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 17608 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17608 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18022 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17629 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 47585 prsthinc 47576 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 47606 df-mndtc 47606 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17652 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17724 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17712 invisoinvl 17733 |
| [Adamek] p. 28 | Example 3.13 | idinv 17732 idiso 17731 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17717 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17691 df-iso 17692 dfiso2 17715 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17698 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17749 |
| [Adamek] p. 29 | Definition 3.15 | cic 17742 df-cic 17739 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17804 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17713 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17714 isoco 17720 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17804 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17827 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17820 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 47542 prsthinc 47576 thincciso 47571 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 47606 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17834 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18057 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18115 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17852 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17851 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18115 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17876 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17882 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17881 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18100 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18100 |
| [Adamek] p. 39 | Definition 3.41 | funcoppc 17821 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18045 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17870 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17869 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18054 |
| [Adamek] p. 40 | Definition 3.47 | df-catc 18045 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17784 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17785 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17796 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17755 |
| [Adamek] p. 49 | Remark 4.4(2) | ressffth 17885 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 17890 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 17913 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 17917 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 17891 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 17919 |
| [Adamek] p. 101 | Definition 7.1 | df-inito 17930 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 46869 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 17931 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 17958 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 17962 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 17932 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 46872 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 17965 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17690 |
| [Adamek] p. 185 | Section 10.67 | updjud 9925 |
| [Adamek] p. 478 | Item Rng | df-ringc 46805 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 47136 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 47158 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14517 df-pfx 14617 df-substr 14587 df-word 14461 lencl 14479 wrd0 14485 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24207 df-nmoo 29976 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 31384 hmopidmchi 31382 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 31432 pjcmul2i 31433 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 31149 unoplin 31151 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 31150 unopadj2 31169 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 31244 lnopunii 31243 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 31317 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 27394 |
| [Alling] p. 184 | Axiom B | bdayfo 27160 |
| [Alling] p. 184 | Axiom O | sltso 27159 |
| [Alling] p. 184 | Axiom SD | nodense 27175 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27260 |
| [Alling] p. 185 | Theorem | conway 27280 |
| [Alling] p. 185 | Axiom FE | noeta 27226 |
| [Alling] p. 186 | Theorem 4 | slerec 27300 |
| [Alling], p. 2 | Definition | rp-brsslt 42107 |
| [Alling], p. 3 | Note | nla0001 42110 nla0002 42108 nla0003 42109 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11394 addcan2d 11414 addcan2i 11404 addcand 11413 addcani 11403 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11446 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11504 negsubd 11573 negsubi 11534 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11506 negnegd 11558 negnegi 11526 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11643 subdid 11666 subdii 11659 subdir 11644 subdird 11667 subdiri 11660 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11389 mul01d 11409 mul01i 11400 mul02 11388 mul02d 11408 mul02i 11399 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11847 mulcan2d 11844 mulcand 11843 mulcani 11849 |
| [Apostol] p. 18 | Theorem I.8 | receu 11855 xreceu 32066 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11884 divrecd 11989 divreci 11955 divreczi 11948 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11907 recreci 11942 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11850 mul0ord 11860 mul0ori 11858 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11649 mul2negd 11665 mul2negi 11658 mulneg1 11646 mulneg1d 11663 mulneg1i 11656 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11925 divadddivd 12030 divadddivi 11972 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11910 divmuldivd 12027 divmuldivi 11970 rdivmuldivd 20216 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11911 divdivdivd 12033 divdivdivi 11973 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 12992 rpaddcld 13027 rpmulcl 12993 rpmulcld 13028 |
| [Apostol] p. 20 | Axiom 8 | rpneg 13002 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 13005 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11336 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11803 ltadd1dd 11821 ltadd1i 11764 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12060 ltmul1a 12059 ltmul1i 12128 ltmul1ii 12138 ltmul2 12061 ltmul2d 13054 ltmul2dd 13068 ltmul2i 12131 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11730 msqgt0d 11777 msqgt0i 11747 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11732 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11716 lt0neg1d 11779 ltneg 11710 ltnegd 11788 ltnegi 11754 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11695 lt2addd 11833 lt2addi 11772 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 12971 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12056 recgt0d 12144 recgt0i 12115 recgt0ii 12116 |
| [Apostol] p. 22 | Definition of integers | df-z 12555 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12222 |
| [Apostol] p. 22 | Definition of rationals | df-q 12929 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9445 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12464 |
| [Apostol] p. 26 | Theorem I.29 | arch 12465 archd 43789 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12661 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12466 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12927 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12926 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13174 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16278 zneo 12641 zneoALTV 46272 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26219 msqsqrtd 15383 resqrtth 15198 sqrtth 15307 sqrtthi 15313 sqsqrtd 15382 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12211 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12893 |
| [Apostol] p. 361 | Remark | crreczi 14187 |
| [Apostol] p. 363 | Remark | absgt0i 15342 |
| [Apostol] p. 363 | Example | abssubd 15396 abssubi 15346 |
| [ApostolNT] p. 7 | Remark | fmtno0 46143 fmtno1 46144 fmtno2 46153 fmtno3 46154 fmtno4 46155 fmtno5fac 46185 fmtnofz04prm 46180 |
| [ApostolNT] p. 7 | Definition | df-fmtno 46131 |
| [ApostolNT] p. 8 | Definition | df-ppi 26584 |
| [ApostolNT] p. 14 | Definition | df-dvds 16194 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16209 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16233 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16228 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16222 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16224 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16210 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16211 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16216 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16250 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16252 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16254 |
| [ApostolNT] p. 15 | Definition | df-gcd 16432 dfgcd2 16484 |
| [ApostolNT] p. 16 | Definition | isprm2 16615 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16586 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16844 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16450 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16485 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16487 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16465 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16457 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16644 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16646 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16857 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16851 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16342 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16520 |
| [ApostolNT] p. 24 | Definition | df-mu 26585 |
| [ApostolNT] p. 25 | Definition | df-phi 16695 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 26675 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16719 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16705 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16709 |
| [ApostolNT] p. 32 | Definition | df-vma 26582 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 26677 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 26699 |
| [ApostolNT] p. 38 | Remark | df-sgm 26586 |
| [ApostolNT] p. 38 | Definition | df-sgm 26586 |
| [ApostolNT] p. 75 | Definition | df-chp 26583 df-cht 26581 |
| [ApostolNT] p. 104 | Definition | congr 16597 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16197 |
| [ApostolNT] p. 106 | Definition | moddvds 16204 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16285 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16286 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13849 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13886 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14197 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16227 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16600 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17003 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16602 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16712 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16730 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16713 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 26556 |
| [ApostolNT] p. 179 | Definition | df-lgs 26778 lgsprme0 26822 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 26823 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 26799 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 26814 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 26871 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 26890 2lgsoddprm 26899 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 26857 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 26866 |
| [ApostolNT] p. 188 | Definition | df-lgs 26778 lgs1 26824 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 26815 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 26817 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 26825 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 26826 |
| [Baer] p. 40 | Property (b) | mapdord 40447 |
| [Baer] p. 40 | Property (c) | mapd11 40448 |
| [Baer] p. 40 | Property (e) | mapdin 40471 mapdlsm 40473 |
| [Baer] p. 40 | Property (f) | mapd0 40474 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 40434 mapd1o 40457 |
| [Baer] p. 41 | Property (g) | mapdat 40476 |
| [Baer] p. 44 | Part (1) | mapdpg 40515 |
| [Baer] p. 45 | Part (2) | hdmap1eq 40610 mapdheq 40537 mapdheq2 40538 mapdheq2biN 40539 |
| [Baer] p. 45 | Part (3) | baerlem3 40522 |
| [Baer] p. 46 | Part (4) | mapdheq4 40541 mapdheq4lem 40540 |
| [Baer] p. 46 | Part (5) | baerlem5a 40523 baerlem5abmN 40527 baerlem5amN 40525 baerlem5b 40524 baerlem5bmN 40526 |
| [Baer] p. 47 | Part (6) | hdmap1l6 40630 hdmap1l6a 40618 hdmap1l6e 40623 hdmap1l6f 40624 hdmap1l6g 40625 hdmap1l6lem1 40616 hdmap1l6lem2 40617 mapdh6N 40556 mapdh6aN 40544 mapdh6eN 40549 mapdh6fN 40550 mapdh6gN 40551 mapdh6lem1N 40542 mapdh6lem2N 40543 |
| [Baer] p. 48 | Part 9 | hdmapval 40637 |
| [Baer] p. 48 | Part 10 | hdmap10 40649 |
| [Baer] p. 48 | Part 11 | hdmapadd 40652 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 40626 mapdh6hN 40552 |
| [Baer] p. 48 | Part (7) | mapdh75cN 40562 mapdh75d 40563 mapdh75e 40561 mapdh75fN 40564 mapdh7cN 40558 mapdh7dN 40559 mapdh7eN 40557 mapdh7fN 40560 |
| [Baer] p. 48 | Part (8) | mapdh8 40597 mapdh8a 40584 mapdh8aa 40585 mapdh8ab 40586 mapdh8ac 40587 mapdh8ad 40588 mapdh8b 40589 mapdh8c 40590 mapdh8d 40592 mapdh8d0N 40591 mapdh8e 40593 mapdh8g 40594 mapdh8i 40595 mapdh8j 40596 |
| [Baer] p. 48 | Part (9) | mapdh9a 40598 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 40578 |
| [Baer] p. 49 | Part 12 | hdmap11 40657 hdmapeq0 40653 hdmapf1oN 40674 hdmapneg 40655 hdmaprnN 40673 hdmaprnlem1N 40658 hdmaprnlem3N 40659 hdmaprnlem3uN 40660 hdmaprnlem4N 40662 hdmaprnlem6N 40663 hdmaprnlem7N 40664 hdmaprnlem8N 40665 hdmaprnlem9N 40666 hdmapsub 40656 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 40677 hdmap14lem10 40686 hdmap14lem1a 40675 hdmap14lem2N 40678 hdmap14lem2a 40676 hdmap14lem3 40679 hdmap14lem8 40684 hdmap14lem9 40685 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 40687 hdmap14lem12 40688 hdmap14lem13 40689 hdmap14lem14 40690 hdmap14lem15 40691 hgmapval 40696 |
| [Baer] p. 50 | Part 15 | hgmapadd 40703 hgmapmul 40704 hgmaprnlem2N 40706 hgmapvs 40700 |
| [Baer] p. 50 | Part 16 | hgmaprnN 40710 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 40726 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 40727 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 40728 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 40729 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 40731 hgmapvv 40735 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 40730 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 40732 |
| [Baer] p. 111 | Line 15 | hdmapg 40739 hdmapglem7 40738 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26220 2irrexpqALT 26285 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 23 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2564 |
| [BellMachover] p. 460 | Notation | df-mo 2535 |
| [BellMachover] p. 460 | Definition | mo3 2559 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2704 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2708 |
| [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 35883 bm1.3ii 5301 |
| [BellMachover] p. 466 | Problem | axpow2 5364 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5365 |
| [BellMachover] p. 466 | Axiom Union | axun2 7722 |
| [BellMachover] p. 468 | Definition | df-ord 6364 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6379 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6386 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6381 |
| [BellMachover] p. 471 | Definition of N | df-om 7851 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7784 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6366 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9633 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7866 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9755 |
| [BellMachover] p. 478 | Definition | rankval2 9809 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9773 r1ord3g 9770 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9586 |
| [BellMachover] p. 488 | Axiom AC | ac5 10468 dfac4 10113 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10101 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 38127 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 31584 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 31626 chirredi 31625 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 31614 |
| [Beran] p. 3 | Definition of join | sshjval3 30585 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 30847 cmcm2i 30824 cmcm2ii 30829 cmt2N 38058 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 30848 lecmi 30833 lecmii 30834 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 30822 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 30851 cm2ji 30856 cm2mi 30857 |
| [Beran] p. 95 | Definition | df-sh 30438 issh2 30440 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 30317 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 30330 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 30321 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 31059 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 31061 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 31060 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 31062 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 30313 his1i 30331 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 30314 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 30315 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 30316 |
| [Beran] p. 96 | Definition of norm | df-hnorm 30199 dfhnorm2 30353 normval 30355 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 30415 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 30204 |
| [Beran] p. 96 | Definition of complete subspace | isch3 30472 |
| [Beran] p. 96 | Definition of converge | df-hlim 30203 hlimi 30419 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 30364 norm-i 30360 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 30368 norm-ii 30369 normlem0 30340 normlem1 30341 normlem2 30342 normlem3 30343 normlem4 30344 normlem5 30345 normlem6 30346 normlem7 30347 normlem7tALT 30350 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 30370 norm-iii 30371 |
| [Beran] p. 98 | Remark 3.4 | bcs 30412 bcsiALT 30410 bcsiHIL 30411 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 30352 normpar 30386 normpari 30385 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 30377 normpyth 30376 normpythi 30373 |
| [Beran] p. 99 | Remark | lnfn0 31278 lnfn0i 31273 lnop0 31197 lnop0i 31201 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 31257 nmcfnex 31284 nmcfnexi 31282 nmcopex 31260 nmcopexi 31258 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 31285 nmcfnlbi 31283 nmcoplb 31261 nmcoplbi 31259 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 31287 lnfnconi 31286 lnopcon 31266 lnopconi 31265 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 30387 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 30384 norm3adifii 30379 norm3dif 30381 norm3difi 30378 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 30532 pjhth 30624 pjhtheu 30625 pjpjhth 30656 pjpjhthi 30657 pjth 24938 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 30637 ococi 30636 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 31292 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 31293 riesz4 31295 riesz4i 31294 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 31310 cnlnadjeu 31309 cnlnadjeui 31308 cnlnadji 31307 cnlnadjlem1 31298 nmopadjlei 31319 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 31322 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 31321 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 31323 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 31167 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 31333 nmopcoadji 31332 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 31324 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 31334 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 31331 pjadj2coi 31435 pjadjcoi 31392 |
| [Beran] p. 107 | Definition | df-ch 30452 isch2 30454 |
| [Beran] p. 107 | Remark 3.12 | choccl 30537 isch3 30472 occl 30535 ocsh 30514 shoccl 30536 shocsh 30515 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 30639 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 30563 |
| [Beran] p. 109 | Property (i) | pjadj2 31418 pjadj3 31419 pjadji 30916 pjadjii 30905 |
| [Beran] p. 109 | Property (ii) | pjidmco 31412 pjidmcoi 31408 pjidmi 30904 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 31404 |
| [Beran] p. 111 | Remark | ho0val 30981 pjch1 30901 |
| [Beran] p. 111 | Definition | df-hfmul 30965 df-hfsum 30964 df-hodif 30963 df-homul 30962 df-hosum 30961 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 30902 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 30925 pjchi 30663 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 30670 pjoc2i 30669 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 30911 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 31396 pjssmii 30912 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 31395 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 31394 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 31399 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 31397 pjssge0ii 30913 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 31398 pjdifnormii 30914 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1779 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1777 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1780 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1775 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 33229 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 33237 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 33235 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 33239 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 33259 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 33290 df-sitm 33268 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 33290 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 33267 |
