atpsubN 38927 df-pointsN 38676 pointpsubN 38925 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 38678 pmap11 38936 pmaple 38935 pmapsub 38942 pmapval 38931 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 38939 pmap1N 38941 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 38944 pmapglb2N 38945 pmapglb2xN 38946 pmapglbx 38943 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 39026 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 38651 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 38970 paddclN 39016 paddidm 39015 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 38652 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 39012 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 38651 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 38652 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19584 lsmmod2 19585 lssats 38185 shatomici 31878 shatomistici 31881 shmodi 30910 shmodsi 30909 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 31820 mdsymlem7 31929 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 31109 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31013 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 31935 |
| [Margaris] p. 40 | Rule C | exlimiv 1931 |
| [Margaris] p. 49 | Axiom A1 | ax-1 6 |
| [Margaris] p. 49 | Axiom A2 | ax-2 7 |
| [Margaris] p. 49 | Axiom A3 | ax-3 8 |
| [Margaris] p. 49 | Definition | df-an 395 df-ex 1780 df-or 844 dfbi2 473 |
| [Margaris] p. 51 | Theorem 1 | idALT 23 |
| [Margaris] p. 56 | Theorem 3 | conventions 29920 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 43978 |
| [Margaris] p. 60 | Theorem 8 | jcn 162 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 43979 |
| [Margaris] p. 79 | Rule C | exinst01 43688 exinst11 43689 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1978 19.2g 2179 r19.2z 4493 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2193 rr19.3v 3656 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2154 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1826 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1781 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2172 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2196 19.9h 2280 exlimd 2209 exlimdh 2284 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2160 excomim 2161 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2318 |
| [Margaris] p. 90 | Section 19 | conventions-labels 29921 conventions-labels 29921 conventions-labels 29921 conventions-labels 29921 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1827 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 43439 albi 1818 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2216 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2217 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 43441 exbi 1847 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2220 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 43438 2alimdv 1919 alimd 2203 alimdh 1817 alimdv 1917 ax-4 1809 ralimdaa 3255 ralimdv 3167 ralimdva 3165 ralimdvva 3202 sbcimdv 3850 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2198 19.21h 2281 19.21t 2197 19.21vv 43437 alrimd 2206 alrimdd 2205 alrimdh 1864 alrimdv 1930 alrimi 2204 alrimih 1824 alrimiv 1928 alrimivv 1929 hbralrimi 3142 r19.21be 3247 r19.21bi 3246 ralrimd 3259 ralrimdv 3150 ralrimdva 3152 ralrimdvv 3199 ralrimdvva 3207 ralrimi 3252 ralrimia 3253 ralrimiv 3143 ralrimiva 3144 ralrimivv 3196 ralrimivva 3198 ralrimivvva 3201 ralrimivw 3148 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 43440 2eximdv 1920 exim 1834 eximd 2207 eximdh 1865 eximdv 1918 rexim 3085 reximd2a 3264 reximdai 3256 reximdd 44142 reximddv 3169 reximddv2 3210 reximddv3 44141 reximdv 3168 reximdv2 3162 reximdva 3166 reximdvai 3163 reximdvva 3203 reximi2 3077 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2202 19.23bi 2182 19.23h 2282 19.23t 2201 exlimdv 1934 exlimdvv 1935 exlimexi 43587 exlimiv 1931 exlimivv 1933 rexlimd3 44134 rexlimdv 3151 rexlimdv3a 3157 rexlimdva 3153 rexlimdva2 3155 rexlimdvaa 3154 rexlimdvv 3208 rexlimdvva 3209 rexlimdvw 3158 rexlimiv 3146 rexlimiva 3145 rexlimivv 3197 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 1987 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1881 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1871 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2218 r19.27z 4503 r19.27zv 4504 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2219 19.28vv 43447 r19.28z 4496 r19.28zf 44154 r19.28zv 4499 rr19.28v 3657 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1874 r19.29d2r 3138 r19.29imd 3116 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1882 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2225 19.31vv 43445 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2224 r19.32 46104 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 43443 19.33 1885 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 1988 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1878 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2221 19.36vv 43444 r19.36zv 4505 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2223 19.37vv 43446 r19.37zv 4500 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1839 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 1986 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1888 19.40 1887 r19.40 3117 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2226 19.41rg 43613 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2227 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1883 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2228 r19.44zv 4502 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2229 r19.45zv 4501 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2604 |
| [Mayet] p. 370 | Remark | jpi 31790 largei 31787 stri 31777 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 31732 ishst 31734 |
| [Mayet3] p. 10 | Theorem | hstrbi 31786 hstri 31785 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 31248 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 31249 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 31798 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 30852 chsupcl 30860 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 31880 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 31874 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 31901 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 39157 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18444 latj32 18442 latjass 18440 |
| [Megill] p. 444 | Axiom C5 | ax-5 1911 ax5ALT 38080 |
| [Megill] p. 444 | Section 7 | conventions 29920 |
| [Megill] p. 445 | Lemma L12 | aecom-o 38074 ax-c11n 38061 axc11n 2423 |
| [Megill] p. 446 | Lemma L17 | equtrr 2023 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 38069 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 38101 hbnae 2429 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2478 sbid 2245 sbidd-misc 47851 sbidd 47850 |
| [Megill] p. 448 | Remark 9.6 | axc14 2460 |
| [Megill] p. 448 | Scheme C4' | ax-c4 38057 |
| [Megill] p. 448 | Scheme C5' | ax-c5 38056 sp 2174 |
| [Megill] p. 448 | Scheme C6' | ax-11 2152 |
| [Megill] p. 448 | Scheme C7' | ax-c7 38058 |
| [Megill] p. 448 | Scheme C8' | ax-7 2009 |
| [Megill] p. 448 | Scheme C9' | ax-c9 38063 |
| [Megill] p. 448 | Scheme C10' | ax-6 1969 ax-c10 38059 |
| [Megill] p. 448 | Scheme C11' | ax-c11 38060 |
| [Megill] p. 448 | Scheme C12' | ax-8 2106 |
| [Megill] p. 448 | Scheme C13' | ax-9 2114 |
| [Megill] p. 448 | Scheme C14' | ax-c14 38064 |
| [Megill] p. 448 | Scheme C15' | ax-c15 38062 |
| [Megill] p. 448 | Scheme C16' | ax-c16 38065 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 38077 dral1 2436 dral2-o 38103 dral2 2435 drex1 2438 drex2 2439 drsb1 2492 drsb2 2255 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2159 sbequ 2084 sbid2v 2506 |
| [Megill] p. 450 | Example in Appendix | hba1-o 38070 hba1 2287 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 45900 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 23 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3872 rspsbca 3873 stdpc4 2069 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 38057 ra4 3879 stdpc5 2199 |
| [Mendelson] p. 81 | Rule C | exlimiv 1931 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2029 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2240 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3775 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5513 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4393 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4394 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4265 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4322 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4266 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4135 |
| [Mendelson] p. 231 | Definition of union | dfun3 4264 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5450 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4904 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5569 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4619 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5570 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4934 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5825 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6266 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7764 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6369 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8597 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9142 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 9057 xpsneng 9058 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9065 xpcomeng 9066 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9068 |
| [Mendelson] p. 255 | Definition | brsdom 8973 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9060 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8826 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 9039 mapsnend 9038 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9148 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9147 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8878 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 9042 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9061 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10175 djucomen 10174 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10179 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10173 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8533 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8560 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10556 |
| [Mendelson] p. 281 | Definition | df-r1 9761 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9810 |
| [Mendelson] p. 287 | Axiom system MK | ru 3775 |
| [MertziosUnger] p. 152 | Definition | df-frgr 29779 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 29814 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 29816 vdgn1frgrv3 29817 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 29818 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 29811 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 29804 2pthfrgrrn 29802 2pthfrgrrn2 29803 |
| [Mittelstaedt] p. 9 | Definition | df-oc 30772 |
