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 17612 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17612 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18026 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17633 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 47683 prsthinc 47674 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 47704 df-mndtc 47704 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17656 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17728 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17716 invisoinvl 17737 |
| [Adamek] p. 28 | Example 3.13 | idinv 17736 idiso 17735 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17721 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17695 df-iso 17696 dfiso2 17719 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17702 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17753 |
| [Adamek] p. 29 | Definition 3.15 | cic 17746 df-cic 17743 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17808 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17717 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17718 isoco 17724 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17808 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17831 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17824 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 47640 prsthinc 47674 thincciso 47669 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 47704 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17838 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18061 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18119 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17856 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17855 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18119 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17880 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17886 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17885 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18104 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18104 |
| [Adamek] p. 39 | Definition 3.41 | funcoppc 17825 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18049 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17874 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17873 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18058 |
| [Adamek] p. 40 | Definition 3.47 | df-catc 18049 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17788 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17789 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17800 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17759 |
| [Adamek] p. 49 | Remark 4.4(2) | ressffth 17889 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 17894 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 17917 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 17921 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 17895 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 17923 |
| [Adamek] p. 101 | Definition 7.1 | df-inito 17934 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 46967 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 17935 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 17962 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 17966 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 17936 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 46970 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 17969 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17694 |
| [Adamek] p. 185 | Section 10.67 | updjud 9929 |
| [Adamek] p. 478 | Item Rng | df-ringc 46903 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 47234 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 47256 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14521 df-pfx 14621 df-substr 14591 df-word 14465 lencl 14483 wrd0 14489 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24225 df-nmoo 29998 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 31406 hmopidmchi 31404 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 31454 pjcmul2i 31455 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 31171 unoplin 31173 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 31172 unopadj2 31191 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 31266 lnopunii 31265 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 31339 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 27414 |
| [Alling] p. 184 | Axiom B | bdayfo 27180 |
| [Alling] p. 184 | Axiom O | sltso 27179 |
| [Alling] p. 184 | Axiom SD | nodense 27195 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27280 |
| [Alling] p. 185 | Theorem | conway 27300 |
| [Alling] p. 185 | Axiom FE | noeta 27246 |
| [Alling] p. 186 | Theorem 4 | slerec 27320 |
| [Alling], p. 2 | Definition | rp-brsslt 42174 |
| [Alling], p. 3 | Note | nla0001 42177 nla0002 42175 nla0003 42176 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11398 addcan2d 11418 addcan2i 11408 addcand 11417 addcani 11407 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11450 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11508 negsubd 11577 negsubi 11538 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11510 negnegd 11562 negnegi 11530 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11647 subdid 11670 subdii 11663 subdir 11648 subdird 11671 subdiri 11664 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11393 mul01d 11413 mul01i 11404 mul02 11392 mul02d 11412 mul02i 11403 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11851 mulcan2d 11848 mulcand 11847 mulcani 11853 |
| [Apostol] p. 18 | Theorem I.8 | receu 11859 xreceu 32088 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11888 divrecd 11993 divreci 11959 divreczi 11952 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11911 recreci 11946 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11854 mul0ord 11864 mul0ori 11862 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11653 mul2negd 11669 mul2negi 11662 mulneg1 11650 mulneg1d 11667 mulneg1i 11660 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11929 divadddivd 12034 divadddivi 11976 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11914 divmuldivd 12031 divmuldivi 11974 rdivmuldivd 20227 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11915 divdivdivd 12037 divdivdivi 11977 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 12996 rpaddcld 13031 rpmulcl 12997 rpmulcld 13032 |