| [Bollobas] p. 1 | Section I.1 | df-edg 28288 isuhgrop 28310 isusgrop 28402 isuspgrop 28401 |
| [Bollobas] p. 2 | Section I.1 | df-subgr 28505 uhgrspan1 28540 uhgrspansubgr 28528 |
| [Bollobas] p. 3 | Definition | isomuspgr 46437 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 28691 df-cusgr 28649 df-nbgr 28570 fusgrmaxsize 28701 |
| [Bollobas] p. 4 | Definition | df-upwlks 46447 df-wlks 28836 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 28787 finsumvtxdgeven 28789 fusgr1th 28788 fusgrvtxdgonume 28791 vtxdgoddnumeven 28790 |
| [Bollobas] p. 5 | Notation | df-pths 28953 |
| [Bollobas] p. 5 | Definition | df-crcts 29023 df-cycls 29024 df-trls 28929 df-wlkson 28837 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 28299 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 46545 df-cllaw 46531 df-mgm 18557 df-mgm2 46564 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 46546 df-asslaw 46533 df-sgrp 18606 df-sgrp2 46566 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 46565 df-comlaw 46532 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18622 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20049 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 46584 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7280 fcofo 7281 |
| [BourbakiTop1] p. | Remark | xnegmnf 13185 xnegpnf 13184 |
| [BourbakiTop1] p. | Remark | rexneg 13186 |
| [BourbakiTop1] p. | Remark 3 | ust0 23706 ustfilxp 23699 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 23576 |
| [BourbakiTop1] p. | Criterion | ishmeo 23245 |
| [BourbakiTop1] p. | Example 1 | cstucnd 23771 iducn 23770 snfil 23350 |
| [BourbakiTop1] p. | Example 2 | neifil 23366 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 23553 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 23791 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 32875 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23349 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 23763 df-ust 23687 filintn0 23347 filn0 23348 istgp 23563 ucnprima 23769 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 23774 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 23785 df-usp 23744 df-utop 23718 trust 23716 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 32774 |
| [BourbakiTop1] p. | Property V_i | ssnei2 22602 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 22755 |
| [BourbakiTop1] p. | Condition F_I | ustssel 23692 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 23695 |
| [BourbakiTop1] p. | Property V_ii | innei 22611 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 22619 neissex 22613 |
| [BourbakiTop1] p. | Proposition 1 | neips 22599 neiss 22595 ucncn 23772 ustund 23708 ustuqtop 23733 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 22753 neiptopreu 22619 utop2nei 23737 utop3cls 23738 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 23779 uspreg 23761 utopreg 23739 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23177 imasncls 23178 imasnopn 23176 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 23486 |
| [BourbakiTop1] p. | Condition F_II | ustincl 23694 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 23696 |
| [BourbakiTop1] p. | Property V_iii | elnei 22597 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 23790 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 23693 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 23697 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 22873 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23332 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 22378 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 32771 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 44713 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 44715 stoweid 44714 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 44652 stoweidlem10 44661 stoweidlem14 44665 stoweidlem15 44666 stoweidlem35 44686 stoweidlem36 44687 stoweidlem37 44688 stoweidlem38 44689 stoweidlem40 44691 stoweidlem41 44692 stoweidlem43 44694 stoweidlem44 44695 stoweidlem46 44697 stoweidlem5 44656 stoweidlem50 44701 stoweidlem52 44703 stoweidlem53 44704 stoweidlem55 44706 stoweidlem56 44707 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 44674 stoweidlem24 44675 stoweidlem27 44678 stoweidlem28 44679 stoweidlem30 44681 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 44685 stoweidlem59 44710 stoweidlem60 44711 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 44696 stoweidlem49 44700 stoweidlem7 44658 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 44682 stoweidlem39 44690 stoweidlem42 44693 stoweidlem48 44699 stoweidlem51 44702 stoweidlem54 44705 stoweidlem57 44708 stoweidlem58 44709 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 44676 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 44668 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 44662 stoweidlem13 44664 stoweidlem26 44677 stoweidlem61 44712 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 44669 |
| [Bruck] p. 1 | Section I.1 | df-clintop 46545 df-mgm 18557 df-mgm2 46564 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18606 df-sgrp2 46566 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 18918 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5231 |
| [Church] p. 129 | Section II.24 | df-ifp 1063 dfifp2 1064 |
| [Clemente] p. 10 | Definition IT | natded 29636 |
| [Clemente] p. 10 | Definition I` `m,n | natded 29636 |
| [Clemente] p. 11 | Definition E=>m,n | natded 29636 |
| [Clemente] p. 11 | Definition I=>m,n | natded 29636 |
| [Clemente] p. 11 | Definition E` `(1) | natded 29636 |
| [Clemente] p. 11 | Definition E` `(2) | natded 29636 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 29636 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 29636 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 29636 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 29636 |
| [Clemente] p. 14 | Proof 5.11 | natded 29636 |
| [Clemente] p. 14 | Definition E` `n | natded 29636 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 29638 ex-natded5.2 29637 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 29641 ex-natded5.3 29640 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 29643 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 29645 ex-natded5.7 29644 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 29647 ex-natded5.8 29646 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 29649 ex-natded5.13 29648 |
| [Clemente] p. 32 | Definition I` `n | natded 29636 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 29636 |
| [Clemente] p. 32 | Definition E` `n,t | natded 29636 |
| [Clemente] p. 32 | Definition I` `n,t | natded 29636 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 29650 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 29651 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 29653 ex-natded9.26 29652 |
| [Cohen] p. 301 | Remark | relogoprlem 26081 |
| [Cohen] p. 301 | Property 2 | relogmul 26082 relogmuld 26115 |
| [Cohen] p. 301 | Property 3 | relogdiv 26083 relogdivd 26116 |
| [Cohen] p. 301 | Property 4 | relogexp 26086 |
| [Cohen] p. 301 | Property 1a | log1 26076 |
| [Cohen] p. 301 | Property 1b | loge 26077 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26272 |
| [Cohen4] p. 349 | Property | relogbf 26276 |
| [Cohen4] p. 352 | Definition | elogb 26255 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26262 |
| [Cohen4] p. 361 | Property 3 | logbrec 26267 relogbdiv 26264 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26260 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26265 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26253 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26254 |
| [Cohen4] p. 367 | Property | logbchbase 26256 |
| [Cohen4] p. 377 | Property 2 | logblt 26269 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 33222 sxbrsigalem4 33224 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18506 acsinfd 18505 acsinfdimd 18507 acsmap2d 18504 acsmapd 18503 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 33227 |
| [Connell] p. 57 | Definition | df-scmat 21975 df-scmatalt 46982 |
| [Conway] p. 4 | Definition | slerec 27300 |
| [Conway] p. 5 | Definition | addsval 27426 addsval2 27427 df-adds 27424 df-muls 27543 df-negs 27476 |
| [Conway] p. 7 | Theorem | 0slt1s 27310 |
| [Conway] p. 16 | Theorem 0(i) | ssltright 27346 |
| [Conway] p. 16 | Theorem 0(ii) | ssltleft 27345 |
| [Conway] p. 16 | Theorem 0(iii) | slerflex 27246 |
| [Conway] p. 17 | Theorem 3 | addsass 27468 addsassd 27469 addscom 27430 addscomd 27431 addsrid 27428 addsridd 27429 |
| [Conway] p. 17 | Definition | df-0s 27305 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 27498 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 27495 negsidd 27496 |
| [Conway] p. 18 | Theorem 5 | sleadd1 27452 sleadd1d 27458 |
| [Conway] p. 18 | Definition | df-1s 27306 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 27490 negscld 27491 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 27444 |
| [Conway] p. 19 | Theorem 7 | addsdi 27590 addsdid 27591 addsdird 27592 mulnegs1d 27595 mulnegs2d 27596 mulsass 27601 mulsassd 27602 mulscom 27575 mulscomd 27576 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 27570 mulscld 27571 |
| [Conway] p. 19 | Theorem 8(iii) | slemuld 27574 sltmul 27572 sltmuld 27573 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 27580 mulsgt0d 27581 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 27644 |
| [Conway] p. 29 | Remark | madebday 27374 newbday 27376 oldbday 27375 |
| [Conway] p. 29 | Definition | df-made 27322 df-new 27324 df-old 27323 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13822 |
| [Crawley] p. 1 | Definition of poset | df-poset 18262 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 38195 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 38999 dalaw 38695 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 40774 |
| [Crawley] p. 111 | Definition of set W | df-watsN 38799 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 38915 df-ldil 38913 isldil 38919 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 38914 df-trnN 38916 isltrn 38928 ltrnu 38930 |
| [Crawley] p. 112 | Lemma A | cdlema1N 38600 cdlema2N 38601 exatleN 38213 |
| [Crawley] p. 112 | Lemma B | 1cvrat 38285 cdlemb 38603 cdlemb2 38850 cdlemb3 39415 idltrn 38959 l1cvat 37863 lhpat 38852 lhpat2 38854 lshpat 37864 ltrnel 38948 ltrnmw 38960 |
| [Crawley] p. 112 | Lemma C | cdlemc1 39000 cdlemc2 39001 ltrnnidn 38983 trlat 38978 trljat1 38975 trljat2 38976 trljat3 38977 trlne 38994 trlnidat 38982 trlnle 38995 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 38800 |
| [Crawley] p. 113 | Lemma C | cdlemc 39006 cdlemc3 39002 cdlemc4 39003 |
| [Crawley] p. 113 | Lemma D | cdlemd 39016 cdlemd1 39007 cdlemd2 39008 cdlemd3 39009 cdlemd4 39010 cdlemd5 39011 cdlemd6 39012 cdlemd7 39013 cdlemd8 39014 cdlemd9 39015 cdleme31sde 39194 cdleme31se 39191 cdleme31se2 39192 cdleme31snd 39195 cdleme32a 39250 cdleme32b 39251 cdleme32c 39252 cdleme32d 39253 cdleme32e 39254 cdleme32f 39255 cdleme32fva 39246 cdleme32fva1 39247 cdleme32fvcl 39249 cdleme32le 39256 cdleme48fv 39308 cdleme4gfv 39316 cdleme50eq 39350 cdleme50f 39351 cdleme50f1 39352 cdleme50f1o 39355 cdleme50laut 39356 cdleme50ldil 39357 cdleme50lebi 39349 cdleme50rn 39354 cdleme50rnlem 39353 cdlemeg49le 39320 cdlemeg49lebilem 39348 |
| [Crawley] p. 113 | Lemma E | cdleme 39369 cdleme00a 39018 cdleme01N 39030 cdleme02N 39031 cdleme0a 39020 cdleme0aa 39019 cdleme0b 39021 cdleme0c 39022 cdleme0cp 39023 cdleme0cq 39024 cdleme0dN 39025 cdleme0e 39026 cdleme0ex1N 39032 cdleme0ex2N 39033 cdleme0fN 39027 cdleme0gN 39028 cdleme0moN 39034 cdleme1 39036 cdleme10 39063 cdleme10tN 39067 cdleme11 39079 cdleme11a 39069 cdleme11c 39070 cdleme11dN 39071 cdleme11e 39072 cdleme11fN 39073 cdleme11g 39074 cdleme11h 39075 cdleme11j 39076 cdleme11k 39077 cdleme11l 39078 cdleme12 39080 cdleme13 39081 cdleme14 39082 cdleme15 39087 cdleme15a 39083 cdleme15b 39084 cdleme15c 39085 cdleme15d 39086 cdleme16 39094 cdleme16aN 39068 cdleme16b 39088 cdleme16c 39089 cdleme16d 39090 cdleme16e 39091 cdleme16f 39092 cdleme16g 39093 cdleme19a 39112 cdleme19b 39113 cdleme19c 39114 cdleme19d 39115 cdleme19e 39116 cdleme19f 39117 cdleme1b 39035 cdleme2 39037 cdleme20aN 39118 cdleme20bN 39119 cdleme20c 39120 cdleme20d 39121 cdleme20e 39122 cdleme20f 39123 cdleme20g 39124 cdleme20h 39125 cdleme20i 39126 cdleme20j 39127 cdleme20k 39128 cdleme20l 39131 cdleme20l1 39129 cdleme20l2 39130 cdleme20m 39132 cdleme20y 39111 cdleme20zN 39110 cdleme21 39146 cdleme21d 39139 cdleme21e 39140 cdleme22a 39149 cdleme22aa 39148 cdleme22b 39150 cdleme22cN 39151 cdleme22d 39152 cdleme22e 39153 cdleme22eALTN 39154 cdleme22f 39155 cdleme22f2 39156 cdleme22g 39157 cdleme23a 39158 cdleme23b 39159 cdleme23c 39160 cdleme26e 39168 cdleme26eALTN 39170 cdleme26ee 39169 cdleme26f 39172 cdleme26f2 39174 cdleme26f2ALTN 39173 cdleme26fALTN 39171 cdleme27N 39178 cdleme27a 39176 cdleme27cl 39175 cdleme28c 39181 cdleme3 39046 cdleme30a 39187 cdleme31fv 39199 cdleme31fv1 39200 cdleme31fv1s 39201 cdleme31fv2 39202 cdleme31id 39203 cdleme31sc 39193 cdleme31sdnN 39196 cdleme31sn 39189 cdleme31sn1 39190 cdleme31sn1c 39197 cdleme31sn2 39198 cdleme31so 39188 cdleme35a 39257 cdleme35b 39259 cdleme35c 39260 cdleme35d 39261 cdleme35e 39262 cdleme35f 39263 cdleme35fnpq 39258 cdleme35g 39264 cdleme35h 39265 cdleme35h2 39266 cdleme35sn2aw 39267 cdleme35sn3a 39268 cdleme36a 39269 cdleme36m 39270 cdleme37m 39271 cdleme38m 39272 cdleme38n 39273 cdleme39a 39274 cdleme39n 39275 cdleme3b 39038 cdleme3c 39039 cdleme3d 39040 cdleme3e 39041 cdleme3fN 39042 cdleme3fa 39045 cdleme3g 39043 cdleme3h 39044 cdleme4 39047 cdleme40m 39276 cdleme40n 39277 cdleme40v 39278 cdleme40w 39279 cdleme41fva11 39286 cdleme41sn3aw 39283 cdleme41sn4aw 39284 cdleme41snaw 39285 cdleme42a 39280 cdleme42b 39287 cdleme42c 39281 cdleme42d 39282 cdleme42e 39288 cdleme42f 39289 cdleme42g 39290 cdleme42h 39291 cdleme42i 39292 cdleme42k 39293 cdleme42ke 39294 cdleme42keg 39295 cdleme42mN 39296 cdleme42mgN 39297 cdleme43aN 39298 cdleme43bN 39299 cdleme43cN 39300 cdleme43dN 39301 cdleme5 39049 cdleme50ex 39368 cdleme50ltrn 39366 cdleme51finvN 39365 cdleme51finvfvN 39364 cdleme51finvtrN 39367 cdleme6 39050 cdleme7 39058 cdleme7a 39052 cdleme7aa 39051 cdleme7b 39053 cdleme7c 39054 cdleme7d 39055 cdleme7e 39056 cdleme7ga 39057 cdleme8 39059 cdleme8tN 39064 cdleme9 39062 cdleme9a 39060 cdleme9b 39061 cdleme9tN 39066 cdleme9taN 39065 cdlemeda 39107 cdlemedb 39106 cdlemednpq 39108 cdlemednuN 39109 cdlemefr27cl 39212 cdlemefr32fva1 39219 cdlemefr32fvaN 39218 cdlemefrs32fva 39209 cdlemefrs32fva1 39210 cdlemefs27cl 39222 cdlemefs32fva1 39232 cdlemefs32fvaN 39231 cdlemesner 39105 cdlemeulpq 39029 |
| [Crawley] p. 114 | Lemma E | 4atex 38885 4atexlem7 38884 cdleme0nex 39099 cdleme17a 39095 cdleme17c 39097 cdleme17d 39307 cdleme17d1 39098 cdleme17d2 39304 cdleme18a 39100 cdleme18b 39101 cdleme18c 39102 cdleme18d 39104 cdleme4a 39048 |
| [Crawley] p. 115 | Lemma E | cdleme21a 39134 cdleme21at 39137 cdleme21b 39135 cdleme21c 39136 cdleme21ct 39138 cdleme21f 39141 cdleme21g 39142 cdleme21h 39143 cdleme21i 39144 cdleme22gb 39103 |
| [Crawley] p. 116 | Lemma F | cdlemf 39372 cdlemf1 39370 cdlemf2 39371 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 39376 cdlemg16 39466 cdlemg28 39513 cdlemg28a 39502 cdlemg28b 39512 cdlemg3a 39406 cdlemg42 39538 cdlemg43 39539 cdlemg44 39542 cdlemg44a 39540 cdlemg46 39544 cdlemg47 39545 cdlemg9 39443 ltrnco 39528 ltrncom 39547 tgrpabl 39560 trlco 39536 |
| [Crawley] p. 116 | Definition of G | df-tgrp 39552 |
| [Crawley] p. 117 | Lemma G | cdlemg17 39486 cdlemg17b 39471 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 39565 df-edring 39566 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 39569 |
| [Crawley] p. 118 | Remark | tendopltp 39589 |
| [Crawley] p. 118 | Lemma H | cdlemh 39626 cdlemh1 39624 cdlemh2 39625 |
| [Crawley] p. 118 | Lemma I | cdlemi 39629 cdlemi1 39627 cdlemi2 39628 |
| [Crawley] p. 118 | Lemma J | cdlemj1 39630 cdlemj2 39631 cdlemj3 39632 tendocan 39633 |
| [Crawley] p. 118 | Lemma K | cdlemk 39783 cdlemk1 39640 cdlemk10 39652 cdlemk11 39658 cdlemk11t 39755 cdlemk11ta 39738 cdlemk11tb 39740 cdlemk11tc 39754 cdlemk11u-2N 39698 cdlemk11u 39680 cdlemk12 39659 cdlemk12u-2N 39699 cdlemk12u 39681 cdlemk13-2N 39685 cdlemk13 39661 cdlemk14-2N 39687 cdlemk14 39663 cdlemk15-2N 39688 cdlemk15 39664 cdlemk16-2N 39689 cdlemk16 39666 cdlemk16a 39665 cdlemk17-2N 39690 cdlemk17 39667 cdlemk18-2N 39695 cdlemk18-3N 39709 cdlemk18 39677 cdlemk19-2N 39696 cdlemk19 39678 cdlemk19u 39779 cdlemk1u 39668 cdlemk2 39641 cdlemk20-2N 39701 cdlemk20 39683 cdlemk21-2N 39700 cdlemk21N 39682 cdlemk22-3 39710 cdlemk22 39702 cdlemk23-3 39711 cdlemk24-3 39712 cdlemk25-3 39713 cdlemk26-3 39715 cdlemk26b-3 39714 cdlemk27-3 39716 cdlemk28-3 39717 cdlemk29-3 39720 cdlemk3 39642 cdlemk30 39703 cdlemk31 39705 cdlemk32 39706 cdlemk33N 39718 cdlemk34 39719 cdlemk35 39721 cdlemk36 39722 cdlemk37 39723 cdlemk38 39724 cdlemk39 39725 cdlemk39u 39777 cdlemk4 39643 cdlemk41 39729 cdlemk42 39750 cdlemk42yN 39753 cdlemk43N 39772 cdlemk45 39756 cdlemk46 39757 cdlemk47 39758 cdlemk48 39759 cdlemk49 39760 cdlemk5 39645 cdlemk50 39761 cdlemk51 39762 cdlemk52 39763 cdlemk53 39766 cdlemk54 39767 cdlemk55 39770 cdlemk55u 39775 cdlemk56 39780 cdlemk5a 39644 cdlemk5auN 39669 cdlemk5u 39670 cdlemk6 39646 cdlemk6u 39671 cdlemk7 39657 cdlemk7u-2N 39697 cdlemk7u 39679 cdlemk8 39647 cdlemk9 39648 cdlemk9bN 39649 cdlemki 39650 cdlemkid 39745 cdlemkj-2N 39691 cdlemkj 39672 cdlemksat 39655 cdlemksel 39654 cdlemksv 39653 cdlemksv2 39656 cdlemkuat 39675 cdlemkuel-2N 39693 cdlemkuel-3 39707 cdlemkuel 39674 cdlemkuv-2N 39692 cdlemkuv2-2 39694 cdlemkuv2-3N 39708 cdlemkuv2 39676 cdlemkuvN 39673 cdlemkvcl 39651 cdlemky 39735 cdlemkyyN 39771 tendoex 39784 |
| [Crawley] p. 120 | Remark | dva1dim 39794 |
| [Crawley] p. 120 | Lemma L | cdleml1N 39785 cdleml2N 39786 cdleml3N 39787 cdleml4N 39788 cdleml5N 39789 cdleml6 39790 cdleml7 39791 cdleml8 39792 cdleml9 39793 dia1dim 39870 |
| [Crawley] p. 120 | Lemma M | dia11N 39857 diaf11N 39858 dialss 39855 diaord 39856 dibf11N 39970 djajN 39946 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 39841 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 39927 dia2dimlem1 39873 dia2dimlem2 39874 dia2dimlem3 39875 dia2dimlem4 39876 dia2dimlem5 39877 diaf1oN 39939 diarnN 39938 dvheveccl 39921 dvhopN 39925 |
| [Crawley] p. 121 | Lemma N | cdlemn 40021 cdlemn10 40015 cdlemn11 40020 cdlemn11a 40016 cdlemn11b 40017 cdlemn11c 40018 cdlemn11pre 40019 cdlemn2 40004 cdlemn2a 40005 cdlemn3 40006 cdlemn4 40007 cdlemn4a 40008 cdlemn5 40010 cdlemn5pre 40009 cdlemn6 40011 cdlemn7 40012 cdlemn8 40013 cdlemn9 40014 diclspsn 40003 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 39982 |
| [Crawley] p. 122 | Lemma N | dih11 40074 dihf11 40076 dihjust 40026 dihjustlem 40025 dihord 40073 dihord1 40027 dihord10 40032 dihord11b 40031 dihord11c 40033 dihord2 40036 dihord2a 40028 dihord2b 40029 dihord2cN 40030 dihord2pre 40034 dihord2pre2 40035 dihordlem6 40022 dihordlem7 40023 dihordlem7b 40024 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 40039 dihfval 40040 dihval 40041 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 28649 df-nbgr 28570 |
| [Diestel] p. 4 | Section 1.1 | df-subgr 28505 uhgrspan1 28540 uhgrspansubgr 28528 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 28791 vtxdgoddnumeven 28790 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 28299 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 32782 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 32794 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 32786 zarcls1 32787 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 32797 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 32800 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 32803 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3950 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9638 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8818 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9646 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9971 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10546 |
| [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 31767 iunin2 5073 uniin1 31761 uniin2 31762 |
| [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 7753 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 7898 rnexg 7890 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5912 rnuni 6145 |
| [Enderton] p. 42 | Definition of a function | dffun7 6572 dffun8 6573 |
| [Enderton] p. 43 | Definition of function value | funfv2 6975 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6614 |
| [Enderton] p. 44 | Definition (d) | dfima2 6059 dfima3 6060 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6984 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10464 ac7g 10465 df-ac 10107 dfac2 10122 dfac2a 10120 dfac2b 10121 dfac3 10112 dfac7 10123 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7240 |
| [Enderton] p. 52 | Definition | df-map 8818 |
| [Enderton] p. 53 | Exercise 21 | coass 6261 |
| [Enderton] p. 53 | Exercise 27 | dmco 6250 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6621 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6098 |
| [Enderton] p. 54 | Remark | ixpf 8910 ixpssmap 8922 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8888 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10474 ac9s 10484 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 37418 erref 8719 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 37421 erthi 8750 |
| [Enderton] p. 57 | Definition | df-ec 8701 |
| [Enderton] p. 58 | Definition | df-qs 8705 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8701 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5908 |
| [Enderton] p. 68 | Definition of successor | df-suc 6367 |