| [Monk1] p. 22 | Remark | conventions 29920 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 29920 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4229 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5781 ssrelf 32111 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5783 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5210 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6260 coi2 6261 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5919 rn0 5924 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 6140 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5693 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5927 rnxp 6168 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5773 xp0 6156 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6075 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6072 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7909 imaexALTV 37502 imaexg 7908 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6069 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7076 funfvop 7050 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6946 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6956 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6593 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7256 dff13f 7257 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7222 funrnex 7942 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7248 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6225 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4967 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 7994 df-1st 7977 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 7995 df-2nd 7978 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9851 ranksnb 9824 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9852 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9853 rankunb 9847 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9835 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9761 r1val2 9834 |
| [Monk1] p. 117 | Lemma | zorn2 10503 zorn2g 10500 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9983 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10558 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9978 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1809 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2009 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2169 ax-c15 38062 ax12v2 2171 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 38057 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2152 |
| [Monk2] p. 109 | Lemma 15 | equvini 2452 equvinv 2030 eqvinop 5486 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1911 ax5ALT 38080 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2135 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2152 |
| [Monk2] p. 114 | Lemma 21 | sp 2174 |
| [Monk2] p. 114 | Lemma 22 | axc4 2312 hba1-o 38070 hba1 2287 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2148 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2168 nfra2 3370 nfra2w 3294 |
| [Moore] p. 53 | Part I | df-mre 17534 |
| [Munkres] p. 77 | Example 2 | distop 22718 indistop 22725 indistopon 22724 |
| [Munkres] p. 77 | Example 3 | fctop 22727 fctop2 22728 |
| [Munkres] p. 77 | Example 4 | cctop 22729 |
| [Munkres] p. 78 | Definition of basis | df-bases 22669 isbasis3g 22672 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17393 tgval2 22679 |
| [Munkres] p. 79 | Remark | tgcl 22692 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 22686 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 22710 tgss3 22709 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 22711 basgen2 22712 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 36533 topdifinfeq 36534 topdifinffin 36532 topdifinfindis 36530 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 22884 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 22762 topcld 22759 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 22763 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 22765 |
| [Munkres] p. 94 | Definition of closure | clsval 22761 |
| [Munkres] p. 94 | Definition of interior | ntrval 22760 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 22799 elcls 22797 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 22807 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 22872 neindisj 22841 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 22874 |
| [Munkres] p. 97 | Definition of limit point | islp2 22869 lpval 22863 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23039 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 22951 iscn 22959 iscn2 22962 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23004 cncnp2 23005 cncnpi 23002 df-cnp 22952 iscnp 22961 iscnp2 22963 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24272 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25059 |
| [Nathanson] p. 123 | Remark | reprgt 33931 reprinfz1 33932 reprlt 33929 |
| [Nathanson] p. 123 | Definition | df-repr 33919 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 33951 |
| [Nathanson] p. 123 | Proposition | breprexp 33943 breprexpnat 33944 itgexpif 33916 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 31624 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 46776 |
| [Pfenning] p. 17 | Definition XM | natded 29923 |
| [Pfenning] p. 17 | Definition NNC | natded 29923 notnotrd 133 |
| [Pfenning] p. 17 | Definition ` `C | natded 29923 |
| [Pfenning] p. 18 | Rule" | natded 29923 |
| [Pfenning] p. 18 | Definition /\I | natded 29923 |
| [Pfenning] p. 18 | Definition ` `E | natded 29923 natded 29923 natded 29923 natded 29923 natded 29923 |
| [Pfenning] p. 18 | Definition ` `I | natded 29923 natded 29923 natded 29923 natded 29923 natded 29923 |
| [Pfenning] p. 18 | Definition ` `EL | natded 29923 |
| [Pfenning] p. 18 | Definition ` `ER | natded 29923 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 29923 |
| [Pfenning] p. 18 | Definition ` `IR | natded 29923 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 29923 |
| [Pfenning] p. 127 | Definition =E | natded 29923 |
| [Pfenning] p. 127 | Definition =I | natded 29923 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 24950 df-dip 30221 dip0l 30238 ip0l 21408 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 24991 ipval 30223 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 30234 ipcj 21406 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 24953 dipdir 30362 ipdir 21411 ipdiri 30350 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 30230 nmsq 24942 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 30345 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 30347 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 30348 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 24959 dipass 30365 ipass 21417 ipassi 30361 |
| [Prugovecki] p. 186 | Definition of bra | braval 31464 df-bra 31370 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 31371 kbval 31474 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 31902 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 39062 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 31916 atcvat4i 31917 cvrat3 38616 cvrat4 38617 lsatcvat3 38225 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 31802 cvrval 38442 df-cv 31799 df-lcv 38192 lspsncv0 20904 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 39074 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 39075 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2708 rabid 3450 rabidd 44150 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2273 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2722 |
| [Quine] p. 19 | Definition 2.9 | conventions 29920 df-v 3474 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2871 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2868 abid2f 2934 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2265 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2086 sbalex 2233 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2808 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2730 eqid1 29987 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2737 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3777 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3778 dfsbcq2 3779 |
| [Quine] p. 43 | Theorem 6.8 | vex 3476 |
| [Quine] p. 43 | Theorem 6.9 | isset 3485 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3580 spcgv 3585 spcimgf 3578 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3789 spsbcd 3790 |
| [Quine] p. 44 | Theorem 6.12 | elex 3491 |
| [Quine] p. 44 | Theorem 6.13 | elab 3667 elabg 3665 elabgf 3663 |
| [Quine] p. 44 | Theorem 6.14 | noel 4329 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4720 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4630 df-sn 4628 |
| [Quine] p. 49 | Theorem 7.4 | snss 4788 snssg 4786 |
| [Quine] p. 49 | Theorem 7.5 | prss 4822 prssg 4821 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4765 prid1g 4763 prid2 4766 prid2g 4764 snid 4663 snidg 4661 |
| [Quine] p. 51 | Theorem 7.12 | snex 5430 |
| [Quine] p. 51 | Theorem 7.13 | prex 5431 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4929 unisnALT 43989 unisng 4928 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4933 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4940 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4938 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6509 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 46092 dfiota2 6495 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 46101 iotaval 6513 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6520 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6515 |
| [Quine] p. 58 | Definition 9.1 | df-op 4634 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5524 opabidw 5523 opelopab 5541 opelopaba 5535 opelopabaf 5543 opelopabf 5544 opelopabg 5537 opelopabga 5532 opelopabgf 5539 oprabid 7443 oprabidw 7442 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5681 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5683 |
| [Quine] p. 64 | Definition 9.15 | df-id 5573 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6612 |
| [Quine] p. 65 | Theorem 10.4 | funi 6579 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6600 funsng 6598 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6544 |
| [Quine] p. 65 | Definition 10.2 | args 6090 dffv4 6887 |
| [Quine] p. 68 | Definition 10.11 | conventions 29920 df-fv 6550 fv2 6885 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14236 nn0opth2i 14235 nn0opthi 14234 omopthi 8662 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8412 |
| [Quine] p. 232 | Equation i | carddom 10551 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6635 funimaexg 6633 |
| [Quine] p. 331 | Axiom system NF | ru 3775 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 30604 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 30221 polid 30679 polid2i 30677 polidi 30678 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 30333 |
| [ReedSimon] p. 195 | Remark | lnophm 31539 lnophmi 31538 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 31652 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 31654 leopmuli 31653 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 31657 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 31372 leoppos 31646 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 31656 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 31645 |
| [Roman] p. 4 | Definition | df-dmat 22212 df-dmatalt 47166 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20047 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20129 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 47253 |