| [Apostol] p. 20 | Axiom 8 | rpneg 13006 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 13009 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11340 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11807 ltadd1dd 11825 ltadd1i 11768 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12064 ltmul1a 12063 ltmul1i 12132 ltmul1ii 12142 ltmul2 12065 ltmul2d 13058 ltmul2dd 13072 ltmul2i 12135 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11734 msqgt0d 11781 msqgt0i 11751 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11736 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11720 lt0neg1d 11783 ltneg 11714 ltnegd 11792 ltnegi 11758 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11699 lt2addd 11837 lt2addi 11776 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 12975 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12060 recgt0d 12148 recgt0i 12119 recgt0ii 12120 |
| [Apostol] p. 22 | Definition of integers | df-z 12559 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12226 |
| [Apostol] p. 22 | Definition of rationals | df-q 12933 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9449 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12468 |
| [Apostol] p. 26 | Theorem I.29 | arch 12469 archd 43856 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12665 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12470 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12931 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12930 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13178 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16282 zneo 12645 zneoALTV 46337 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26238 msqsqrtd 15387 resqrtth 15202 sqrtth 15311 sqrtthi 15317 sqsqrtd 15386 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12215 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12897 |
| [Apostol] p. 361 | Remark | crreczi 14191 |
| [Apostol] p. 363 | Remark | absgt0i 15346 |
| [Apostol] p. 363 | Example | abssubd 15400 abssubi 15350 |
| [ApostolNT] p. 7 | Remark | fmtno0 46208 fmtno1 46209 fmtno2 46218 fmtno3 46219 fmtno4 46220 fmtno5fac 46250 fmtnofz04prm 46245 |
| [ApostolNT] p. 7 | Definition | df-fmtno 46196 |
| [ApostolNT] p. 8 | Definition | df-ppi 26604 |
| [ApostolNT] p. 14 | Definition | df-dvds 16198 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16213 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16237 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16232 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16226 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16228 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16214 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16215 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16220 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16254 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16256 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16258 |
| [ApostolNT] p. 15 | Definition | df-gcd 16436 dfgcd2 16488 |
| [ApostolNT] p. 16 | Definition | isprm2 16619 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16590 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16848 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16454 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16489 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16491 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16469 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16461 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16648 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16650 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16861 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16855 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16346 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16524 |
| [ApostolNT] p. 24 | Definition | df-mu 26605 |
| [ApostolNT] p. 25 | Definition | df-phi 16699 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 26695 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16723 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16709 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16713 |
| [ApostolNT] p. 32 | Definition | df-vma 26602 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 26697 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 26719 |
| [ApostolNT] p. 38 | Remark | df-sgm 26606 |
| [ApostolNT] p. 38 | Definition | df-sgm 26606 |
| [ApostolNT] p. 75 | Definition | df-chp 26603 df-cht 26601 |
| [ApostolNT] p. 104 | Definition | congr 16601 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16201 |
| [ApostolNT] p. 106 | Definition | moddvds 16208 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16289 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16290 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13853 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13890 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14201 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16231 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16604 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17007 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16606 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16716 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16734 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16717 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 26576 |
| [ApostolNT] p. 179 | Definition | df-lgs 26798 lgsprme0 26842 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 26843 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 26819 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 26834 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 26891 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 26910 2lgsoddprm 26919 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 26877 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 26886 |
| [ApostolNT] p. 188 | Definition | df-lgs 26798 lgs1 26844 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 26835 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 26837 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 26845 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 26846 |