| [Enderton] p. 71 | Definition | df-tr 5265 dftr4 5271 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6440 unisucg 6439 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6440 unisucg 6439 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5280 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5282 trintALT 43575 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8600 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8602 onasuc 8523 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7407 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8601 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8603 onmsuc 8524 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8618 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8605 nnacom 8613 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8619 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8620 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8622 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8606 nnmsucr 8621 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8634 |
| [Enderton] p. 129 | Definition | df-en 8936 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7357 |
| [Enderton] p. 133 | Exercise 1 | xpomen 10006 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16152 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9206 |
| [Enderton] p. 135 | Corollary 6C | php3 9208 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9205 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9252 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9254 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9164 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9169 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9137 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10170 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10171 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10166 dju1en 10162 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9336 unifi 9337 unifi2 9338 |
| [Enderton] p. 144 | Corollary 6K | undif2 4475 unfi 9168 unfi2 9311 |
| [Enderton] p. 145 | Figure 38 | ffoss 7927 |
| [Enderton] p. 145 | Definition | df-dom 8937 |
| [Enderton] p. 146 | Example 1 | domen 8953 domeng 8954 |
| [Enderton] p. 146 | Example 3 | nndomo 9229 nnsdom 9645 nnsdomg 9298 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10174 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9138 xpdom1 9067 xpdom1g 9065 xpdom2g 9064 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9144 |
| [Enderton] p. 151 | Theorem 6M | zorn 10498 zorng 10495 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10483 dfac5 10119 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10566 |
| [Enderton] p. 164 | Example | infdif 10200 |
| [Enderton] p. 168 | Definition | df-po 5587 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6475 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6407 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6474 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6415 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7822 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7763 |
| [Enderton] p. 194 | Remark | onprc 7760 |
| [Enderton] p. 194 | Exercise 16 | suc11 6468 |
| [Enderton] p. 197 | Definition | df-card 9930 |
| [Enderton] p. 197 | Theorem 7P | carden 10542 |
| [Enderton] p. 200 | Exercise 25 | tfis 7839 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9767 |
| [Enderton] p. 202 | Definition | df-r1 9755 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9777 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9858 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9597 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9848 rankprb 9842 rankpw 9834 rankpwi 9814 rankuniss 9857 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9609 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9610 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10101 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 10067 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10081 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8336 |
| [Enderton] p. 222 | Definition of kard | karden 9886 kardex 9885 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8593 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8595 |
| [Enderton] p. 240 | Exercise 25 | oarec 8558 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10241 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17582 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17528 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18502 mrieqv2d 17579 mrieqvd 17578 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17583 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17588 mreexexlem2d 17585 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18508 mreexfidimd 17590 |
| [Frege1879] p. 11 | Statement | df3or2 42452 |
| [Frege1879] p. 12 | Statement | df3an2 42453 dfxor4 42450 dfxor5 42451 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 42474 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 42475 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 42479 |
| [Frege1879] p. 31 | Proposition 4 | frege4 42483 |
| [Frege1879] p. 32 | Proposition 5 | frege5 42484 |
| [Frege1879] p. 33 | Proposition 6 | frege6 42490 |
| [Frege1879] p. 34 | Proposition 7 | frege7 42492 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 42493 axfrege8 42491 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 90 wl-luk-pm2.04 36264 |
| [Frege1879] p. 35 | Proposition 9 | frege9 42496 |
| [Frege1879] p. 36 | Proposition 10 | frege10 42504 |
| [Frege1879] p. 36 | Proposition 11 | frege11 42498 |
| [Frege1879] p. 37 | Proposition 12 | frege12 42497 |
| [Frege1879] p. 37 | Proposition 13 | frege13 42506 |
| [Frege1879] p. 37 | Proposition 14 | frege14 42507 |
| [Frege1879] p. 38 | Proposition 15 | frege15 42510 |
| [Frege1879] p. 38 | Proposition 16 | frege16 42500 |
| [Frege1879] p. 39 | Proposition 17 | frege17 42505 |
| [Frege1879] p. 39 | Proposition 18 | frege18 42502 |
| [Frege1879] p. 39 | Proposition 19 | frege19 42508 |
| [Frege1879] p. 40 | Proposition 20 | frege20 42512 |
| [Frege1879] p. 40 | Proposition 21 | frege21 42511 |
| [Frege1879] p. 41 | Proposition 22 | frege22 42503 |
| [Frege1879] p. 42 | Proposition 23 | frege23 42509 |
| [Frege1879] p. 42 | Proposition 24 | frege24 42499 |
| [Frege1879] p. 42 | Proposition 25 | frege25 42501 rp-frege25 42489 |
| [Frege1879] p. 42 | Proposition 26 | frege26 42494 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 42514 |
| [Frege1879] p. 43 | Proposition 27 | frege27 42495 |
| [Frege1879] p. 43 | Proposition 28 | con3 153 |
| [Frege1879] p. 43 | Proposition 29 | frege29 42515 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 42518 axfrege31 42517 |
| [Frege1879] p. 44 | Proposition 30 | frege30 42516 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 130 |
| [Frege1879] p. 44 | Proposition 32 | frege32 42519 |
| [Frege1879] p. 44 | Proposition 33 | frege33 42520 |
| [Frege1879] p. 45 | Proposition 34 | frege34 42521 |
| [Frege1879] p. 45 | Proposition 35 | frege35 42522 |
| [Frege1879] p. 45 | Proposition 36 | frege36 42523 |
| [Frege1879] p. 46 | Proposition 37 | frege37 42524 |
| [Frege1879] p. 46 | Proposition 38 | frege38 42525 |
| [Frege1879] p. 46 | Proposition 39 | frege39 42526 |
| [Frege1879] p. 46 | Proposition 40 | frege40 42527 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 42529 axfrege41 42528 |
| [Frege1879] p. 47 | Proposition 41 | notnot 142 |
| [Frege1879] p. 47 | Proposition 42 | frege42 42530 |
| [Frege1879] p. 47 | Proposition 43 | frege43 42531 |
| [Frege1879] p. 47 | Proposition 44 | frege44 42532 |
| [Frege1879] p. 47 | Proposition 45 | frege45 42533 |
| [Frege1879] p. 48 | Proposition 46 | frege46 42534 |
| [Frege1879] p. 48 | Proposition 47 | frege47 42535 |
| [Frege1879] p. 49 | Proposition 48 | frege48 42536 |
| [Frege1879] p. 49 | Proposition 49 | frege49 42537 |
| [Frege1879] p. 49 | Proposition 50 | frege50 42538 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 42541 ax-frege52c 42572 frege52aid 42542 frege52b 42573 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 42546 ax-frege54c 42576 frege54b 42577 |
| [Frege1879] p. 50 | Proposition 51 | frege51 42539 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3778 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 42544 frege53aid 42543 frege53b 42574 frege53c 42598 |
| [Frege1879] p. 50 | Proposition 54 | biid 261 eqid 2733 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 42552 frege55aid 42549 frege55b 42581 frege55c 42602 frege55cor1a 42553 frege55lem2a 42551 frege55lem2b 42580 frege55lem2c 42601 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 42555 frege56aid 42554 frege56b 42582 frege56c 42603 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 42559 ax-frege58b 42585 frege58bid 42586 frege58c 42605 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 42557 frege57aid 42556 frege57b 42583 frege57c 42604 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3789 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 42561 frege59b 42588 frege59c 42606 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 42562 frege60b 42589 frege60c 42607 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 42563 frege61b 42590 frege61c 42608 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 42564 frege62b 42591 frege62c 42609 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 42565 frege63b 42592 frege63c 42610 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 42566 frege64b 42593 frege64c 42611 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 42567 frege65b 42594 frege65c 42612 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 42568 frege66b 42595 frege66c 42613 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 42569 frege67b 42596 frege67c 42614 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 42570 frege68b 42597 frege68c 42615 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 42616 |
| [Frege1879] p. 58 | Proposition 70 | frege70 42617 |
| [Frege1879] p. 59 | Proposition 71 | frege71 42618 |
| [Frege1879] p. 59 | Proposition 72 | frege72 42619 |
| [Frege1879] p. 59 | Proposition 73 | frege73 42620 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 42623 |
| [Frege1879] p. 60 | Proposition 74 | frege74 42621 |
| [Frege1879] p. 60 | Proposition 75 | frege75 42622 |
| [Frege1879] p. 62 | Proposition 77 | frege77 42624 frege77d 42430 |
| [Frege1879] p. 63 | Proposition 78 | frege78 42625 |
| [Frege1879] p. 63 | Proposition 79 | frege79 42626 |
| [Frege1879] p. 63 | Proposition 80 | frege80 42627 |
| [Frege1879] p. 63 | Proposition 81 | frege81 42628 frege81d 42431 |
| [Frege1879] p. 64 | Proposition 82 | frege82 42629 |
| [Frege1879] p. 65 | Proposition 83 | frege83 42630 frege83d 42432 |
| [Frege1879] p. 65 | Proposition 84 | frege84 42631 |
| [Frege1879] p. 66 | Proposition 85 | frege85 42632 |
| [Frege1879] p. 66 | Proposition 86 | frege86 42633 |
| [Frege1879] p. 66 | Proposition 87 | frege87 42634 frege87d 42434 |
| [Frege1879] p. 67 | Proposition 88 | frege88 42635 |
| [Frege1879] p. 68 | Proposition 89 | frege89 42636 |
| [Frege1879] p. 68 | Proposition 90 | frege90 42637 |
| [Frege1879] p. 68 | Proposition 91 | frege91 42638 frege91d 42435 |
| [Frege1879] p. 69 | Proposition 92 | frege92 42639 |
| [Frege1879] p. 70 | Proposition 93 | frege93 42640 |
| [Frege1879] p. 70 | Proposition 94 | frege94 42641 |
| [Frege1879] p. 70 | Proposition 95 | frege95 42642 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 42646 |
| [Frege1879] p. 71 | Proposition 96 | frege96 42643 frege96d 42433 |
| [Frege1879] p. 71 | Proposition 97 | frege97 42644 frege97d 42436 |
| [Frege1879] p. 71 | Proposition 98 | frege98 42645 frege98d 42437 |
| [Frege1879] p. 72 | Proposition 100 | frege100 42647 |
| [Frege1879] p. 72 | Proposition 101 | frege101 42648 |
| [Frege1879] p. 72 | Proposition 102 | frege102 42649 frege102d 42438 |
| [Frege1879] p. 73 | Proposition 103 | frege103 42650 |
| [Frege1879] p. 73 | Proposition 104 | frege104 42651 |
| [Frege1879] p. 73 | Proposition 105 | frege105 42652 |
| [Frege1879] p. 73 | Proposition 106 | frege106 42653 frege106d 42439 |
| [Frege1879] p. 74 | Proposition 107 | frege107 42654 |
| [Frege1879] p. 74 | Proposition 108 | frege108 42655 frege108d 42440 |
| [Frege1879] p. 74 | Proposition 109 | frege109 42656 frege109d 42441 |
| [Frege1879] p. 75 | Proposition 110 | frege110 42657 |
| [Frege1879] p. 75 | Proposition 111 | frege111 42658 frege111d 42443 |
| [Frege1879] p. 76 | Proposition 112 | frege112 42659 |
| [Frege1879] p. 76 | Proposition 113 | frege113 42660 |
| [Frege1879] p. 76 | Proposition 114 | frege114 42661 frege114d 42442 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 42662 |
| [Frege1879] p. 77 | Proposition 116 | frege116 42663 |
| [Frege1879] p. 78 | Proposition 117 | frege117 42664 |
| [Frege1879] p. 78 | Proposition 118 | frege118 42665 |
| [Frege1879] p. 78 | Proposition 119 | frege119 42666 |
| [Frege1879] p. 78 | Proposition 120 | frege120 42667 |
| [Frege1879] p. 79 | Proposition 121 | frege121 42668 |
| [Frege1879] p. 79 | Proposition 122 | frege122 42669 frege122d 42444 |
| [Frege1879] p. 79 | Proposition 123 | frege123 42670 |
| [Frege1879] p. 80 | Proposition 124 | frege124 42671 frege124d 42445 |
| [Frege1879] p. 81 | Proposition 125 | frege125 42672 |
| [Frege1879] p. 81 | Proposition 126 | frege126 42673 frege126d 42446 |
| [Frege1879] p. 82 | Proposition 127 | frege127 42674 |
| [Frege1879] p. 83 | Proposition 128 | frege128 42675 |
| [Frege1879] p. 83 | Proposition 129 | frege129 42676 frege129d 42447 |
| [Frege1879] p. 84 | Proposition 130 | frege130 42677 |
| [Frege1879] p. 85 | Proposition 131 | frege131 42678 frege131d 42448 |
| [Frege1879] p. 86 | Proposition 132 | frege132 42679 |
| [Frege1879] p. 86 | Proposition 133 | frege133 42680 frege133d 42449 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 44964 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 45287 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 44987 |
| [Fremlin1] p. 14 | Definition 112A | ismea 45102 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 45122 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 45113 meadjunre 45127 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 45114 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 45115 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 45111 meaiunle 45120 meaiunlelem 45119 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 45132 meaiuninc2 45133 meaiuninc3 45136 meaiuninc3v 45135 meaiunincf 45134 meaiuninclem 45131 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 45138 meaiininc2 45139 meaiininclem 45137 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 45157 caragendifcl 45165 caratheodory 45179 omelesplit 45169 |
| [Fremlin1] p. 19 | Definition 113A | isome 45145 isomennd 45182 isomenndlem 45181 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 45167 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 45186 voncmpl 45272 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 45149 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 45174 carageniuncllem1 45172 carageniuncllem2 45173 caragenuncl 45164 caragenuncllem 45163 caragenunicl 45175 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 45183 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 45177 caratheodorylem2 45178 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 45186 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 45245 hoidmv1lelem1 45242 hoidmv1lelem2 45243 hoidmv1lelem3 45244 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 45289 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 45245 hoidmvle 45251 hoidmvlelem1 45246 hoidmvlelem2 45247 hoidmvlelem3 45248 hoidmvlelem4 45249 hoidmvlelem5 45250 hsphoidmvle2 45236 hsphoif 45227 hsphoival 45230 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 45199 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 45207 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 45234 hoidmvn0val 45235 hoidmvval 45228 hoidmvval0 45238 hoidmvval0b 45241 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 45239 hsphoidmvle 45237 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 45188 df-voln 45190 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 45255 ovn0 45217 ovn0lem 45216 ovnf 45214 ovnome 45224 ovnssle 45212 ovnsslelem 45211 ovnsupge0 45208 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 45254 ovnhoilem1 45252 ovnhoilem2 45253 vonhoi 45318 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 45271 hoidifhspf 45269 hoidifhspval 45259 hoidifhspval2 45266 hoidifhspval3 45270 hspmbl 45280 hspmbllem1 45277 hspmbllem2 45278 hspmbllem3 45279 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 45272 vonmea 45225 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 45223 ovnsubadd2 45297 ovnsubadd2lem 45296 ovnsubaddlem1 45221 ovnsubaddlem2 45222 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 45282 hoimbl2 45316 hoimbllem 45281 hspdifhsp 45267 opnvonmbl 45285 opnvonmbllem2 45284 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 45287 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 45330 iccvonmbllem 45329 ioovonmbl 45328 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 45336 vonicclem2 45335 vonioo 45333 vonioolem2 45332 vonn0icc 45339 vonn0icc2 45343 vonn0ioo 45338 vonn0ioo2 45341 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 45340 snvonmbl 45337 vonct 45344 vonsn 45342 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 45010 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 45009 subsaliuncllem 45008 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 45376 salpreimalegt 45360 salpreimaltle 45377 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 45379 issmff 45385 issmflem 45378 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 45396 issmflelem 45395 smfpreimale 45405 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 45407 issmfgtlem 45406 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 45347 issmf 45379 issmff 45385 issmfge 45421 issmfgelem 45420 issmfgt 45407 issmfgtlem 45406 issmfle 45396 issmflelem 45395 issmflem 45378 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 45358 salpreimagtlt 45381 salpreimalelt 45380 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 45421 issmfgelem 45420 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 45404 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 45402 cnfsmf 45391 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 45418 decsmflem 45417 incsmf 45393 incsmflem 45392 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 45352 pimconstlt1 45353 smfconst 45400 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 45416 smfaddlem1 45414 smfaddlem2 45415 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 45447 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 45446 smfmullem1 45442 smfmullem2 45443 smfmullem3 45444 smfmullem4 45445 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 45448 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 45451 smfpimbor1lem2 45450 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 45453 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 45441 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 45440 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 45449 smfresal 45439 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 45428 smflim2 45457 smflimlem1 45422 smflimlem2 45423 smflimlem3 45424 smflimlem4 45425 smflimlem5 45426 smflimlem6 45427 smflimmpt 45461 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 45465 smfsuplem1 45462 smfsuplem2 45463 smfsuplem3 45464 smfsupmpt 45466 smfsupxr 45467 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 45469 smfinflem 45468 smfinfmpt 45470 |
| [Fremlin1] p. 39 | Remark 121G | smflim 45428 smflim2 45457 smflimmpt 45461 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 45459 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 45489 smfdivdmmbl2 45492 smfinfdmmbl 45500 smfinfdmmbllem 45499 smfsupdmmbl 45496 smfsupdmmbllem 45495 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 45479 smflimsuplem2 45472 smflimsuplem6 45476 smflimsuplem7 45477 smflimsuplem8 45478 smflimsupmpt 45480 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 45482 smfliminflem 45481 smfliminfmpt 45483 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 45347 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 45493 fsupdm2 45494 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 45484 adddmmbl2 45485 finfdm 45497 finfdm2 45498 fsupdm 45493 fsupdm2 45494 muldmmbl 45486 muldmmbl2 45487 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 45497 finfdm2 45498 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25035 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25078 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25088 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 36504 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 36507 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9629 inf1 9613 inf2 9614 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10902 enqer 10912 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10907 df-nq 10903 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10899 df-plq 10905 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7639 df-mpq 10900 df-mq 10906 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10908 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10966 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10967 ltbtwnnq 10969 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10962 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10963 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10970 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10972 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 10984 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 10986 |
| [Gleason] p. 122 | Definition | df-1p 10973 |