| [Roman] p. 112 | Note | isldepslvec2 47253 ldepsnlinc 47276 zlmodzxznm 47265 |
| [Roman] p. 112 | Example | zlmodzxzequa 47264 zlmodzxzequap 47267 zlmodzxzldep 47272 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 22612 |
| [Rosenlicht] p. 80 | Theorem | heicant 36826 |
| [Rosser] p. 281 | Definition | df-op 4634 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 33955 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 33956 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 47130 pmtr3ncom 19384 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19380 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19323 cayleyth 19324 |
| [Rudin] p. 164 | Equation 27 | efcan 16043 |
| [Rudin] p. 164 | Equation 30 | efzval 16049 |
| [Rudin] p. 167 | Equation 48 | absefi 16143 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 196 |
| [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 6115 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6118 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6112 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6110 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17534 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17535 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17535 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17537 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10133 |
| [Schechter] p. 141 | Definition (MC) | dfac11 42106 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10443 axdc3 10451 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20131 isrngo 37068 |
| [Schechter] p. 276 | Remark 11.6.e | span0 31062 |
| [Schechter] p. 276 | Definition of span | df-span 30829 spanval 30853 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 22716 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6388 onelord 42302 ordelon 6387 ordelord 6385 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 42303 sucidg 6444 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6417 onsuc 7801 ord0 6416 ordsuci 7798 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 42304 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5268 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 42069 elon2 6374 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6369 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5582 epelg 5580 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9594 epirron 42305 ordirr 6381 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 42307 oneptr 42306 ontr1 6409 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 42309 oneptri 42308 ordtri3or 6395 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8503 ord0eln0 6418 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6430 onsucss 42318 trsucss 6451 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7808 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6457 ordnbtwn 6456 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 42320 ordnexbtwnsuc 42319 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10398 onsucf1lem 42321 onsucf1o 42324 onsucf1olem 42322 onsucrn 42323 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 42325 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7836 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 42314 ordne0gt0 42313 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 42316 limnsuc 42317 onsucelab 42315 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9640 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7851 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9643 ordom 7867 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9644 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8641 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7769 ssorduni 7768 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8533 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9647 limom 7873 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8468 df1o2 8475 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8518 oa0suclim 42327 oalim 8534 oasuc 8526 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8519 om0suclim 42328 omlim 8535 omsuc 8528 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8524 oe0m1 8523 oe0suclim 42329 oelim 8536 oesuc 8529 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 42280 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 42331 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 42332 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 42333 limexissupab 42335 limiun 42334 limuni 6424 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8540 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8544 om1om1r 42336 om1r 8545 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8537 oaomoecl 42330 oecl 8539 omcl 8538 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 42282 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8546 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8547 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 42337 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 42338 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8613 nnamecl 42339 nnecl 8615 nnmcl 8614 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 42340 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8554 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8555 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8562 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 42342 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 42343 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 42345 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8561 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 42349 omword1 8575 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 42348 oaordnrex 42347 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 42344 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 42350 omword2 8576 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 42351 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 42352 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 42353 omordi 8568 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8570 omord2com 42354 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 42355 df-2o 8469 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 42358 oewordi 8593 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 42359 oeworde 8595 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 42360 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 42361 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 42357 omnord1ex 42356 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 42362 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 42364 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 42368 oenord1ex 42367 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 42369 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8563 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 42363 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8581 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8582 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 42371 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8599 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 42372 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 42373 cantnfub2 42374 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 42377 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 28439 axtgcgrrflx 27980 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 28440 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 28441 axtgcgrid 27981 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 27966 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 28452 axtgsegcon 27982 df-trkgcb 27968 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 28463 axtg5seg 27983 df-trkgcb 27968 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 28464 axtgbtwnid 27984 df-trkgb 27967 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 28466 axtgpasch 27985 df-trkgb 27967 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 28485 df-trkg2d 33975 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 27988 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 27989 df-trkg2d 33975 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 28488 axtgeucl 27990 df-trkge 27969 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 28501 axtgcont 27987 axtgcont1 27986 df-trkgb 27967 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 35263 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 35265 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 35268 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 35272 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 35273 tgcgrcomimp 27995 tgcgrcoml 27997 tgcgrcomr 27996 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 35278 tgcgrtriv 28002 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 35282 tg5segofs 33983 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 33980 df-ofs 35259 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 35284 tgcgrextend 28003 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 35286 tgsegconeq 28004 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 35298 btwntriv2 35288 tgbtwntriv2 28005 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 35289 tgbtwncom 28006 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 35292 tgbtwntriv1 28009 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 35293 tgbtwnswapid 28010 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 35299 btwnintr 35295 tgbtwnexch2 28014 tgbtwnintr 28011 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 35301 btwnexch3 35296 tgbtwnexch 28016 tgbtwnexch3 28012 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 35300 tgbtwnouttr 28015 tgbtwnouttr2 28013 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 28484 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 35303 tgbtwndiff 28024 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28017 trisegint 35304 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 35320 tgifscgr 28026 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28076 colrot1 28077 colrot2 28078 lncom 28140 lnrot1 28141 lnrot2 28142 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 35316 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 35321 tgcgrsub 28027 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 35331 tgcgrxfr 28036 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28035 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 35317 df-cgrg 28029 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28029 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 35332 tgbtwnxfr 28048 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 35338 colinearperm2 35340 colinearperm3 35339 colinearperm4 35341 colinearperm5 35342 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28051 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 35315 tgellng 28071 tglng 28064 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 35343 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 35351 lnxfr 28084 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 35352 lnext 28085 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 35356 tgfscgr 28086 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 35357 lncgr 28087 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 35318 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 35359 lnid 28088 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 35360 tgidinside 28089 