| [Baer] p. 40 | Property (b) | mapdord 40509 |
| [Baer] p. 40 | Property (c) | mapd11 40510 |
| [Baer] p. 40 | Property (e) | mapdin 40533 mapdlsm 40535 |
| [Baer] p. 40 | Property (f) | mapd0 40536 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 40496 mapd1o 40519 |
| [Baer] p. 41 | Property (g) | mapdat 40538 |
| [Baer] p. 44 | Part (1) | mapdpg 40577 |
| [Baer] p. 45 | Part (2) | hdmap1eq 40672 mapdheq 40599 mapdheq2 40600 mapdheq2biN 40601 |
| [Baer] p. 45 | Part (3) | baerlem3 40584 |
| [Baer] p. 46 | Part (4) | mapdheq4 40603 mapdheq4lem 40602 |
| [Baer] p. 46 | Part (5) | baerlem5a 40585 baerlem5abmN 40589 baerlem5amN 40587 baerlem5b 40586 baerlem5bmN 40588 |
| [Baer] p. 47 | Part (6) | hdmap1l6 40692 hdmap1l6a 40680 hdmap1l6e 40685 hdmap1l6f 40686 hdmap1l6g 40687 hdmap1l6lem1 40678 hdmap1l6lem2 40679 mapdh6N 40618 mapdh6aN 40606 mapdh6eN 40611 mapdh6fN 40612 mapdh6gN 40613 mapdh6lem1N 40604 mapdh6lem2N 40605 |
| [Baer] p. 48 | Part 9 | hdmapval 40699 |
| [Baer] p. 48 | Part 10 | hdmap10 40711 |
| [Baer] p. 48 | Part 11 | hdmapadd 40714 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 40688 mapdh6hN 40614 |
| [Baer] p. 48 | Part (7) | mapdh75cN 40624 mapdh75d 40625 mapdh75e 40623 mapdh75fN 40626 mapdh7cN 40620 mapdh7dN 40621 mapdh7eN 40619 mapdh7fN 40622 |
| [Baer] p. 48 | Part (8) | mapdh8 40659 mapdh8a 40646 mapdh8aa 40647 mapdh8ab 40648 mapdh8ac 40649 mapdh8ad 40650 mapdh8b 40651 mapdh8c 40652 mapdh8d 40654 mapdh8d0N 40653 mapdh8e 40655 mapdh8g 40656 mapdh8i 40657 mapdh8j 40658 |
| [Baer] p. 48 | Part (9) | mapdh9a 40660 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 40640 |
| [Baer] p. 49 | Part 12 | hdmap11 40719 hdmapeq0 40715 hdmapf1oN 40736 hdmapneg 40717 hdmaprnN 40735 hdmaprnlem1N 40720 hdmaprnlem3N 40721 hdmaprnlem3uN 40722 hdmaprnlem4N 40724 hdmaprnlem6N 40725 hdmaprnlem7N 40726 hdmaprnlem8N 40727 hdmaprnlem9N 40728 hdmapsub 40718 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 40739 hdmap14lem10 40748 hdmap14lem1a 40737 hdmap14lem2N 40740 hdmap14lem2a 40738 hdmap14lem3 40741 hdmap14lem8 40746 hdmap14lem9 40747 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 40749 hdmap14lem12 40750 hdmap14lem13 40751 hdmap14lem14 40752 hdmap14lem15 40753 hgmapval 40758 |
| [Baer] p. 50 | Part 15 | hgmapadd 40765 hgmapmul 40766 hgmaprnlem2N 40768 hgmapvs 40762 |
| [Baer] p. 50 | Part 16 | hgmaprnN 40772 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 40788 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 40789 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 40790 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 40791 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 40793 hgmapvv 40797 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 40792 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 40794 |
| [Baer] p. 111 | Line 15 | hdmapg 40801 hdmapglem7 40800 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26239 2irrexpqALT 26305 |
| [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 5292 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5300 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 35945 bm1.3ii 5303 |
| [BellMachover] p. 466 | Problem | axpow2 5366 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5367 |
| [BellMachover] p. 466 | Axiom Union | axun2 7727 |
| [BellMachover] p. 468 | Definition | df-ord 6368 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6383 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6390 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6385 |
| [BellMachover] p. 471 | Definition of N | df-om 7856 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7789 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6370 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9637 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7871 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9759 |
| [BellMachover] p. 478 | Definition | rankval2 9813 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9777 r1ord3g 9774 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9590 |
| [BellMachover] p. 488 | Axiom AC | ac5 10472 dfac4 10117 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10105 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 38189 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 31606 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 31648 chirredi 31647 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 31636 |
| [Beran] p. 3 | Definition of join | sshjval3 30607 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 30869 cmcm2i 30846 cmcm2ii 30851 cmt2N 38120 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 30870 lecmi 30855 lecmii 30856 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 30844 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 30873 cm2ji 30878 cm2mi 30879 |
| [Beran] p. 95 | Definition | df-sh 30460 issh2 30462 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 30339 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 30352 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 30343 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 31081 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 31083 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 31082 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 31084 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 30335 his1i 30353 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 30336 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 30337 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 30338 |
| [Beran] p. 96 | Definition of norm | df-hnorm 30221 dfhnorm2 30375 normval 30377 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 30437 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 30226 |
| [Beran] p. 96 | Definition of complete subspace | isch3 30494 |
| [Beran] p. 96 | Definition of converge | df-hlim 30225 hlimi 30441 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 30386 norm-i 30382 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 30390 norm-ii 30391 normlem0 30362 normlem1 30363 normlem2 30364 normlem3 30365 normlem4 30366 normlem5 30367 normlem6 30368 normlem7 30369 normlem7tALT 30372 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 30392 norm-iii 30393 |