| [Gleason] p. 122 | Remark (1) | prub 10985 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 11024 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10976 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 11023 psslinpr 11022 supexpr 11045 suplem1pr 11043 suplem2pr 11044 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 11009 addclprlem1 11007 addclprlem2 11008 df-plp 10974 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 11013 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 11012 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 11025 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 11034 ltexprlem1 11027 ltexprlem2 11028 ltexprlem3 11029 ltexprlem4 11030 ltexprlem5 11031 ltexprlem6 11032 ltexprlem7 11033 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 11036 ltaprlem 11035 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 11037 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 11038 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10975 mulclpr 11011 mulclprlem 11010 reclem2pr 11039 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 11020 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 11015 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 11014 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 11019 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 11042 reclem3pr 11040 reclem4pr 11041 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 11046 enrer 11054 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 11051 df-1r 11052 df-nr 11047 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 11049 df-plr 11048 negexsr 11093 recexsr 11098 recexsrlem 11094 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 11050 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12203 creur 12202 cru 12200 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11179 axcnre 11155 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15058 crimd 15175 crimi 15136 crre 15057 crred 15174 crrei 15135 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15060 remimd 15141 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15227 absval2d 15388 absval2i 15340 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15084 cjaddd 15163 cjaddi 15131 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15085 cjmuld 15164 cjmuli 15132 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15083 cjcjd 15142 cjcji 15114 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15082 cjreb 15066 cjrebd 15145 cjrebi 15117 cjred 15169 rere 15065 rereb 15063 rerebd 15144 rerebi 15116 rered 15167 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15091 addcjd 15155 addcji 15126 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15181 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15222 abscjd 15393 abscji 15344 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15232 abs00d 15389 abs00i 15341 absne0d 15390 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15264 releabsd 15394 releabsi 15345 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15237 absmuld 15397 absmuli 15347 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15225 sqabsaddi 15348 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15273 abstrid 15399 abstrii 15351 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14024 exp0 14027 expp1 14030 expp1d 14108 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26169 cxpaddd 26207 expadd 14066 expaddd 14109 expaddz 14068 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26178 cxpmuld 26226 expmul 14069 expmuld 14110 expmulz 14070 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26175 mulcxpd 26218 mulexp 14063 mulexpd 14122 mulexpz 14064 |
| [Gleason] p. 140 | Exercise 1 | znnen 16151 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13482 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15572 rlimadd 15583 rlimdiv 15588 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15574 rlimsub 15585 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15573 rlimmul 15586 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15577 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15523 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15544 climcj 15545 climim 15547 climre 15546 rlimabs 15549 rlimcj 15550 rlimim 15552 rlimre 15551 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11249 df-xr 11248 ltxr 13091 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15411 limsupval 15414 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15612 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15621 caucvgb 15622 caucvgbf 44135 caucvgr 15618 climcau 15613 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15758 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15825 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15278 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13789 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 20923 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 23831 xmet0 23830 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 23847 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 23838 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 23840 mstri 23957 xmettri 23839 xmstri 23956 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 23870 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23134 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 24809 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24031 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24363 addcn2 15534 mulcn 24365 mulcn2 15536 subcn 24364 subcn2 15535 |
| [Gleason] p. 295 | Remark | bcval3 14262 bcval4 14263 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14277 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14260 df-bc 14259 |
| [Gleason] p. 296 | Remark | bcn0 14266 bcnn 14268 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15772 |
| [Gleason] p. 308 | Equation 2 | ef0 16030 |
| [Gleason] p. 308 | Equation 3 | efcj 16031 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16036 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16040 |
| [Gleason] p. 310 | Equation 14 | sinadd 16103 |
| [Gleason] p. 310 | Equation 15 | cosadd 16104 |
| [Gleason] p. 311 | Equation 17 | sincossq 16115 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16120 sinbnd 16119 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14176 sqeqori 14174 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16012 |
| [Godowski] p. 730 | Equation SF | goeqi 31504 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 30899 |
| [Golan] p. 1 | Remark | srgisid 20023 |
| [Golan] p. 1 | Definition | df-srg 20001 |
| [Golan] p. 149 | Definition | df-slmd 32324 |
| [Gonshor] p. 7 | Definition | df-scut 27265 |
| [Gonshor] p. 9 | Theorem 2.5 | slerec 27300 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 27387 cofcut1d 27388 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 27389 cofcut2d 27390 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 27391 cofcutr1d 27392 cofcutr2d 27393 |
| [Gonshor] p. 13 | Definition | df-adds 27424 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 27440 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 27465 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 27566 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 27585 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 35069 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17526 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17528 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 46533 df-cllaw 46531 df-comlaw 46532 |
| [Hall] p. 2 | Section 1.2 | df-clintop 46545 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 46566 |
| [Halmos] p. 28 | Partition ` ` | df-parts 37573 dfmembpart2 37578 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 31296 riesz2 31297 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 31172 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 31404 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 31416 elpjidm 31415 pjnmopi 31379 |
| [Halmos] p. 44 | Remark | pjinormi 30918 pjinormii 30907 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 31420 pjrn 30938 pjrni 30933 pjvec 30927 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 30958 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 31385 hmopidmpji 31383 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 31422 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 31411 pjocvec 30928 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 31400 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 31403 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 31406 pjssdif2i 31405 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 31086 |
| [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 1798 |
| [Hatcher] p. 25 | Definition | df-phtpc 24490 df-phtpy 24469 |
| [Hatcher] p. 26 | Definition | df-pco 24503 df-pi1 24506 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 24493 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 24548 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 21974 df-dmatalt 46981 |
| [Helfgott] p. 2 | Theorem | tgoldbach 46420 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 46405 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 46417 bgoldbtbnd 46412 bgoldbtbnd 46412 tgblthelfgott 46418 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 33592 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 33593 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 33607 hgt750lemb 33606 hgt750leme 33608 hgt750lemf 33603 hgt750lemg 33604 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 46414 tgoldbachgt 33613 tgoldbachgtALTV 46415 tgoldbachgtd 33612 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 33594 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 29724 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 18826 grpoideu 29740 mndideu 18632 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 18855 grpoinveu 29750 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 18886 grpo2inv 29762 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 18897 grpoinvop 29764 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 18919 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1771 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1772 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1774 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 31651 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 31664 cdj3i 31672 cdj3lem1 31665 cdjreui 31663 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 31662 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 40774 |
| [Holland95] p. 14 | Line 15 | hgmapvs 40700 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 40722 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 40723 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 40720 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 40726 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 40645 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 40740 |
| [Holland95] p. 204 | Definition of involution | df-srng 20442 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 38312 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 40337 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 40290 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 38742 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 40186 poml4N 38762 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 40277 pexmidALTN 38787 pexmidN 38778 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 40342 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 37932 ldualset 37933 |
| [Holland95] p. 222 | Item 1 | df-lines 38310 df-pointsN 38311 |
| [Holland95] p. 222 | Item 2 | df-polarityN 38712 |
| [Holland95] p. 223 | Remark | ispsubcl2N 38756 omllaw4 38054 pol1N 38719 polcon3N 38726 |
| [Holland95] p. 223 | Definition | df-psubclN 38744 |
| [Holland95] p. 223 | Equation for polarity | polval2N 38715 |
| [Holmes] p. 40 | Definition | df-xrn 37179 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 30315 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 31413 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 31194 eigre 31066 eigrei 31065 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 31195 eigorth 31069 eigorthi 31068 |
| [Hughes] p. 137 | Remark (ii) | eigposi 31067 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 29542 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 29538 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 29539 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 29540 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 29558 frgrregorufr0 29557 frgrregorufrg 29559 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 29565 frrusgrord 29574 frrusgrord0 29573 |
| [Huneke] p. 2 | Statement | df-clwwlknon 29321 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 29548 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 29551 frgrwopreg2 29552 frgrwopregasn 29549 frgrwopregbsn 29550 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 29554 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 29568 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 29571 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 29319 numclwlk1 29604 numclwlk1lem1 29602 numclwlk1lem2 29603 numclwwlk1 29594 numclwwlk8 29625 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 29545 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 29008 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 29580 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 29606 numclwwlkovh0 29605 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 29614 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 29211 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 29618 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 29621 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 29624 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 29636 natded 29636 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 29636 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 29636 natded 29636 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 29636 |
| [Jech] p. 4 | Definition of class | cv 1541 cvjust 2727 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10570 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10568 alephmul 10569 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10567 infmap2 10209 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9805 |
| [Jech] p. 72 | Equation 9.3 | scott0 9877 scottex 9876 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9858 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9882 |
| [Jech] p. 78 | Note | opthprc 5738 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 41587 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 41675 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 41676 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 41599 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 41603 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 41604 rmyp1 41605 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 41606 rmym1 41607 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 41597 rmx1 41598 rmxluc 41608 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 41601 rmy1 41602 rmyluc 41609 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 41611 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 41612 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 41632 jm2.17b 41633 jm2.17c 41634 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 41665 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 41669 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 41660 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 41635 jm2.24nn 41631 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 41674 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 41680 rmygeid 41636 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 41692 |
| [Juillerat] p. 11 | Section *5 | etransc 44934 etransclem47 44932 etransclem48 44933 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 44929 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 44931 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 44917 |
| [Juillerat] p. 13 | Proof | etransclem35 44920 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 44923 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 44909 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 44926 |
| [Juillerat] p. 14 | Proof | etransclem23 44908 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1972 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2016 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2021 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2011 cbvaliw 2010 wl-cbvmotv 36320 wl-motae 36322 wl-moteq 36321 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 2000 spimw 1975 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2037 spw 2038 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 30747 chabs1i 30749 chabs2 30748 chabs2i 30750 chjass 30764 chjassi 30717 latabs1 18424 latabs2 18425 |
| [Kalmbach] p. 15 | Definition of atom | df-at 31569 ela 31570 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 31514 cvrval2 38082 |
| [Kalmbach] p. 16 | Definition | df-ol 37986 df-oml 37987 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 30815 cmbri 30821 cmtvalN 38019 df-cm 30814 df-cmtN 37985 |
| [Kalmbach] p. 22 | Remark | omllaw5N 38055 pjoml5 30844 pjoml5i 30819 |
| [Kalmbach] p. 22 | Definition | pjoml2 30842 pjoml2i 30816 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 30845 cmcmi 30823 cmcmii 30828 cmtcomN 38057 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 38053 omlsi 30635 pjoml 30667 pjomli 30666 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 38052 |
| [Kalmbach] p. 23 | Remark | cmbr2i 30827 cmcm3 30846 cmcm3i 30825 cmcm3ii 30830 cmcm4i 30826 cmt3N 38059 cmt4N 38060 cmtbr2N 38061 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 30839 cmbr3i 30831 cmtbr3N 38062 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 30849 fh1i 30852 fh2 30850 fh2i 30853 omlfh1N 38066 |
| [Kalmbach] p. 65 | Remark | chjatom 31588 chslej 30729 chsleji 30689 shslej 30611 shsleji 30601 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 30726 chocini 30685 chsupcl 30571 chsupval2 30641 h0elch 30486 helch 30474 hsupval2 30640 ocin 30527 ococss 30524 shococss 30525 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 30543 |
| [Kalmbach] p. 66 | Remark | df-pjh 30626 pjssmi 31396 pjssmii 30912 |
| [Kalmbach] p. 67 | Lemma 3 | osum 30876 osumi 30873 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 31431 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 31631 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 31541 |
| [Kalmbach] p. 140 | Remark | hatomic 31591 hatomici 31590 hatomistici 31593 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 38127 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 31612 lsatexch 37851 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 31586 cvlcvr1 38147 cvr1 38219 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 31605 cvexchi 31600 cvrexch 38229 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 31595 hlrelat 38211 hlrelat5N 38210 lrelat 37822 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 20742 lsmsatcv 37818 spansncv 30884 spansncvi 30883 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 37837 spansncv2 31524 |
| [Kalmbach] p. 266 | Definition | df-st 31442 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 31080 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10637 fpwwe2 10634 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10638 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10645 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10640 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10642 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10655 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10659 gchxpidm 10660 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10671 gchhar 10670 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10207 unxpwdom 9580 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10661 |
| [Kreyszig] p. 3 | Property M1 | metcl 23820 xmetcl 23819 |
| [Kreyszig] p. 4 | Property M2 | meteq0 23827 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24063 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11927 muleqadd 11854 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 23926 |
| [Kreyszig] p. 19 | Remark | mopntopon 23927 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 23989 mopnm 23932 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 23987 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 23992 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24033 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 22744 lmmbr 24757 lmmbr2 24758 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 22866 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 24812 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 24775 iscmet2 24793 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 24815 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 22947 metelcls 24804 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 24805 metcld2 24806 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 24597 lmodvneg1 20503 nvinv 29870 vcm 29807 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 24593 lmod0vs 20493 slmd0vs 32347 vc0 29805 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20494 slmdvs0 32348 vcz 29806 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 29922 ngpmet 24094 nrmmetd 24065 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 29917 imsdval2 29918 ncvspds 24660 ngpds 24095 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24080 nvnd 29919 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24109 nmge0 24108 nvge0 29904 nvz 29900 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24115 nvabs 29903 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 30032 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 29976 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 30038 blocni 30036 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 30037 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 24703 ipeq0 21175 ipz 29950 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 24715 pythi 30081 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 30085 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 24737 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15798 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 24935 minveco 30115 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 29981 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 24828 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 30104 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 31354 leopg 31353 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 31372 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 30149 |
| [Kulpa] p. 547 | Theorem | poimir 36459 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 36458 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 36457 |
| [Kulpa] p. 548 | Theorem | broucube 36460 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 36452 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 36453 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2383 axnul 5304 |
| [Kunen] p. 11 | Axiom 3 | axnul 5304 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 7936 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8828 mapvalg 8826 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10513 |
| [Kunen] p. 31 | Definition 10.24 | mapex 8822 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9755 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9797 r1elssi 9796 |