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 35377 tgbtwnconn1 28093 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 35378 tgbtwnconn2 28094 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 35379 tgbtwnconn3 28095 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 35385 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 35383 legov 28103 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28104 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28117 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 35386 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 35388 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 35390 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 35391 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 35392 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 35389 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 35394 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28105 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28107 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28108 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28109 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28110 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 35401 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 35402 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 35397 df-outsideof 35396 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 35398 ishlg 28120 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28125 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28127 outsideofrflx 35403 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28121 hlcomd 28122 outsideofcom 35404 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28128 outsideoftr 35405 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 28136 outsideofeu 35407 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 35414 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 35415 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 35408 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 35423 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 35424 tglineelsb2 28150 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 35426 linerflx1 35425 linerflx2 35427 tglinecom 28153 tglinerflx1 28151 tglinerflx2 28152 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 35429 tglinethru 28154 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 35413 tglng 28064 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28112 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 35432 tglinethrueu 28157 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 35433 tglineineq 28161 tglineinteq 28163 tglineintmo 28160 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28167 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28168 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 28169 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 28184 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 28180 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 28172 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 28171 ismir 28177 mirbtwn 28176 mircgr 28175 mirfv 28174 mirval 28173 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 28182 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 28183 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 28184 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 28187 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 28188 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 28193 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 28190 mirbtwni 28189 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 28191 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 28203 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 28207 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 28204 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 28205 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 28206 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 28209 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 28210 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 28216 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 28212 israg 28215 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 28217 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 28218 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 28220 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 28221 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 28222 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 28223 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 28224 ragncol 28227 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 28225 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 28231 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 28235 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 28232 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 28214 isperp 28230 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 28233 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 28240 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 28248 colperpexlem2 28249 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 28251 colperpexlem3 28250 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 28256 midex 28255 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 28253 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 28262 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 28257 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 28266 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 28269 opphllem6 28270 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 28272 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 27985 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 28273 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 28281 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 28276 hpgbr 28278 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 28283 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 28282 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 28284 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 28285 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 28286 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 28287 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 28288 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 28302 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 28292 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 28306 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 28307 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 28308 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 28309 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 28310 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 28313 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 28315 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 28293 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 28316 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 28319 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 28320 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 28321 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 28322 trgcopyeu 28324 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 28348 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 28327 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 28336 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 28334 cgrahl2 28335 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 28337 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 28338 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 28340 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 28341 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 28344 cgrahl 28345 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 28349 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 28350 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 28351 acopyeu 28352 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 28359 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 28363 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 28356 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 28371 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 28364 isleag 28365 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 28373 tgsas1 28372 tgsas2 28374 tgsas3 28375 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 28377 tgasa1 28376 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 28378 tgsss2 28379 tgsss3 28380 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27010 dchrsum 27008 dchrsum2 27007 sumdchr 27011 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27012 sum2dchr 27013 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 19977 ablfacrp2 19978 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 26955 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 26956 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 26963 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27221 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27224 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27278 vmalogdivsum2 27277 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27268 dirith2 27267 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27266 rpvmasum 27265 rpvmasum2 27251 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27226 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27264 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27231 dchrisumlem1 27228 dchrisumlem2 27229 dchrisumlem3 27230 dchrisumlema 27227 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27234 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27263 dchrmusumlem 27261 dchrvmasumlem 27262 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27233 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27235 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27259 dchrisum0re 27252 dchrisumn0 27260 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27245 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27249 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27250 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27305 pntrsumbnd2 27306 pntrsumo1 27304 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27269 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27271 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27273 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27276 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27281 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27282 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27287 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27289 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27290 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27298 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27299 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27296 selberg3lem2 27297 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27300 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27294 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27307 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27308 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27309 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27323 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27335 pntlemb 27336 pntlemc 27334 pntlemd 27333 pntlemg 27337 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27335 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27327 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27332 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27335 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27348 pntleml 27350 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4295 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4400 dif0 4371 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4490 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4473 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4286 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4287 |