| [Beran] p. 98 | Remark 3.4 | bcs 30434 bcsiALT 30432 bcsiHIL 30433 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 30374 normpar 30408 normpari 30407 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 30399 normpyth 30398 normpythi 30395 |
| [Beran] p. 99 | Remark | lnfn0 31300 lnfn0i 31295 lnop0 31219 lnop0i 31223 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 31279 nmcfnex 31306 nmcfnexi 31304 nmcopex 31282 nmcopexi 31280 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 31307 nmcfnlbi 31305 nmcoplb 31283 nmcoplbi 31281 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 31309 lnfnconi 31308 lnopcon 31288 lnopconi 31287 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 30409 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 30406 norm3adifii 30401 norm3dif 30403 norm3difi 30400 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 30554 pjhth 30646 pjhtheu 30647 pjpjhth 30678 pjpjhthi 30679 pjth 24956 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 30659 ococi 30658 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 31314 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 31315 riesz4 31317 riesz4i 31316 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 31332 cnlnadjeu 31331 cnlnadjeui 31330 cnlnadji 31329 cnlnadjlem1 31320 nmopadjlei 31341 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 31344 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 31343 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 31345 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 31189 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 31355 nmopcoadji 31354 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 31346 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 31356 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 31353 pjadj2coi 31457 pjadjcoi 31414 |
| [Beran] p. 107 | Definition | df-ch 30474 isch2 30476 |
| [Beran] p. 107 | Remark 3.12 | choccl 30559 isch3 30494 occl 30557 ocsh 30536 shoccl 30558 shocsh 30537 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 30661 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 30585 |
| [Beran] p. 109 | Property (i) | pjadj2 31440 pjadj3 31441 pjadji 30938 pjadjii 30927 |
| [Beran] p. 109 | Property (ii) | pjidmco 31434 pjidmcoi 31430 pjidmi 30926 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 31426 |
| [Beran] p. 111 | Remark | ho0val 31003 pjch1 30923 |
| [Beran] p. 111 | Definition | df-hfmul 30987 df-hfsum 30986 df-hodif 30985 df-homul 30984 df-hosum 30983 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 30924 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 30947 pjchi 30685 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 30692 pjoc2i 30691 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 30933 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 31418 pjssmii 30934 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 31417 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 31416 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 31421 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 31419 pjssge0ii 30935 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 31420 pjdifnormii 30936 |
| [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 33291 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 33299 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 33297 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 33301 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 33321 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 33352 df-sitm 33330 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 33352 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 33329 |
| [Bollobas] p. 1 | Section I.1 | df-edg 28308 isuhgrop 28330 isusgrop 28422 isuspgrop 28421 |
| [Bollobas] p. 2 | Section I.1 | df-subgr 28525 uhgrspan1 28560 uhgrspansubgr 28548 |
| [Bollobas] p. 3 | Definition | isomuspgr 46502 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 28711 df-cusgr 28669 df-nbgr 28590 fusgrmaxsize 28721 |
| [Bollobas] p. 4 | Definition | df-upwlks 46512 df-wlks 28856 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 28807 finsumvtxdgeven 28809 fusgr1th 28808 fusgrvtxdgonume 28811 vtxdgoddnumeven 28810 |
| [Bollobas] p. 5 | Notation | df-pths 28973 |
| [Bollobas] p. 5 | Definition | df-crcts 29043 df-cycls 29044 df-trls 28949 df-wlkson 28857 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 28319 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 46610 df-cllaw 46596 df-mgm 18561 df-mgm2 46629 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 46611 df-asslaw 46598 df-sgrp 18610 df-sgrp2 46631 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 46630 df-comlaw 46597 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18626 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20058 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 46649 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7285 fcofo 7286 |
| [BourbakiTop1] p. | Remark | xnegmnf 13189 xnegpnf 13188 |
| [BourbakiTop1] p. | Remark | rexneg 13190 |
| [BourbakiTop1] p. | Remark 3 | ust0 23724 ustfilxp 23717 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 23594 |
| [BourbakiTop1] p. | Criterion | ishmeo 23263 |
| [BourbakiTop1] p. | Example 1 | cstucnd 23789 iducn 23788 snfil 23368 |
| [BourbakiTop1] p. | Example 2 | neifil 23384 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 23571 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 23809 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 32937 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23367 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 23781 df-ust 23705 filintn0 23365 filn0 23366 istgp 23581 ucnprima 23787 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 23792 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 23803 df-usp 23762 df-utop 23736 trust 23734 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 32836 |
| [BourbakiTop1] p. | Property V_i | ssnei2 22620 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 22773 |
| [BourbakiTop1] p. | Condition F_I | ustssel 23710 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 23713 |
| [BourbakiTop1] p. | Property V_ii | innei 22629 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 22637 neissex 22631 |