| [Kunen] p. 107 | Exercise 4 | rankop 9849 rankopb 9843 rankuni 9854 rankxplim 9870 rankxpsuc 9873 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 5008 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 32686 |
| [Lang] p. | Definition | df-rn 5686 |
| [Lang] p. 3 | Statement | lidrideqd 18584 mndbn0 18637 |
| [Lang] p. 3 | Definition | df-mnd 18622 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18602 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18718 |
| [Lang] p. 5 | Equation | gsumreidx 19777 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 46527 |
| [Lang] p. 6 | Example | nn0mnd 46524 |
| [Lang] p. 6 | Equation | gsumxp2 19840 |
| [Lang] p. 6 | Statement | cycsubm 19073 |
| [Lang] p. 6 | Definition | mulgnn0gsum 18954 |
| [Lang] p. 6 | Observation | mndlsmidm 19531 |
| [Lang] p. 7 | Definition | dfgrp2e 18844 |
| [Lang] p. 30 | Definition | df-tocyc 32244 |
| [Lang] p. 32 | Property (a) | cyc3genpm 32289 |
| [Lang] p. 32 | Property (b) | cyc3conja 32294 cycpmconjv 32279 |
| [Lang] p. 53 | Definition | df-cat 17608 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18043 cat1lem 18042 |
| [Lang] p. 54 | Definition | df-iso 17692 |
| [Lang] p. 57 | Definition | df-inito 17930 df-termo 17931 |
| [Lang] p. 58 | Example | irinitoringc 46869 |
| [Lang] p. 58 | Statement | initoeu1 17957 termoeu1 17964 |
| [Lang] p. 62 | Definition | df-func 17804 |
| [Lang] p. 65 | Definition | df-nat 17890 |
| [Lang] p. 91 | Note | df-ringc 46805 |
| [Lang] p. 92 | Statement | mxidlprm 32544 |
| [Lang] p. 92 | Definition | isprmidlc 32524 |
| [Lang] p. 128 | Remark | dsmmlmod 21284 |
| [Lang] p. 129 | Proof | lincscm 47013 lincscmcl 47015 lincsum 47012 lincsumcl 47014 |
| [Lang] p. 129 | Statement | lincolss 47017 |
| [Lang] p. 129 | Observation | dsmmfi 21277 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 32657 qusdimsum 32658 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 32638 |
| [Lang] p. 147 | Definition | snlindsntor 47054 |
| [Lang] p. 504 | Statement | mat1 21931 matring 21927 |
| [Lang] p. 504 | Definition | df-mamu 21868 |
| [Lang] p. 505 | Statement | mamuass 21884 mamutpos 21942 matassa 21928 mattposvs 21939 tposmap 21941 |
| [Lang] p. 513 | Definition | mdet1 22085 mdetf 22079 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22175 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22071 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22095 |
| [Lang] p. 515 | Definition | df-minmar1 22119 smadiadetr 22159 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22094 mdetralt 22092 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22107 |
| [Lang] p. 518 | Definition | df-madu 22118 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22129 madurid 22128 matinv 22161 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 22374 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 32685 fedgmul 32661 |
| [Lang], p. 561 | Remark | chpmatply1 22316 |
| [Lang], p. 561 | Definition | df-chpmat 22311 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 43026 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 43021 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 43027 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5304 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2711 |
| [Levy] p. 59 | Definition | df-ttrcl 9699 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9742 |
| [Levy] p. 338 | Axiom | df-clel 2811 df-cleq 2725 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2811 df-cleq 2725 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2711 |
| [Levy] p. 358 | Axiom | df-clab 2711 |
| [Levy58] p. 2 | Definition I | isfin1-3 10377 |
| [Levy58] p. 2 | Definition II | df-fin2 10277 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10276 |
| [Levy58] p. 2 | Definition III | df-fin3 10279 |
| [Levy58] p. 3 | Definition V | df-fin5 10280 |
| [Levy58] p. 3 | Definition IV | df-fin4 10278 |
| [Levy58] p. 4 | Definition VI | df-fin6 10281 |
| [Levy58] p. 4 | Definition VII | df-fin7 10282 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10406 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27169 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27180 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27212 nosupbnd1 27197 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27214 nosupbnd2 27199 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27218 noetasuplem4 27219 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27215 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1771 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1772 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1774 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 31639 |
| [Maeda] p. 168 | Lemma 5 | mdsym 31643 mdsymi 31642 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 31637 mdsymlem6 31639 mdsymlem7 31640 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 31641 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 31544 ssdmd2 31545 ssmd1 31542 ssmd2 31543 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 31540 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 31512 df-md 31511 mdbr 31525 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 31562 mdslj1i 31550 mdslj2i 31551 mdslle1i 31548 mdslle2i 31549 mdslmd1i 31560 mdslmd2i 31561 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 31552 mdsl2bi 31554 mdsl2i 31553 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 31566 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 31563 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 31564 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 31541 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 31546 mdsl3 31547 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 31565 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 31660 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 38129 hlrelat1 38209 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 37847 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 31567 cvmdi 31555 cvnbtwn4 31520 cvrnbtwn4 38087 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 31568 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 38148 cvp 31606 cvrp 38225 lcvp 37848 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 31630 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 31629 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 38141 hlexch4N 38201 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 31632 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 38252 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 38558 atpsubN 38562 df-pointsN 38311 pointpsubN 38560 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 38313 pmap11 38571 pmaple 38570 pmapsub 38577 pmapval 38566 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 38574 pmap1N 38576 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 38579 pmapglb2N 38580 pmapglb2xN 38581 pmapglbx 38578 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 38661 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 38286 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 38605 paddclN 38651 paddidm 38650 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 38287 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 38647 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 38286 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 38287 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19536 lsmmod2 19537 lssats 37820 shatomici 31589 shatomistici 31592 shmodi 30621 shmodsi 30620 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 31531 mdsymlem7 31640 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 30820 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 30724 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 31646 |
| [Margaris] p. 40 | Rule C | exlimiv 1934 |
| [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 398 df-ex 1783 df-or 847 dfbi2 476 |
| [Margaris] p. 51 | Theorem 1 | idALT 23 |
| [Margaris] p. 56 | Theorem 3 | conventions 29633 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 43609 |
| [Margaris] p. 60 | Theorem 8 | jcn 162 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 43610 |
| [Margaris] p. 79 | Rule C | exinst01 43319 exinst11 43320 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1981 19.2g 2182 r19.2z 4493 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2196 rr19.3v 3656 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2157 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1829 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1784 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2175 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2199 19.9h 2283 exlimd 2212 exlimdh 2287 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2163 excomim 2164 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2321 |
| [Margaris] p. 90 | Section 19 | conventions-labels 29634 conventions-labels 29634 conventions-labels 29634 conventions-labels 29634 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1830 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 43070 albi 1821 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2219 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2220 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 43072 exbi 1850 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2223 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 43069 2alimdv 1922 alimd 2206 alimdh 1820 alimdv 1920 ax-4 1812 ralimdaa 3258 ralimdv 3170 ralimdva 3168 ralimdvva 3205 sbcimdv 3850 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2201 19.21h 2284 19.21t 2200 19.21vv 43068 alrimd 2209 alrimdd 2208 alrimdh 1867 alrimdv 1933 alrimi 2207 alrimih 1827 alrimiv 1931 alrimivv 1932 hbralrimi 3145 r19.21be 3250 r19.21bi 3249 ralrimd 3262 ralrimdv 3153 ralrimdva 3155 ralrimdvv 3202 ralrimdvva 3210 ralrimi 3255 ralrimia 3256 ralrimiv 3146 ralrimiva 3147 ralrimivv 3199 ralrimivva 3201 ralrimivvva 3204 ralrimivw 3151 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 43071 2eximdv 1923 exim 1837 eximd 2210 eximdh 1868 eximdv 1921 rexim 3088 reximd2a 3267 reximdai 3259 reximdd 43774 reximddv 3172 reximddv2 3213 reximddv3 43773 reximdv 3171 reximdv2 3165 reximdva 3169 reximdvai 3166 reximdvva 3206 reximi2 3080 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2205 19.23bi 2185 19.23h 2285 19.23t 2204 exlimdv 1937 exlimdvv 1938 exlimexi 43218 exlimiv 1934 exlimivv 1936 rexlimd3 43766 rexlimdv 3154 rexlimdv3a 3160 rexlimdva 3156 rexlimdva2 3158 rexlimdvaa 3157 rexlimdvv 3211 rexlimdvva 3212 rexlimdvw 3161 rexlimiv 3149 rexlimiva 3148 rexlimivv 3200 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 1990 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1884 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1874 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2221 r19.27z 4503 r19.27zv 4504 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2222 19.28vv 43078 r19.28z 4496 r19.28zf 43786 r19.28zv 4499 rr19.28v 3657 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1877 r19.29d2r 3141 r19.29imd 3119 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1885 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2228 19.31vv 43076 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2227 r19.32 45741 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 43074 19.33 1888 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 1991 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1881 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2224 19.36vv 43075 r19.36zv 4505 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2226 19.37vv 43077 r19.37zv 4500 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1842 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 1989 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1891 19.40 1890 r19.40 3120 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2229 19.41rg 43244 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2230 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1886 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2231 r19.44zv 4502 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2232 r19.45zv 4501 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2607 |
| [Mayet] p. 370 | Remark | jpi 31501 largei 31498 stri 31488 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 31443 ishst 31445 |
| [Mayet3] p. 10 | Theorem | hstrbi 31497 hstri 31496 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 30959 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 30960 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 31509 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 30563 chsupcl 30571 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 31591 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 31585 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 31612 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 38792 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18436 latj32 18434 latjass 18432 |
| [Megill] p. 444 | Axiom C5 | ax-5 1914 ax5ALT 37715 |
| [Megill] p. 444 | Section 7 | conventions 29633 |
| [Megill] p. 445 | Lemma L12 | aecom-o 37709 ax-c11n 37696 axc11n 2426 |
| [Megill] p. 446 | Lemma L17 | equtrr 2026 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 37704 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 37736 hbnae 2432 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2481 sbid 2248 sbidd-misc 47666 sbidd 47665 |
| [Megill] p. 448 | Remark 9.6 | axc14 2463 |
| [Megill] p. 448 | Scheme C4' | ax-c4 37692 |
| [Megill] p. 448 | Scheme C5' | ax-c5 37691 sp 2177 |
| [Megill] p. 448 | Scheme C6' | ax-11 2155 |
| [Megill] p. 448 | Scheme C7' | ax-c7 37693 |
| [Megill] p. 448 | Scheme C8' | ax-7 2012 |
| [Megill] p. 448 | Scheme C9' | ax-c9 37698 |
| [Megill] p. 448 | Scheme C10' | ax-6 1972 ax-c10 37694 |
| [Megill] p. 448 | Scheme C11' | ax-c11 37695 |
| [Megill] p. 448 | Scheme C12' | ax-8 2109 |
| [Megill] p. 448 | Scheme C13' | ax-9 2117 |
| [Megill] p. 448 | Scheme C14' | ax-c14 37699 |
| [Megill] p. 448 | Scheme C15' | ax-c15 37697 |
| [Megill] p. 448 | Scheme C16' | ax-c16 37700 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 37712 dral1 2439 dral2-o 37738 dral2 2438 drex1 2441 drex2 2442 drsb1 2495 drsb2 2258 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2162 sbequ 2087 sbid2v 2509 |
| [Megill] p. 450 | Example in Appendix | hba1-o 37705 hba1 2290 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 45537 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 23 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3872 rspsbca 3873 stdpc4 2072 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 37692 ra4 3879 stdpc5 2202 |
| [Mendelson] p. 81 | Rule C | exlimiv 1934 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2032 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2243 |
| [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 5824 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6264 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7757 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6367 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8591 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9136 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 9051 xpsneng 9052 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9059 xpcomeng 9060 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9062 |
| [Mendelson] p. 255 | Definition | brsdom 8967 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9054 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8820 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 9033 mapsnend 9032 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9142 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9141 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8872 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 9036 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9055 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10169 djucomen 10168 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10173 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10167 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8526 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8554 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10550 |
| [Mendelson] p. 281 | Definition | df-r1 9755 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9804 |
| [Mendelson] p. 287 | Axiom system MK | ru 3775 |
| [MertziosUnger] p. 152 | Definition | df-frgr 29492 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 29527 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 29529 vdgn1frgrv3 29530 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 29531 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 29524 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 29517 2pthfrgrrn 29515 2pthfrgrrn2 29516 |
| [Mittelstaedt] p. 9 | Definition | df-oc 30483 |
| [Monk1] p. 22 | Remark | conventions 29633 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 29633 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4229 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5780 ssrelf 31822 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5782 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5210 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6258 coi2 6259 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5918 rn0 5923 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 6138 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5693 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5926 rnxp 6166 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5772 xp0 6154 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6073 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6070 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7902 imaexALTV 37137 imaexg 7901 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6068 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7073 funfvop 7047 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6944 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6954 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6591 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7249 dff13f 7250 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7216 funrnex 7935 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7241 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6223 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4967 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 7987 df-1st 7970 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 7988 df-2nd 7971 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9845 ranksnb 9818 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9846 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9847 rankunb 9841 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9829 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9755 r1val2 9828 |
| [Monk1] p. 117 | Lemma | zorn2 10497 zorn2g 10494 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9977 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10552 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9972 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1812 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2012 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2172 ax-c15 37697 ax12v2 2174 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 37692 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2155 |
| [Monk2] p. 109 | Lemma 15 | equvini 2455 equvinv 2033 eqvinop 5486 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1914 ax5ALT 37715 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2138 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2155 |
| [Monk2] p. 114 | Lemma 21 | sp 2177 |
| [Monk2] p. 114 | Lemma 22 | axc4 2315 hba1-o 37705 hba1 2290 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2151 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2171 nfra2 3373 nfra2w 3297 |
| [Moore] p. 53 | Part I | df-mre 17526 |
| [Munkres] p. 77 | Example 2 | distop 22480 indistop 22487 indistopon 22486 |
| [Munkres] p. 77 | Example 3 | fctop 22489 fctop2 22490 |
| [Munkres] p. 77 | Example 4 | cctop 22491 |
| [Munkres] p. 78 | Definition of basis | df-bases 22431 isbasis3g 22434 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17385 tgval2 22441 |
| [Munkres] p. 79 | Remark | tgcl 22454 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 22448 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 22472 tgss3 22471 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 22473 basgen2 22474 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 36168 topdifinfeq 36169 topdifinffin 36167 topdifinfindis 36165 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 22646 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 22524 topcld 22521 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 22525 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 22527 |
| [Munkres] p. 94 | Definition of closure | clsval 22523 |
| [Munkres] p. 94 | Definition of interior | ntrval 22522 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 22561 elcls 22559 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 22569 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 22634 neindisj 22603 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 22636 |
| [Munkres] p. 97 | Definition of limit point | islp2 22631 lpval 22625 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 22801 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 22713 iscn 22721 iscn2 22724 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 22766 cncnp2 22767 cncnpi 22764 df-cnp 22714 iscnp 22723 iscnp2 22725 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24034 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 24810 |
| [Nathanson] p. 123 | Remark | reprgt 33571 reprinfz1 33572 reprlt 33569 |
| [Nathanson] p. 123 | Definition | df-repr 33559 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 33591 |
| [Nathanson] p. 123 | Proposition | breprexp 33583 breprexpnat 33584 itgexpif 33556 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 31335 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 46413 |
| [Pfenning] p. 17 | Definition XM | natded 29636 |
| [Pfenning] p. 17 | Definition NNC | natded 29636 notnotrd 133 |
| [Pfenning] p. 17 | Definition ` `C | natded 29636 |
| [Pfenning] p. 18 | Rule" | natded 29636 |
| [Pfenning] p. 18 | Definition /\I | natded 29636 |
| [Pfenning] p. 18 | Definition ` `E | natded 29636 natded 29636 natded 29636 natded 29636 natded 29636 |
| [Pfenning] p. 18 | Definition ` `I | natded 29636 natded 29636 natded 29636 natded 29636 natded 29636 |
| [Pfenning] p. 18 | Definition ` `EL | natded 29636 |
| [Pfenning] p. 18 | Definition ` `ER | natded 29636 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 29636 |