| [Stoll] p. 20 | Remark | invdif 4267 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4636 |
| [Stoll] p. 43 | Definition | uniiun 5060 |
| [Stoll] p. 44 | Definition | intiin 5061 |
| [Stoll] p. 45 | Definition | df-iin 4999 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4998 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 400 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4295 |
| [Strang] p. 242 | Section 6.3 | expgrowth 43396 |
| [Suppes] p. 22 | Theorem 2 | eq0 4342 eq0f 4339 |
| [Suppes] p. 22 | Theorem 4 | eqss 3996 eqssd 3998 eqssi 3997 |
| [Suppes] p. 23 | Theorem 5 | ss0 4397 ss0b 4396 |
| [Suppes] p. 23 | Theorem 6 | sstr 3989 sstrALT2 43898 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4099 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4100 |
| [Suppes] p. 23 | Theorem 9 | psstr 4103 |
| [Suppes] p. 23 | Theorem 10 | pssss 4094 |
| [Suppes] p. 25 | Theorem 12 | elin 3963 elun 4147 |
| [Suppes] p. 26 | Theorem 15 | inidm 4217 |
| [Suppes] p. 26 | Theorem 16 | in0 4390 |
| [Suppes] p. 27 | Theorem 23 | unidm 4151 |
| [Suppes] p. 27 | Theorem 24 | un0 4389 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4171 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4179 |
| [Suppes] p. 27 | Theorem 27 | unss 4183 |
| [Suppes] p. 27 | Theorem 28 | indir 4274 |
| [Suppes] p. 27 | Theorem 29 | undir 4275 |
| [Suppes] p. 28 | Theorem 32 | difid 4369 |
| [Suppes] p. 29 | Theorem 33 | difin 4260 |
| [Suppes] p. 29 | Theorem 34 | indif 4268 |
| [Suppes] p. 29 | Theorem 35 | undif1 4474 |
| [Suppes] p. 29 | Theorem 36 | difun2 4479 |
| [Suppes] p. 29 | Theorem 37 | difin0 4472 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4470 |
| [Suppes] p. 29 | Theorem 39 | difundi 4278 |
| [Suppes] p. 29 | Theorem 40 | difindi 4280 |
| [Suppes] p. 30 | Theorem 41 | nalset 5312 |
| [Suppes] p. 39 | Theorem 61 | uniss 4915 |
| [Suppes] p. 39 | Theorem 65 | uniop 5514 |
| [Suppes] p. 41 | Theorem 70 | intsn 4989 |
| [Suppes] p. 42 | Theorem 71 | intpr 4985 intprg 4984 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5470 |
| [Suppes] p. 42 | Theorem 78 | intun 4983 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 5035 dfiun2g 5032 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 5036 |
| [Suppes] p. 47 | Theorem 86 | elpw 4605 elpw2 5344 elpw2g 5343 elpwg 4604 elpwgdedVD 43980 |
| [Suppes] p. 47 | Theorem 87 | pwid 4623 |
| [Suppes] p. 47 | Theorem 89 | pw0 4814 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4815 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5690 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5832 xpindir 5833 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5743 xpundir 5744 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9593 |
| [Suppes] p. 58 | Theorem 2 | relss 5780 |
| [Suppes] p. 59 | Theorem 4 | eldm 5899 eldm2 5900 eldm2g 5898 eldmg 5897 |
| [Suppes] p. 59 | Definition 3 | df-dm 5685 |
| [Suppes] p. 60 | Theorem 6 | dmin 5910 |
| [Suppes] p. 60 | Theorem 8 | rnun 6144 |
| [Suppes] p. 60 | Theorem 9 | rnin 6145 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5887 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5881 brcnvg 5878 |
| [Suppes] p. 62 | Equation 5 | elcnv 5875 elcnv2 5876 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6102 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6143 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6141 |
| [Suppes] p. 63 | Definition | dftrrels2 37748 |
| [Suppes] p. 63 | Theorem 20 | co02 6258 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5969 |
| [Suppes] p. 63 | Definition 7 | df-co 5684 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5884 |
| [Suppes] p. 64 | Theorem 27 | coass 6263 |
| [Suppes] p. 65 | Theorem 31 | resundi 5994 |
| [Suppes] p. 65 | Theorem 34 | elima 6063 elima2 6064 elima3 6065 elimag 6062 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6148 |
| [Suppes] p. 66 | Theorem 40 | dminss 6151 |
| [Suppes] p. 66 | Theorem 41 | imainss 6152 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6155 |
| [Suppes] p. 81 | Definition 34 | dfec2 8708 |
| [Suppes] p. 82 | Theorem 72 | elec 8749 elecALTV 37437 elecg 8748 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 37784 erth 8754 erth2 8755 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 37787 erdisj 8757 |
| [Suppes] p. 83 | Definition 35, | df-parts 37938 dfmembpart2 37943 |
| [Suppes] p. 89 | Theorem 96 | map0b 8879 |
| [Suppes] p. 89 | Theorem 97 | map0 8883 map0g 8880 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8884 mapsnd 8882 |
| [Suppes] p. 89 | Theorem 99 | mapss 8885 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 10065 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 10064 |
| [Suppes] p. 92 | Theorem 1 | enref 8983 enrefg 8982 |
| [Suppes] p. 92 | Theorem 2 | ensym 9001 ensymb 9000 ensymi 9002 |
| [Suppes] p. 92 | Theorem 3 | entr 9004 |
| [Suppes] p. 92 | Theorem 4 | unen 9048 |
| [Suppes] p. 94 | Theorem 15 | endom 8977 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 8998 |
| [Suppes] p. 94 | Theorem 17 | domtr 9005 |
| [Suppes] p. 95 | Theorem 18 | sbth 9095 |
| [Suppes] p. 97 | Theorem 23 | canth2 9132 canth2g 9133 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9099 df-sdom 8944 dfsdom2 9098 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9116 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9101 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9100 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9114 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8980 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9117 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9112 |
| [Suppes] p. 98 | Exercise 4 | fundmen 9033 fundmeng 9034 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9072 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9113 |
| [Suppes] p. 104 | Theorem 37 | fofi 9340 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9180 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9180 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10548 |
| [Suppes] p. 130 | Definition 3 | df-tr 5265 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7769 |
| [Suppes] p. 134 | Definition 6 | df-suc 6369 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7895 finds 7891 finds1 7894 finds2 7893 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9649 isfinite2 9303 isfiniteg 9306 unbnn 9301 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10915 df-ltpq 10907 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7854 tfinds 7851 tfinds2 7855 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8553 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8555 |
| [Suppes] p. 211 | Theorem 25 | oaass 8563 |
| [Suppes] p. 225 | Definition 8 | iscard2 9973 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10560 |
| [Suppes] p. 228 | Theorem 59 | harcard 9975 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 10063 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6414 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7783 onminsb 7784 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10569 |
| [Suppes] p. 229 | Theorem 65 | alephcard 10067 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 10074 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 10068 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9937 |
| [Suppes] p. 242 | Theorem 6 | weth 10492 |
| [Suppes] p. 242 | Theorem 8 | entric 10554 |
| [Suppes] p. 242 | Theorem 9 | carden 10548 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 34969 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 34973 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2701 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2722 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2808 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2724 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2753 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7415 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3775 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5418 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4650 elpr2 4652 elpr2g 4651 elprg 4648 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4642 elsn2 4666 elsn2g 4665 elsng 4641 velsn 4643 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5466 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4637 sneqr 4840 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4646 dfsn2 4640 dfsn2ALT 4647 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7733 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5475 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5463 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5447 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7735 unexg 7738 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4692 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4908 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3954 df-un 3952 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4925 uniprg 4924 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5374 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4691 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6433 elsucg 6431 sstr2 3988 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4152 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4200 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4165 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4218 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4272 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4273 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3966 dfss2 3967 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4603 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4180 |
| [TakeutiZaring] p. 18 | Exercise 9 | df-ss 3964 sseqin2 4214 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 4003 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4227 inss2 4228 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 4045 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4918 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5448 sspwimp 43981 sspwimpALT 43988 sspwimpALT2 43991 sspwimpcf 43983 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5455 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5284 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3431 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5306 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3950 |