| [BourbakiTop1] p. | Proposition 1 | neips 22617 neiss 22613 ucncn 23790 ustund 23726 ustuqtop 23751 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 22771 neiptopreu 22637 utop2nei 23755 utop3cls 23756 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 23797 uspreg 23779 utopreg 23757 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23195 imasncls 23196 imasnopn 23194 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 23504 |
| [BourbakiTop1] p. | Condition F_II | ustincl 23712 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 23714 |
| [BourbakiTop1] p. | Property V_iii | elnei 22615 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 23808 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 23711 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 23715 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 22891 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23350 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 22396 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 32833 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 44778 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 44780 stoweid 44779 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 44717 stoweidlem10 44726 stoweidlem14 44730 stoweidlem15 44731 stoweidlem35 44751 stoweidlem36 44752 stoweidlem37 44753 stoweidlem38 44754 stoweidlem40 44756 stoweidlem41 44757 stoweidlem43 44759 stoweidlem44 44760 stoweidlem46 44762 stoweidlem5 44721 stoweidlem50 44766 stoweidlem52 44768 stoweidlem53 44769 stoweidlem55 44771 stoweidlem56 44772 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 44739 stoweidlem24 44740 stoweidlem27 44743 stoweidlem28 44744 stoweidlem30 44746 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 44750 stoweidlem59 44775 stoweidlem60 44776 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 44761 stoweidlem49 44765 stoweidlem7 44723 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 44747 stoweidlem39 44755 stoweidlem42 44758 stoweidlem48 44764 stoweidlem51 44767 stoweidlem54 44770 stoweidlem57 44773 stoweidlem58 44774 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 44741 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 44733 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 44727 stoweidlem13 44729 stoweidlem26 44742 stoweidlem61 44777 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 44734 |
| [Bruck] p. 1 | Section I.1 | df-clintop 46610 df-mgm 18561 df-mgm2 46629 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18610 df-sgrp2 46631 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 18922 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5233 |
| [Church] p. 129 | Section II.24 | df-ifp 1063 dfifp2 1064 |
| [Clemente] p. 10 | Definition IT | natded 29656 |
| [Clemente] p. 10 | Definition I` `m,n | natded 29656 |
| [Clemente] p. 11 | Definition E=>m,n | natded 29656 |
| [Clemente] p. 11 | Definition I=>m,n | natded 29656 |
| [Clemente] p. 11 | Definition E` `(1) | natded 29656 |
| [Clemente] p. 11 | Definition E` `(2) | natded 29656 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 29656 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 29656 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 29656 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 29656 |
| [Clemente] p. 14 | Proof 5.11 | natded 29656 |
| [Clemente] p. 14 | Definition E` `n | natded 29656 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 29658 ex-natded5.2 29657 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 29661 ex-natded5.3 29660 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 29663 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 29665 ex-natded5.7 29664 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 29667 ex-natded5.8 29666 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 29669 ex-natded5.13 29668 |
| [Clemente] p. 32 | Definition I` `n | natded 29656 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 29656 |
| [Clemente] p. 32 | Definition E` `n,t | natded 29656 |
| [Clemente] p. 32 | Definition I` `n,t | natded 29656 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 29670 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 29671 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 29673 ex-natded9.26 29672 |
| [Cohen] p. 301 | Remark | relogoprlem 26099 |
| [Cohen] p. 301 | Property 2 | relogmul 26100 relogmuld 26133 |
| [Cohen] p. 301 | Property 3 | relogdiv 26101 relogdivd 26134 |
| [Cohen] p. 301 | Property 4 | relogexp 26104 |
| [Cohen] p. 301 | Property 1a | log1 26094 |
| [Cohen] p. 301 | Property 1b | loge 26095 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26292 |
| [Cohen4] p. 349 | Property | relogbf 26296 |
| [Cohen4] p. 352 | Definition | elogb 26275 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26282 |
| [Cohen4] p. 361 | Property 3 | logbrec 26287 relogbdiv 26284 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26280 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26285 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26273 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26274 |
| [Cohen4] p. 367 | Property | logbchbase 26276 |
| [Cohen4] p. 377 | Property 2 | logblt 26289 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 33284 sxbrsigalem4 33286 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18510 acsinfd 18509 acsinfdimd 18511 acsmap2d 18508 acsmapd 18507 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 33289 |
| [Connell] p. 57 | Definition | df-scmat 21993 df-scmatalt 47080 |
| [Conway] p. 4 | Definition | slerec 27320 |
| [Conway] p. 5 | Definition | addsval 27446 addsval2 27447 df-adds 27444 df-muls 27563 df-negs 27496 |
| [Conway] p. 7 | Theorem | 0slt1s 27330 |
| [Conway] p. 16 | Theorem 0(i) | ssltright 27366 |
| [Conway] p. 16 | Theorem 0(ii) | ssltleft 27365 |
| [Conway] p. 16 | Theorem 0(iii) | slerflex 27266 |
| [Conway] p. 17 | Theorem 3 | addsass 27488 addsassd 27489 addscom 27450 addscomd 27451 addsrid 27448 addsridd 27449 |
| [Conway] p. 17 | Definition | df-0s 27325 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 27518 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 27515 negsidd 27516 |
| [Conway] p. 18 | Theorem 5 | sleadd1 27472 sleadd1d 27478 |
| [Conway] p. 18 | Definition | df-1s 27326 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 27510 negscld 27511 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 27464 |