| [Pfenning] p. 18 | Definition ` `IR | natded 29636 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 29636 |
| [Pfenning] p. 127 | Definition =E | natded 29636 |
| [Pfenning] p. 127 | Definition =I | natded 29636 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 24701 df-dip 29932 dip0l 29949 ip0l 21173 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 24742 ipval 29934 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 29945 ipcj 21171 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 24704 dipdir 30073 ipdir 21176 ipdiri 30061 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 29941 nmsq 24693 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 30056 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 30058 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 30059 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 24710 dipass 30076 ipass 21182 ipassi 30072 |
| [Prugovecki] p. 186 | Definition of bra | braval 31175 df-bra 31081 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 31082 kbval 31185 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 31613 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 38697 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 31627 atcvat4i 31628 cvrat3 38251 cvrat4 38252 lsatcvat3 37860 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 31513 cvrval 38077 df-cv 31510 df-lcv 37827 lspsncv0 20747 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 38709 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 38710 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2711 rabid 3453 rabidd 43782 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2276 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2725 |
| [Quine] p. 19 | Definition 2.9 | conventions 29633 df-v 3477 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2874 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2871 abid2f 2937 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2268 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2089 sbalex 2236 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2811 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2733 eqid1 29700 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2740 |
| [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 3479 |
| [Quine] p. 43 | Theorem 6.9 | isset 3488 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3581 spcgv 3586 spcimgf 3579 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3789 spsbcd 3790 |
| [Quine] p. 44 | Theorem 6.12 | elex 3493 |
| [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 43620 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 6507 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 45729 dfiota2 6493 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 45738 iotaval 6511 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6518 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6513 |
| [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 7436 oprabidw 7435 |
| [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 6610 |
| [Quine] p. 65 | Theorem 10.4 | funi 6577 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6598 funsng 6596 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6542 |
| [Quine] p. 65 | Definition 10.2 | args 6088 dffv4 6885 |
| [Quine] p. 68 | Definition 10.11 | conventions 29633 df-fv 6548 fv2 6883 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14228 nn0opth2i 14227 nn0opthi 14226 omopthi 8656 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8405 |
| [Quine] p. 232 | Equation i | carddom 10545 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6633 funimaexg 6631 |
| [Quine] p. 331 | Axiom system NF | ru 3775 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 30315 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 29932 polid 30390 polid2i 30388 polidi 30389 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 30044 |
| [ReedSimon] p. 195 | Remark | lnophm 31250 lnophmi 31249 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 31363 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 31365 leopmuli 31364 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 31368 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 31083 leoppos 31357 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 31367 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 31356 |
| [Roman] p. 4 | Definition | df-dmat 21974 df-dmatalt 46981 |
| [Roman] p. 18 | Part Preliminaries | df-rng 46584 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20049 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 47068 |
| [Roman] p. 112 | Note | isldepslvec2 47068 ldepsnlinc 47091 zlmodzxznm 47080 |
| [Roman] p. 112 | Example | zlmodzxzequa 47079 zlmodzxzequap 47082 zlmodzxzldep 47087 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 22374 |
| [Rosenlicht] p. 80 | Theorem | heicant 36461 |
| [Rosser] p. 281 | Definition | df-op 4634 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 33595 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 33596 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 46944 pmtr3ncom 19336 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19332 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19275 cayleyth 19276 |
| [Rudin] p. 164 | Equation 27 | efcan 16035 |
| [Rudin] p. 164 | Equation 30 | efzval 16041 |
| [Rudin] p. 167 | Equation 48 | absefi 16135 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 196 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1774 |
| [Sanford] p. 39 | Rule 4 | mptxor 1772 |
| [Sanford] p. 40 | Rule 1 | mptnan 1771 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6113 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6116 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6110 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6108 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17526 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17527 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17527 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17529 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10127 |
| [Schechter] p. 141 | Definition (MC) | dfac11 41737 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10437 axdc3 10445 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20051 isrngo 36703 |
| [Schechter] p. 276 | Remark 11.6.e | span0 30773 |
| [Schechter] p. 276 | Definition of span | df-span 30540 spanval 30564 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 22478 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6386 onelord 41933 ordelon 6385 ordelord 6383 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 41934 sucidg 6442 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6415 onsuc 7794 ord0 6414 ordsuci 7791 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 41935 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5268 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 41700 elon2 6372 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6367 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5582 epelg 5580 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9588 epirron 41936 ordirr 6379 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 41938 oneptr 41937 ontr1 6407 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 41940 oneptri 41939 ordtri3or 6393 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8496 ord0eln0 6416 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6428 onsucss 41949 trsucss 6449 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7801 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6455 ordnbtwn 6454 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 41951 ordnexbtwnsuc 41950 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10392 onsucf1lem 41952 onsucf1o 41955 onsucf1olem 41953 onsucrn 41954 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 41956 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7829 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 41945 ordne0gt0 41944 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 41947 limnsuc 41948 onsucelab 41946 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9634 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7844 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9637 ordom 7860 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9638 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8635 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7762 ssorduni 7761 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8526 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9641 limom 7866 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8461 df1o2 8468 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8511 oa0suclim 41958 oalim 8527 oasuc 8519 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8512 om0suclim 41959 omlim 8528 omsuc 8521 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8517 oe0m1 8516 oe0suclim 41960 oelim 8529 oesuc 8522 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 41911 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 41962 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 41963 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 41964 limexissupab 41966 limiun 41965 limuni 6422 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8533 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8538 om1om1r 41967 om1r 8539 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8530 oaomoecl 41961 oecl 8532 omcl 8531 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 41913 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8540 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8541 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 41968 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 41969 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8607 nnamecl 41970 nnecl 8609 nnmcl 8608 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 41971 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8548 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8549 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8556 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 41973 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 41974 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 41976 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8555 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 41980 omword1 8569 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 41979 oaordnrex 41978 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 41975 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 41981 omword2 8570 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 41982 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 41983 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 41984 omordi 8562 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8564 omord2com 41985 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 41986 df-2o 8462 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 41989 oewordi 8587 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 41990 oeworde 8589 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 41991 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 41992 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 41988 omnord1ex 41987 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 41993 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 41995 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 41999 oenord1ex 41998 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 42000 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8557 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 41994 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8575 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8576 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 42002 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8593 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 42003 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 42004 cantnfub2 42005 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 42008 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 28152 axtgcgrrflx 27693 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 28153 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 28154 axtgcgrid 27694 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 27679 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 28165 axtgsegcon 27695 df-trkgcb 27681 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 28176 axtg5seg 27696 df-trkgcb 27681 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 28177 axtgbtwnid 27697 df-trkgb 27680 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 28179 axtgpasch 27698 df-trkgb 27680 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 28198 df-trkg2d 33615 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 27701 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 27702 df-trkg2d 33615 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 28201 axtgeucl 27703 df-trkge 27682 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 28214 axtgcont 27700 axtgcont1 27699 df-trkgb 27680 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 34897 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 34899 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 34902 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 34906 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 34907 tgcgrcomimp 27708 tgcgrcoml 27710 tgcgrcomr 27709 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 34912 tgcgrtriv 27715 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 34916 tg5segofs 33623 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 33620 df-ofs 34893 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 34918 tgcgrextend 27716 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 34920 tgsegconeq 27717 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 34932 btwntriv2 34922 tgbtwntriv2 27718 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 34923 tgbtwncom 27719 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 34926 tgbtwntriv1 27722 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 34927 tgbtwnswapid 27723 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 34933 btwnintr 34929 tgbtwnexch2 27727 tgbtwnintr 27724 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 34935 btwnexch3 34930 tgbtwnexch 27729 tgbtwnexch3 27725 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 34934 tgbtwnouttr 27728 tgbtwnouttr2 27726 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 28197 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 34937 tgbtwndiff 27737 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 27730 trisegint 34938 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 34954 tgifscgr 27739 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 27789 colrot1 27790 colrot2 27791 lncom 27853 lnrot1 27854 lnrot2 27855 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 34950 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 34955 tgcgrsub 27740 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 34965 tgcgrxfr 27749 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 27748 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 34951 df-cgrg 27742 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 27742 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 34966 tgbtwnxfr 27761 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 34972 colinearperm2 34974 colinearperm3 34973 colinearperm4 34975 colinearperm5 34976 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 27764 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 34949 tgellng 27784 tglng 27777 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 34977 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 34985 lnxfr 27797 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 34986 lnext 27798 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 34990 tgfscgr 27799 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 34991 lncgr 27800 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 34952 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 34993 lnid 27801 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 34994 tgidinside 27802 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 35011 tgbtwnconn1 27806 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 35012 tgbtwnconn2 27807 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 35013 tgbtwnconn3 27808 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 35019 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 35017 legov 27816 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 27817 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 27830 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 35020 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 35022 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 35024 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 35025 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 35026 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 35023 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 35028 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 27818 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 27820 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 27821 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 27822 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 27823 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 35035 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 35036 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 35031 df-outsideof 35030 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 35032 ishlg 27833 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 27838 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 27840 outsideofrflx 35037 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 27834 hlcomd 27835 outsideofcom 35038 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 27841 outsideoftr 35039 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 27849 outsideofeu 35041 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 35048 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 35049 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 35042 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 35057 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 35058 tglineelsb2 27863 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 35060 linerflx1 35059 linerflx2 35061 tglinecom 27866 tglinerflx1 27864 tglinerflx2 27865 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 35063 tglinethru 27867 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 35047 tglng 27777 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 27825 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 35066 tglinethrueu 27870 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 35067 tglineineq 27874 tglineinteq 27876 tglineintmo 27873 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 27880 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 27881 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 27882 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 27897 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 27893 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 27885 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 27884 ismir 27890 mirbtwn 27889 mircgr 27888 mirfv 27887 mirval 27886 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 27895 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 27896 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 27897 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 27900 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 27901 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 27906 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 27903 mirbtwni 27902 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 27904 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 27916 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 27920 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 27917 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 27918 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 27919 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 27922 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 27923 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 27929 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 27925 israg 27928 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 27930 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 27931 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 27933 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 27934 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 27935 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 27936 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 27937 ragncol 27940 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 27938 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 27944 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 27948 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 27945 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 27927 isperp 27943 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 27946 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 27953 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 27961 colperpexlem2 27962 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 27964 colperpexlem3 27963 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 27969 midex 27968 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 27966 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 27975 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 27970 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 27979 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 27982 opphllem6 27983 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 27985 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 27698 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 27986 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 27994 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 27989 hpgbr 27991 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 27996 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 27995 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 27997 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 27998 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 27999 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 28000 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 28001 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 28015 