| [TakeutiZaring] p. 20 | Definition 5.14 | dfnul2 4324 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4369 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4345 n0f 4341 neq0 4344 neq0f 4340 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9592 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9729 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9731 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3474 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5314 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4395 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5320 ssexg 5322 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5316 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9599 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9594 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4362 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4129 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4289 undif3VD 43945 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4130 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4137 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3060 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3069 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7742 xpexg 7739 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5682 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6618 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6796 fun11 6621 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6558 svrelfun 6619 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5886 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5888 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5687 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5688 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5684 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6192 dfrel2 6187 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5691 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5810 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5817 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5831 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 6009 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5986 opelresi 5988 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 6002 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 6005 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 6010 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6589 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6106 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6587 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6798 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2603 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 29920 df-fv 6550 fv3 6908 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7918 cnvexg 7917 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7904 dmexg 7896 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7905 rnexg 7897 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 43515 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7913 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6903 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 46180 tz6.12-1-afv2 46247 tz6.12-1 6913 tz6.12-afv 46179 tz6.12-afv2 46246 tz6.12 6915 tz6.12c-afv2 46248 tz6.12c 6912 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 46243 tz6.12-2 6878 tz6.12i-afv2 46249 tz6.12i 6918 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6545 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6546 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6548 wfo 6540 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6547 wf1 6539 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6549 wf1o 6541 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 7031 eqfnfv2 7032 eqfnfv2f 7035 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6988 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7220 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7218 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6635 funimaexg 6633 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5148 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5588 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5639 dffr3 6097 eliniseg 6092 iniseg 6095 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5579 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5653 fr3nr 7761 frirr 5652 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5630 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7763 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5642 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5662 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6347 tz6.26i 6349 wefrc 5669 wereu2 5672 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6350 wfii 6352 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6551 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7328 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7329 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7335 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7336 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7337 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7341 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7348 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7350 |
| [TakeutiZaring] p. 35 | Notation | wtr 5264 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 43516 tz7.2 5659 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5270 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6376 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6384 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6385 ordelordALT 43600 ordelordALTVD 43930 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6391 ordelssne 6390 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6389 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6393 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7771 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7772 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6367 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6395 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 43612 ordon 7766 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7767 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7844 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6410 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5266 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7782 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7821 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6467 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6466 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7768 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4940 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6369 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6443 sucidg 6444 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7801 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6457 ordnbtwn 6456 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7818 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6368 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7872 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7877 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7832 ordelsuc 7810 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7812 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7842 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7859 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7881 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7883 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7884 |
| [TakeutiZaring] p. 43 | Remark | omon 7869 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9632 omex 9640 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7867 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7889 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7885 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7886 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7862 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4965 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5283 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4966 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5336 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7785 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6413 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4950 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9657 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7780 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8378 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8399 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8400 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8401 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8408 tz7.44-2 8409 tz7.44-3 8410 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8369 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8364 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8348 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8447 tz7.49c 8448 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8445 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8444 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8446 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2649 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 10008 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 10009 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8534 oasuc 8526 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7852 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8537 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8518 oa0r 8540 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8538 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8550 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8621 nnaordi 8620 oaord 8549 oaordi 8548 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5051 uniss2 4944 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8552 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8557 oawordex 8559 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8613 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8649 |