| [Conway] p. 19 | Theorem 7 | addsdi 27610 addsdid 27611 addsdird 27612 mulnegs1d 27615 mulnegs2d 27616 mulsass 27621 mulsassd 27622 mulscom 27595 mulscomd 27596 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 27590 mulscld 27591 |
| [Conway] p. 19 | Theorem 8(iii) | slemuld 27594 sltmul 27592 sltmuld 27593 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 27600 mulsgt0d 27601 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 27664 |
| [Conway] p. 29 | Remark | madebday 27394 newbday 27396 oldbday 27395 |
| [Conway] p. 29 | Definition | df-made 27342 df-new 27344 df-old 27343 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13826 |
| [Crawley] p. 1 | Definition of poset | df-poset 18266 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 38257 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 39061 dalaw 38757 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 40836 |
| [Crawley] p. 111 | Definition of set W | df-watsN 38861 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 38977 df-ldil 38975 isldil 38981 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 38976 df-trnN 38978 isltrn 38990 ltrnu 38992 |
| [Crawley] p. 112 | Lemma A | cdlema1N 38662 cdlema2N 38663 exatleN 38275 |
| [Crawley] p. 112 | Lemma B | 1cvrat 38347 cdlemb 38665 cdlemb2 38912 cdlemb3 39477 idltrn 39021 l1cvat 37925 lhpat 38914 lhpat2 38916 lshpat 37926 ltrnel 39010 ltrnmw 39022 |
| [Crawley] p. 112 | Lemma C | cdlemc1 39062 cdlemc2 39063 ltrnnidn 39045 trlat 39040 trljat1 39037 trljat2 39038 trljat3 39039 trlne 39056 trlnidat 39044 trlnle 39057 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 38862 |
| [Crawley] p. 113 | Lemma C | cdlemc 39068 cdlemc3 39064 cdlemc4 39065 |
| [Crawley] p. 113 | Lemma D | cdlemd 39078 cdlemd1 39069 cdlemd2 39070 cdlemd3 39071 cdlemd4 39072 cdlemd5 39073 cdlemd6 39074 cdlemd7 39075 cdlemd8 39076 cdlemd9 39077 cdleme31sde 39256 cdleme31se 39253 cdleme31se2 39254 cdleme31snd 39257 cdleme32a 39312 cdleme32b 39313 cdleme32c 39314 cdleme32d 39315 cdleme32e 39316 cdleme32f 39317 cdleme32fva 39308 cdleme32fva1 39309 cdleme32fvcl 39311 cdleme32le 39318 cdleme48fv 39370 cdleme4gfv 39378 cdleme50eq 39412 cdleme50f 39413 cdleme50f1 39414 cdleme50f1o 39417 cdleme50laut 39418 cdleme50ldil 39419 cdleme50lebi 39411 cdleme50rn 39416 cdleme50rnlem 39415 cdlemeg49le 39382 cdlemeg49lebilem 39410 |
| [Crawley] p. 113 | Lemma E | cdleme 39431 cdleme00a 39080 cdleme01N 39092 cdleme02N 39093 cdleme0a 39082 cdleme0aa 39081 cdleme0b 39083 cdleme0c 39084 cdleme0cp 39085 cdleme0cq 39086 cdleme0dN 39087 cdleme0e 39088 cdleme0ex1N 39094 cdleme0ex2N 39095 cdleme0fN 39089 cdleme0gN 39090 cdleme0moN 39096 cdleme1 39098 cdleme10 39125 cdleme10tN 39129 cdleme11 39141 cdleme11a 39131 cdleme11c 39132 cdleme11dN 39133 cdleme11e 39134 cdleme11fN 39135 cdleme11g 39136 cdleme11h 39137 cdleme11j 39138 cdleme11k 39139 cdleme11l 39140 cdleme12 39142 cdleme13 39143 cdleme14 39144 cdleme15 39149 cdleme15a 39145 cdleme15b 39146 cdleme15c 39147 cdleme15d 39148 cdleme16 39156 cdleme16aN 39130 cdleme16b 39150 cdleme16c 39151 cdleme16d 39152 cdleme16e 39153 cdleme16f 39154 cdleme16g 39155 cdleme19a 39174 cdleme19b 39175 cdleme19c 39176 cdleme19d 39177 cdleme19e 39178 cdleme19f 39179 cdleme1b 39097 cdleme2 39099 cdleme20aN 39180 cdleme20bN 39181 cdleme20c 39182 cdleme20d 39183 cdleme20e 39184 cdleme20f 39185 cdleme20g 39186 cdleme20h 39187 cdleme20i 39188 cdleme20j 39189 cdleme20k 39190 cdleme20l 39193 cdleme20l1 39191 cdleme20l2 39192 cdleme20m 39194 cdleme20y 39173 cdleme20zN 39172 cdleme21 39208 cdleme21d 39201 cdleme21e 39202 cdleme22a 39211 cdleme22aa 39210 cdleme22b 39212 cdleme22cN 39213 cdleme22d 39214 cdleme22e 39215 cdleme22eALTN 39216 cdleme22f 39217 cdleme22f2 39218 cdleme22g 39219 cdleme23a 39220 cdleme23b 39221 cdleme23c 39222 cdleme26e 39230 cdleme26eALTN 39232 cdleme26ee 39231 cdleme26f 39234 cdleme26f2 39236 cdleme26f2ALTN 39235 cdleme26fALTN 39233 cdleme27N 39240 cdleme27a 39238 cdleme27cl 39237 cdleme28c 39243 cdleme3 39108 cdleme30a 39249 cdleme31fv 39261 cdleme31fv1 39262 cdleme31fv1s 39263 cdleme31fv2 39264 cdleme31id 39265 cdleme31sc 39255 cdleme31sdnN 39258 cdleme31sn 39251 cdleme31sn1 39252 cdleme31sn1c 39259 cdleme31sn2 39260 cdleme31so 39250 cdleme35a 39319 cdleme35b 39321 cdleme35c 39322 cdleme35d 39323 cdleme35e 39324 cdleme35f 39325 cdleme35fnpq 39320 cdleme35g 39326 cdleme35h 39327 cdleme35h2 39328 cdleme35sn2aw 39329 cdleme35sn3a 39330 cdleme36a 39331 cdleme36m 39332 cdleme37m 39333 cdleme38m 39334 cdleme38n 39335 cdleme39a 39336 cdleme39n 39337 cdleme3b 39100 cdleme3c 39101 cdleme3d 39102 cdleme3e 39103 cdleme3fN 39104 cdleme3fa 39107 cdleme3g 39105 cdleme3h 39106 cdleme4 39109 cdleme40m 39338 cdleme40n 39339 cdleme40v 39340 cdleme40w 39341 cdleme41fva11 39348 cdleme41sn3aw 39345 cdleme41sn4aw 39346 cdleme41snaw 39347 cdleme42a 39342 cdleme42b 39349 cdleme42c 39343 cdleme42d 39344 cdleme42e 39350 cdleme42f 39351 cdleme42g 39352 cdleme42h 39353 cdleme42i 39354 cdleme42k 39355 cdleme42ke 39356 cdleme42keg 39357 cdleme42mN 39358 cdleme42mgN 39359 cdleme43aN 39360 cdleme43bN 39361 cdleme43cN 39362 cdleme43dN 39363 cdleme5 39111 cdleme50ex 39430 cdleme50ltrn 39428 cdleme51finvN 39427 cdleme51finvfvN 39426 cdleme51finvtrN 39429 cdleme6 39112 cdleme7 39120 cdleme7a 39114 cdleme7aa 39113 cdleme7b 39115 cdleme7c 39116 cdleme7d 39117 cdleme7e 39118 cdleme7ga 39119 cdleme8 39121 cdleme8tN 39126 cdleme9 39124 cdleme9a 39122 cdleme9b 39123 cdleme9tN 39128 cdleme9taN 39127 cdlemeda 39169 cdlemedb 39168 cdlemednpq 39170 cdlemednuN 39171 cdlemefr27cl 39274 cdlemefr32fva1 39281 cdlemefr32fvaN 39280 cdlemefrs32fva 39271 cdlemefrs32fva1 39272 cdlemefs27cl 39284 cdlemefs32fva1 39294 cdlemefs32fvaN 39293 cdlemesner 39167 cdlemeulpq 39091 |
| [Crawley] p. 114 | Lemma E | 4atex 38947 4atexlem7 38946 cdleme0nex 39161 cdleme17a 39157 cdleme17c 39159 cdleme17d 39369 cdleme17d1 39160 cdleme17d2 39366 cdleme18a 39162 cdleme18b 39163 cdleme18c 39164 cdleme18d 39166 cdleme4a 39110 |
| [Crawley] p. 115 | Lemma E | cdleme21a 39196 cdleme21at 39199 cdleme21b 39197 cdleme21c 39198 cdleme21ct 39200 cdleme21f 39203 cdleme21g 39204 cdleme21h 39205 cdleme21i 39206 cdleme22gb 39165 |