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 28005 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 28019 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 28020 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 28021 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 28022 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 28023 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 28026 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 28028 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 28006 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 28029 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 28032 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 28033 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 28034 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 28035 trgcopyeu 28037 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 28061 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 28040 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 28049 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 28047 cgrahl2 28048 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 28050 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 28051 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 28053 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 28054 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 28057 cgrahl 28058 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 28062 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 28063 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 28064 acopyeu 28065 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 28072 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 28076 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 28069 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 28084 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 28077 isleag 28078 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 28086 tgsas1 28085 tgsas2 28087 tgsas3 28088 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 28090 tgasa1 28089 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 28091 tgsss2 28092 tgsss3 28093 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 26754 dchrsum 26752 dchrsum2 26751 sumdchr 26755 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 26756 sum2dchr 26757 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 19928 ablfacrp2 19929 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 26699 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 26700 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 26707 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 26965 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 26968 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27022 vmalogdivsum2 27021 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27012 dirith2 27011 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27010 rpvmasum 27009 rpvmasum2 26995 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 26970 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27008 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 26975 dchrisumlem1 26972 dchrisumlem2 26973 dchrisumlem3 26974 dchrisumlema 26971 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 26978 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27007 dchrmusumlem 27005 dchrvmasumlem 27006 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 26977 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 26979 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27003 dchrisum0re 26996 dchrisumn0 27004 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 26989 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 26993 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 26994 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27049 pntrsumbnd2 27050 pntrsumo1 27048 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27013 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27015 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27017 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27020 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27025 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27026 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27031 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27033 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27034 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27042 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27043 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27040 selberg3lem2 27041 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27044 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27038 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27051 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27052 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27053 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27067 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27079 pntlemb 27080 pntlemc 27078 pntlemd 27077 pntlemg 27081 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27079 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27071 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27076 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27079 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27092 pntleml 27094 |
| [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 403 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4295 |
| [Strang] p. 242 | Section 6.3 | expgrowth 43027 |
| [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 43529 |
| [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 43611 |
| [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 5831 xpindir 5832 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5742 xpundir 5743 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9587 |
| [Suppes] p. 58 | Theorem 2 | relss 5779 |
| [Suppes] p. 59 | Theorem 4 | eldm 5898 eldm2 5899 eldm2g 5897 eldmg 5896 |
| [Suppes] p. 59 | Definition 3 | df-dm 5685 |
| [Suppes] p. 60 | Theorem 6 | dmin 5909 |
| [Suppes] p. 60 | Theorem 8 | rnun 6142 |
| [Suppes] p. 60 | Theorem 9 | rnin 6143 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5886 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5880 brcnvg 5877 |
| [Suppes] p. 62 | Equation 5 | elcnv 5874 elcnv2 5875 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6100 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6141 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6139 |
| [Suppes] p. 63 | Definition | dftrrels2 37383 |
| [Suppes] p. 63 | Theorem 20 | co02 6256 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5968 |
| [Suppes] p. 63 | Definition 7 | df-co 5684 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5883 |
| [Suppes] p. 64 | Theorem 27 | coass 6261 |
| [Suppes] p. 65 | Theorem 31 | resundi 5993 |
| [Suppes] p. 65 | Theorem 34 | elima 6062 elima2 6063 elima3 6064 elimag 6061 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6146 |
| [Suppes] p. 66 | Theorem 40 | dminss 6149 |
| [Suppes] p. 66 | Theorem 41 | imainss 6150 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6153 |
| [Suppes] p. 81 | Definition 34 | dfec2 8702 |
| [Suppes] p. 82 | Theorem 72 | elec 8743 elecALTV 37072 elecg 8742 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 37419 erth 8748 erth2 8749 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 37422 erdisj 8751 |
| [Suppes] p. 83 | Definition 35, | df-parts 37573 dfmembpart2 37578 |
| [Suppes] p. 89 | Theorem 96 | map0b 8873 |
| [Suppes] p. 89 | Theorem 97 | map0 8877 map0g 8874 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8878 mapsnd 8876 |
| [Suppes] p. 89 | Theorem 99 | mapss 8879 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 10059 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 10058 |
| [Suppes] p. 92 | Theorem 1 | enref 8977 enrefg 8976 |
| [Suppes] p. 92 | Theorem 2 | ensym 8995 ensymb 8994 ensymi 8996 |
| [Suppes] p. 92 | Theorem 3 | entr 8998 |
| [Suppes] p. 92 | Theorem 4 | unen 9042 |
| [Suppes] p. 94 | Theorem 15 | endom 8971 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 8992 |
| [Suppes] p. 94 | Theorem 17 | domtr 8999 |
| [Suppes] p. 95 | Theorem 18 | sbth 9089 |
| [Suppes] p. 97 | Theorem 23 | canth2 9126 canth2g 9127 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9093 df-sdom 8938 dfsdom2 9092 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9110 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9095 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9094 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9108 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8974 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9111 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9106 |
| [Suppes] p. 98 | Exercise 4 | fundmen 9027 fundmeng 9028 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9066 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9107 |
| [Suppes] p. 104 | Theorem 37 | fofi 9334 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9174 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9174 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10542 |
| [Suppes] p. 130 | Definition 3 | df-tr 5265 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7762 |
| [Suppes] p. 134 | Definition 6 | df-suc 6367 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7888 finds 7884 finds1 7887 finds2 7886 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9643 isfinite2 9297 isfiniteg 9300 unbnn 9295 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10909 df-ltpq 10901 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7847 tfinds 7844 tfinds2 7848 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8547 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8549 |
| [Suppes] p. 211 | Theorem 25 | oaass 8557 |
| [Suppes] p. 225 | Definition 8 | iscard2 9967 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10554 |
| [Suppes] p. 228 | Theorem 59 | harcard 9969 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 10057 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6412 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7776 onminsb 7777 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10563 |
| [Suppes] p. 229 | Theorem 65 | alephcard 10061 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 10068 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 10062 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9931 |
| [Suppes] p. 242 | Theorem 6 | weth 10486 |
| [Suppes] p. 242 | Theorem 8 | entric 10548 |
| [Suppes] p. 242 | Theorem 9 | carden 10542 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2704 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2725 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2811 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2727 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2756 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7408 |
| [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 7726 |
| [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 7728 unexg 7731 |
| [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 6431 elsucg 6429 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 43612 sspwimpALT 43619 sspwimpALT2 43622 sspwimpcf 43614 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5455 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5284 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3434 |
| [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 9586 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9723 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9725 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3477 |
| [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 9593 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9588 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4362 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4129 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4289 undif3VD 43576 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4130 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4137 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3063 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3072 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7735 xpexg 7732 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5682 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6616 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6794 fun11 6619 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6556 svrelfun 6617 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5885 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5887 |
| [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 6190 dfrel2 6185 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5691 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5809 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5816 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5830 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 6008 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5985 opelresi 5987 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 6001 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 6004 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 6009 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6587 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6104 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6585 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6796 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2606 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 29633 df-fv 6548 fv3 6906 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7911 cnvexg 7910 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7897 dmexg 7889 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7898 rnexg 7890 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 43146 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7906 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6901 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 45817 tz6.12-1-afv2 45884 tz6.12-1 6911 tz6.12-afv 45816 tz6.12-afv2 45883 tz6.12 6913 tz6.12c-afv2 45885 tz6.12c 6910 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 45880 tz6.12-2 6876 tz6.12i-afv2 45886 tz6.12i 6916 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6543 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6544 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6546 wfo 6538 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6545 wf1 6537 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6547 wf1o 6539 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 7028 eqfnfv2 7029 eqfnfv2f 7032 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6985 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7214 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7212 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6633 funimaexg 6631 |
| [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 6095 eliniseg 6090 iniseg 6093 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5579 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5653 fr3nr 7754 frirr 5652 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5630 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7756 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5642 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5662 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6345 tz6.26i 6347 wefrc 5669 wereu2 5672 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6348 wfii 6350 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6549 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7321 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7322 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7328 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7329 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7330 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7334 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7341 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7343 |
| [TakeutiZaring] p. 35 | Notation | wtr 5264 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 43147 tz7.2 5659 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5270 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6374 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6382 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6383 ordelordALT 43231 ordelordALTVD 43561 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6389 ordelssne 6388 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6387 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6391 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7764 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7765 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6365 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6393 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 43243 ordon 7759 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7760 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7837 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6408 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5266 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7775 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7814 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6465 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6464 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7761 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4940 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6367 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6441 sucidg 6442 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7794 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6455 ordnbtwn 6454 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7811 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6366 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7865 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7870 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7825 ordelsuc 7803 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7805 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7835 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7852 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7874 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7876 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7877 |
| [TakeutiZaring] p. 43 | Remark | omon 7862 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9626 omex 9634 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7860 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7882 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7878 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7879 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7855 |
| [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 7778 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6411 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4950 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9651 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7773 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8371 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8392 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8393 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8394 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8401 tz7.44-2 8402 tz7.44-3 8403 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8362 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8357 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8341 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8440 tz7.49c 8441 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8438 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8437 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8439 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2652 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 10002 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 10003 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8527 oasuc 8519 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7845 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8530 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8511 oa0r 8533 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8531 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8544 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8615 nnaordi 8614 oaord 8543 oaordi 8542 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5051 uniss2 4944 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8546 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8551 oawordex 8553 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8607 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8643 |