| [TakeutiZaring] p. 60 | Remark | oancom 9648 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8562 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8618 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8554 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8521 omlim 8535 omsuc 8528 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8519 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8615 nnmcl 8614 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8634 nnmordi 8633 omord 8570 omordi 8568 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8571 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8638 omwordri 8574 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8541 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8544 om1r 8545 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8577 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8579 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8580 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8581 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8582 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8610 oe0 8524 oelim 8536 oesuc 8529 onesuc 8532 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8522 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8588 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8589 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8523 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8547 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8590 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8596 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8594 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8595 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8599 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8601 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9725 tz9.1 9726 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9761 r10 9765 r1lim 9769 r1limg 9768 r1suc 9767 r1sucg 9766 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9777 r1ord2 9778 r1ordg 9775 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9787 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9812 tz9.13 9788 tz9.13g 9789 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9762 rankval 9813 rankvalb 9794 rankvalg 9814 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9836 rankelb 9821 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9850 rankval3 9837 rankval3b 9823 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9826 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9792 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9831 rankr1c 9818 rankr1g 9829 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9832 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9846 rankssb 9845 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9839 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9838 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10472 dfac3 10118 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 10027 numth 10469 numth2 10468 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10543 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10544 cardid2 9950 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9957 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10548 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9956 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9941 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9962 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9954 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9152 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 9015 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9157 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9076 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9960 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10095 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9211 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9230 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10096 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9216 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10085 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 10063 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9969 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10214 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9323 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8945 isfi 8974 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9232 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10531 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9069 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10523 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10182 unxpdom 9255 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9971 cardsdomelir 9970 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9257 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 10011 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8824 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10559 infxpidm2 10014 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10205 infxp 10212 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9081 pw2f1o 9079 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9145 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10484 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10479 ac6s5 10488 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10540 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10541 uniimadomf 10542 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10271 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10266 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10251 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10248 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10254 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10261 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10270 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10579 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10249 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10273 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10094 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10093 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10105 alephfp2 10106 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10696 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10109 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10566 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10580 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10581 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 38056 |
| [Tarski] p. 67 | Scheme B5 | sp 2174 |
| [Tarski] p. 68 | Lemma 6 | avril1 29983 equid 2013 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2018 |
| [Tarski] p. 70 | Lemma 14 | spim 2384 spime 2386 spimew 1973 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2169 ax-c15 38062 ax12i 1968 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2086 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1970 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1911 ax5ALT 38080 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2009 ax-8 2106 ax-9 2114 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 27982 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 27983 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 27985 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 27985 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 27986 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16190 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 36830 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 36832 |
| [Weierstrass] p. 272 | Definition | df-mdet 22307 mdetuni 22344 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 900 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 864 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 865 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 916 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 964 |
| [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 36629 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 42853 imim2 58 wl-luk-imim2 36624 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 46027 imim1 83 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 893 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2656 syl 17 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 899 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 22 wl-luk-id 36627 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 891 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 142 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 894 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 130 notnotrALT2 43990 wl-luk-notnotr 36628 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 146 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 42883 axfrege28 42882 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 863 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 921 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 123 wl-luk-pm2.21 36621 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 124 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 886 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 936 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 29921 pm2.27 42 wl-luk-pm2.27 36619 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 919 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 37535 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 920 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 966 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 967 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 965 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1086 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 903 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 904 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 939 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 56 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 878 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 879 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5 169 pm2.5g 168 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6 190 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 880 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 881 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 882 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 172 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 847 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 848 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 885 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 887 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 191 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 896 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 937 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 938 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 192 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 888 pm2.67 889 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 176 pm2.521g 174 pm2.521g2 175 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 895 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 969 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 897 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 202 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 970 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 971 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 930 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 928 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 968 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 972 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 84 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 929 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 109 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 988 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 468 pm3.2im 160 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 989 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 990 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 991 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 992 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 470 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 458 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 401 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 799 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 447 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 448 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 481 simplim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 483 simprim 166 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 761 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 762 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 804 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 620 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 806 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 491 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 492 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 957 pm3.44 956 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 805 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 472 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 960 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34b 315 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 260 |