| [Crawley] p. 116 | Lemma F | cdlemf 39434 cdlemf1 39432 cdlemf2 39433 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 39438 cdlemg16 39528 cdlemg28 39575 cdlemg28a 39564 cdlemg28b 39574 cdlemg3a 39468 cdlemg42 39600 cdlemg43 39601 cdlemg44 39604 cdlemg44a 39602 cdlemg46 39606 cdlemg47 39607 cdlemg9 39505 ltrnco 39590 ltrncom 39609 tgrpabl 39622 trlco 39598 |
| [Crawley] p. 116 | Definition of G | df-tgrp 39614 |
| [Crawley] p. 117 | Lemma G | cdlemg17 39548 cdlemg17b 39533 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 39627 df-edring 39628 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 39631 |
| [Crawley] p. 118 | Remark | tendopltp 39651 |
| [Crawley] p. 118 | Lemma H | cdlemh 39688 cdlemh1 39686 cdlemh2 39687 |
| [Crawley] p. 118 | Lemma I | cdlemi 39691 cdlemi1 39689 cdlemi2 39690 |
| [Crawley] p. 118 | Lemma J | cdlemj1 39692 cdlemj2 39693 cdlemj3 39694 tendocan 39695 |
| [Crawley] p. 118 | Lemma K | cdlemk 39845 cdlemk1 39702 cdlemk10 39714 cdlemk11 39720 cdlemk11t 39817 cdlemk11ta 39800 cdlemk11tb 39802 cdlemk11tc 39816 cdlemk11u-2N 39760 cdlemk11u 39742 cdlemk12 39721 cdlemk12u-2N 39761 cdlemk12u 39743 cdlemk13-2N 39747 cdlemk13 39723 cdlemk14-2N 39749 cdlemk14 39725 cdlemk15-2N 39750 cdlemk15 39726 cdlemk16-2N 39751 cdlemk16 39728 cdlemk16a 39727 cdlemk17-2N 39752 cdlemk17 39729 cdlemk18-2N 39757 cdlemk18-3N 39771 cdlemk18 39739 cdlemk19-2N 39758 cdlemk19 39740 cdlemk19u 39841 cdlemk1u 39730 cdlemk2 39703 cdlemk20-2N 39763 cdlemk20 39745 cdlemk21-2N 39762 cdlemk21N 39744 cdlemk22-3 39772 cdlemk22 39764 cdlemk23-3 39773 cdlemk24-3 39774 cdlemk25-3 39775 cdlemk26-3 39777 cdlemk26b-3 39776 cdlemk27-3 39778 cdlemk28-3 39779 cdlemk29-3 39782 cdlemk3 39704 cdlemk30 39765 cdlemk31 39767 cdlemk32 39768 cdlemk33N 39780 cdlemk34 39781 cdlemk35 39783 cdlemk36 39784 cdlemk37 39785 cdlemk38 39786 cdlemk39 39787 cdlemk39u 39839 cdlemk4 39705 cdlemk41 39791 cdlemk42 39812 cdlemk42yN 39815 cdlemk43N 39834 cdlemk45 39818 cdlemk46 39819 cdlemk47 39820 cdlemk48 39821 cdlemk49 39822 cdlemk5 39707 cdlemk50 39823 cdlemk51 39824 cdlemk52 39825 cdlemk53 39828 cdlemk54 39829 cdlemk55 39832 cdlemk55u 39837 cdlemk56 39842 cdlemk5a 39706 cdlemk5auN 39731 cdlemk5u 39732 cdlemk6 39708 cdlemk6u 39733 cdlemk7 39719 cdlemk7u-2N 39759 cdlemk7u 39741 cdlemk8 39709 cdlemk9 39710 cdlemk9bN 39711 cdlemki 39712 cdlemkid 39807 cdlemkj-2N 39753 cdlemkj 39734 cdlemksat 39717 cdlemksel 39716 cdlemksv 39715 cdlemksv2 39718 cdlemkuat 39737 cdlemkuel-2N 39755 cdlemkuel-3 39769 cdlemkuel 39736 cdlemkuv-2N 39754 cdlemkuv2-2 39756 cdlemkuv2-3N 39770 cdlemkuv2 39738 cdlemkuvN 39735 cdlemkvcl 39713 cdlemky 39797 cdlemkyyN 39833 tendoex 39846 |
| [Crawley] p. 120 | Remark | dva1dim 39856 |
| [Crawley] p. 120 | Lemma L | cdleml1N 39847 cdleml2N 39848 cdleml3N 39849 cdleml4N 39850 cdleml5N 39851 cdleml6 39852 cdleml7 39853 cdleml8 39854 cdleml9 39855 dia1dim 39932 |
| [Crawley] p. 120 | Lemma M | dia11N 39919 diaf11N 39920 dialss 39917 diaord 39918 dibf11N 40032 djajN 40008 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 39903 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 39989 dia2dimlem1 39935 dia2dimlem2 39936 dia2dimlem3 39937 dia2dimlem4 39938 dia2dimlem5 39939 diaf1oN 40001 diarnN 40000 dvheveccl 39983 dvhopN 39987 |
| [Crawley] p. 121 | Lemma N | cdlemn 40083 cdlemn10 40077 cdlemn11 40082 cdlemn11a 40078 cdlemn11b 40079 cdlemn11c 40080 cdlemn11pre 40081 cdlemn2 40066 cdlemn2a 40067 cdlemn3 40068 cdlemn4 40069 cdlemn4a 40070 cdlemn5 40072 cdlemn5pre 40071 cdlemn6 40073 cdlemn7 40074 cdlemn8 40075 cdlemn9 40076 diclspsn 40065 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 40044 |
| [Crawley] p. 122 | Lemma N | dih11 40136 dihf11 40138 dihjust 40088 dihjustlem 40087 dihord 40135 dihord1 40089 dihord10 40094 dihord11b 40093 dihord11c 40095 dihord2 40098 dihord2a 40090 dihord2b 40091 dihord2cN 40092 dihord2pre 40096 dihord2pre2 40097 dihordlem6 40084 dihordlem7 40085 dihordlem7b 40086 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 40101 dihfval 40102 dihval 40103 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 28669 df-nbgr 28590 |
| [Diestel] p. 4 | Section 1.1 | df-subgr 28525 uhgrspan1 28560 uhgrspansubgr 28548 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 28811 vtxdgoddnumeven 28810 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 28319 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 32844 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 32856 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 32848 zarcls1 32849 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 32859 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 32862 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 32865 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3952 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9642 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8822 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9650 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9975 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10550 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5306 |
| [Enderton] p. 19 | Definition | df-tp 4634 |
| [Enderton] p. 26 | Exercise 5 | unissb 4944 |
| [Enderton] p. 26 | Exercise 10 | pwel 5380 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5573 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5083 iinin2 5082 iinun2 5077 iunin1 5076 iunin1f 31789 iunin2 5075 uniin1 31783 uniin2 31784 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5081 iundif2 5078 |
| [Enderton] p. 32 | Exercise 20 | unineq 4278 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5102 |
| [Enderton] p. 33 | Exercise 25 | iununi 5103 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5110 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7758 iunpwss 5111 |
| [Enderton] p. 36 | Definition | opthwiener 5515 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5451 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4950 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5471 rnex 7903 rnexg 7895 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5915 rnuni 6149 |
| [Enderton] p. 42 | Definition of a function | dffun7 6576 dffun8 6577 |
| [Enderton] p. 43 | Definition of function value | funfv2 6980 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6618 |
| [Enderton] p. 44 | Definition (d) | dfima2 6062 dfima3 6063 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6989 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10468 ac7g 10469 df-ac 10111 dfac2 10126 dfac2a 10124 dfac2b 10125 dfac3 10116 dfac7 10127 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7245 |