| [TakeutiZaring] p. 60 | Remark | oancom 9642 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8556 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8612 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8548 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8514 omlim 8528 omsuc 8521 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8512 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8609 nnmcl 8608 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8628 nnmordi 8627 omord 8564 omordi 8562 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8565 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8632 omwordri 8568 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8534 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8538 om1r 8539 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8571 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8573 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8574 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8575 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8576 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8604 oe0 8517 oelim 8529 oesuc 8522 onesuc 8525 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8515 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8582 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8583 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8516 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8541 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8584 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8590 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8588 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8589 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8593 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8595 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9719 tz9.1 9720 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9755 r10 9759 r1lim 9763 r1limg 9762 r1suc 9761 r1sucg 9760 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9771 r1ord2 9772 r1ordg 9769 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9781 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9806 tz9.13 9782 tz9.13g 9783 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9756 rankval 9807 rankvalb 9788 rankvalg 9808 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9830 rankelb 9815 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9844 rankval3 9831 rankval3b 9817 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9820 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9786 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9825 rankr1c 9812 rankr1g 9823 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9826 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9840 rankssb 9839 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9833 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9832 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10466 dfac3 10112 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 10021 numth 10463 numth2 10462 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10537 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10538 cardid2 9944 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9951 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10542 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9950 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9935 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9956 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9948 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9146 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 9009 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9151 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9070 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9954 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10089 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9205 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9224 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10090 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9210 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10079 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 10057 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9963 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10208 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9317 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8939 isfi 8968 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9226 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10525 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9063 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10517 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10176 unxpdom 9249 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9965 cardsdomelir 9964 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9251 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 10005 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8818 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10553 infxpidm2 10008 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10199 infxp 10206 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9075 pw2f1o 9073 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9139 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10478 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10473 ac6s5 10482 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10534 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10535 uniimadomf 10536 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10265 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10260 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10245 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10242 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10248 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10255 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10264 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10573 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10243 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10267 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10088 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10087 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10099 alephfp2 10100 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10690 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10103 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10560 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10574 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10575 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 37691 |
| [Tarski] p. 67 | Scheme B5 | sp 2177 |
| [Tarski] p. 68 | Lemma 6 | avril1 29696 equid 2016 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2021 |
| [Tarski] p. 70 | Lemma 14 | spim 2387 spime 2389 spimew 1976 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2172 ax-c15 37697 ax12i 1971 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2089 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1973 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1914 ax5ALT 37715 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2012 ax-8 2109 ax-9 2117 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 27695 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 27696 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 27698 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 27698 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 27699 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16182 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 36465 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 36467 |
| [Weierstrass] p. 272 | Definition | df-mdet 22069 mdetuni 22106 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 903 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 867 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 868 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 919 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 967 |
| [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 36264 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 42484 imim2 58 wl-luk-imim2 36259 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 45664 imim1 83 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 896 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2659 syl 17 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 902 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 22 wl-luk-id 36262 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 894 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 142 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 897 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 130 notnotrALT2 43621 wl-luk-notnotr 36263 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 146 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 42514 axfrege28 42513 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 866 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 924 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 123 wl-luk-pm2.21 36256 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 124 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 889 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 939 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 29634 pm2.27 42 wl-luk-pm2.27 36254 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 922 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 37170 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 923 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 969 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 970 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 968 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1089 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 906 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 907 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 942 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 56 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 881 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 882 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5 169 pm2.5g 168 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6 190 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 883 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 884 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 885 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 172 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 850 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 851 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 888 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 890 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 191 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 899 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 940 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 941 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 192 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 891 pm2.67 892 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 176 pm2.521g 174 pm2.521g2 175 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 898 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 972 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 900 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 202 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 973 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 974 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 933 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 931 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 971 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 975 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 84 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 932 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 109 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 991 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 471 pm3.2im 160 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 992 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 993 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 994 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 995 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 473 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 461 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 404 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 802 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 450 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 451 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 484 simplim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 486 simprim 166 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 764 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 765 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 807 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 623 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 809 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 494 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 495 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 960 pm3.44 959 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 808 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 475 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 963 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34b 316 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 261 |
| [WhiteheadRussell] p. 117 | Theorem *4.11 | notbi 319 |
| [WhiteheadRussell] p. 117 | Theorem *4.12 | con2bi 354 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotb 315 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14 806 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 832 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 221 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 805 bitr 804 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 565 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 904 pm4.25 905 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 462 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1007 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 869 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 470 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 921 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 633 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 917 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 637 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 976 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1090 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1005 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1053 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1022 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 996 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 998 pm4.45 997 pm4.45im 827 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 982 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 852 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 547 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 981 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 984 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 985 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 986 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 987 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 983 pm4.56 988 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 989 pm4.57 990 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 406 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 855 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 399 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 848 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 407 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 849 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67 400 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 559 pm4.71d 563 pm4.71i 561 pm4.71r 560 pm4.71rd 564 pm4.71ri 562 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 949 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 529 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 936 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 519 pm4.76 520 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 961 pm4.77 962 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 934 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1003 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 394 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81 395 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 1023 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1024 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 348 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 349 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 352 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 389 impexp 452 pm4.87 842 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 823 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 944 pm5.11g 943 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 945 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 947 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 946 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1012 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1013 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1011 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbn 385 pm5.18 383 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 388 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 824 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1014 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1049 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1050 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 901 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 574 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 390 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 362 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6 1001 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 953 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 830 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 575 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 835 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 825 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 833 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 391 pm5.41 392 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 545 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 544 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 1004 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1017 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 948 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1000 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1018 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1019 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1027 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 367 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 270 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 1028 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 43050 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 43051 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1874 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 43052 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 43053 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 43054 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1897 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 43055 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 43056 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 43057 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 43058 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 43059 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 43061 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 43062 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 43063 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 43060 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2094 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 43066 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 43067 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2074 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2158 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1832 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1833 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 43068 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 43069 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 43070 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 43071 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 43073 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 43072 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1891 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 43075 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 43076 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 43074 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1831 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 43077 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 43078 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1849 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 43079 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2343 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1864 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 43084 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 43080 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 43081 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 43082 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 43083 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 43088 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 43085 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 43086 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 43087 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 43089 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2564 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 43099 pm13.13b 43100 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 43101 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3023 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3024 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3655 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 43107 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 43108 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 43102 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 43246 pm13.193 43103 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 43104 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 43105 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 43106 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 43113 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 43112 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 43111 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3844 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 43114 pm14.122b 43115 pm14.122c 43116 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 43117 pm14.123b 43118 pm14.123c 43119 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 43121 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 43120 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 43122 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6521 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 43123 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6522 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 43124 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 43126 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2630 eupickbi 2633 sbaniota 43127 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 43125 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2579 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 43129 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 29633 df-fv 6548 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 9992 pm54.43lem 9991 |
| [Young] p. 141 | Definition of operator ordering | leop2 31355 |
| [Young] p. 142 | Example 12.2(i) | 0leop 31361 idleop 31362 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 41499 |
| [vandenDries] p. 43 | Theorem 62 | pellex 41506 pellexlem1 41500 |