| [WhiteheadRussell] p. 117 | Theorem *4.11 | notbi 318 |
| [WhiteheadRussell] p. 117 | Theorem *4.12 | con2bi 352 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotb 314 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14 803 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 829 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 221 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 802 bitr 801 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 562 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 901 pm4.25 902 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 459 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1004 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 866 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 467 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 918 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 630 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 914 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 634 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 973 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1087 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1002 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1050 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1019 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 993 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 995 pm4.45 994 pm4.45im 824 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 979 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 849 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 544 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 978 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 981 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 982 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 983 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 984 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 980 pm4.56 985 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 986 pm4.57 987 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 403 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 852 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 396 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 845 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 404 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 846 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67 397 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 556 pm4.71d 560 pm4.71i 558 pm4.71r 557 pm4.71rd 561 pm4.71ri 559 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 946 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 526 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 933 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 516 pm4.76 517 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 958 pm4.77 959 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 931 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1000 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 391 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81 392 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 1020 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1021 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 346 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 347 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 350 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 386 impexp 449 pm4.87 839 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 820 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 941 pm5.11g 940 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 942 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 944 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 943 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1009 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1010 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1008 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbn 382 pm5.18 380 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 385 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 821 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1011 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1046 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1047 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 898 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 571 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 387 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 360 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6 998 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 950 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 827 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 572 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 832 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 822 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 830 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 388 pm5.41 389 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 542 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 541 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 1001 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1014 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 945 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 997 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1015 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1016 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1024 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 365 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 269 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 1025 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 43419 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 43420 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1871 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 43421 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 43422 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 43423 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1894 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 43424 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 43425 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 43426 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 43427 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 43428 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 43430 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 43431 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 43432 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 43429 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2091 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 43435 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 43436 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2071 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2155 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1829 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1830 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 43437 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 43438 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 43439 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 43440 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 43442 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 43441 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1888 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 43444 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 43445 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 43443 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1828 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 43446 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 43447 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1846 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 43448 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2340 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1861 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 43453 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 43449 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 43450 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 43451 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 43452 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 43457 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 43454 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 43455 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 43456 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 43458 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2561 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 43468 pm13.13b 43469 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 43470 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3020 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3021 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3655 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 43476 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 43477 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 43471 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 43615 pm13.193 43472 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 43473 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 43474 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 43475 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 43482 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 43481 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 43480 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3844 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 43483 pm14.122b 43484 pm14.122c 43485 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 43486 pm14.123b 43487 pm14.123c 43488 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 43490 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 43489 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 43491 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6523 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 43492 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6524 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 43493 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 43495 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2627 eupickbi 2630 sbaniota 43496 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 43494 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2576 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 43498 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 29920 df-fv 6550 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 9998 pm54.43lem 9997 |
| [Young] p. 141 | Definition of operator ordering | leop2 31644 |
| [Young] p. 142 | Example 12.2(i) | 0leop 31650 idleop 31651 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 41868 |
| [vandenDries] p. 43 | Theorem 62 | pellex 41875 pellexlem1 41869 |