| [Enderton] p. 52 | Definition | df-map 8822 |
| [Enderton] p. 53 | Exercise 21 | coass 6265 |
| [Enderton] p. 53 | Exercise 27 | dmco 6254 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6625 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6102 |
| [Enderton] p. 54 | Remark | ixpf 8914 ixpssmap 8926 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8892 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10478 ac9s 10488 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 37480 erref 8723 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 37483 erthi 8754 |
| [Enderton] p. 57 | Definition | df-ec 8705 |
| [Enderton] p. 58 | Definition | df-qs 8709 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8705 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5911 |
| [Enderton] p. 68 | Definition of successor | df-suc 6371 |
| [Enderton] p. 71 | Definition | df-tr 5267 dftr4 5273 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6444 unisucg 6443 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6444 unisucg 6443 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5282 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5284 trintALT 43642 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8604 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8606 onasuc 8528 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7412 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8605 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8607 onmsuc 8529 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8622 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8609 nnacom 8617 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8623 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8624 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8626 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8610 nnmsucr 8625 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8638 |
| [Enderton] p. 129 | Definition | df-en 8940 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7362 |
| [Enderton] p. 133 | Exercise 1 | xpomen 10010 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16156 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9210 |
| [Enderton] p. 135 | Corollary 6C | php3 9212 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9209 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9256 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9258 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9168 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9173 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9141 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10174 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10175 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10170 dju1en 10166 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9340 unifi 9341 unifi2 9342 |
| [Enderton] p. 144 | Corollary 6K | undif2 4477 unfi 9172 unfi2 9315 |
| [Enderton] p. 145 | Figure 38 | ffoss 7932 |
| [Enderton] p. 145 | Definition | df-dom 8941 |
| [Enderton] p. 146 | Example 1 | domen 8957 domeng 8958 |
| [Enderton] p. 146 | Example 3 | nndomo 9233 nnsdom 9649 nnsdomg 9302 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10178 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9142 xpdom1 9071 xpdom1g 9069 xpdom2g 9068 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9148 |
| [Enderton] p. 151 | Theorem 6M | zorn 10502 zorng 10499 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10487 dfac5 10123 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10570 |
| [Enderton] p. 164 | Example | infdif 10204 |
| [Enderton] p. 168 | Definition | df-po 5589 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6479 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6411 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6478 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6419 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7827 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7768 |
| [Enderton] p. 194 | Remark | onprc 7765 |
| [Enderton] p. 194 | Exercise 16 | suc11 6472 |
| [Enderton] p. 197 | Definition | df-card 9934 |
| [Enderton] p. 197 | Theorem 7P | carden 10546 |
| [Enderton] p. 200 | Exercise 25 | tfis 7844 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9771 |
| [Enderton] p. 202 | Definition | df-r1 9759 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9781 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9862 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9601 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9852 rankprb 9846 rankpw 9838 rankpwi 9818 rankuniss 9861 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9613 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9614 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10105 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 10071 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10085 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8341 |
| [Enderton] p. 222 | Definition of kard | karden 9890 kardex 9889 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8597 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8599 |
| [Enderton] p. 240 | Exercise 25 | oarec 8562 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10245 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17586 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17532 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18506 mrieqv2d 17583 mrieqvd 17582 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17587 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17592 mreexexlem2d 17589 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18512 mreexfidimd 17594 |
| [Frege1879] p. 11 | Statement | df3or2 42519 |
| [Frege1879] p. 12 | Statement | df3an2 42520 dfxor4 42517 dfxor5 42518 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 42541 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 42542 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 42546 |
| [Frege1879] p. 31 | Proposition 4 | frege4 42550 |
| [Frege1879] p. 32 | Proposition 5 | frege5 42551 |
| [Frege1879] p. 33 | Proposition 6 | frege6 42557 |
| [Frege1879] p. 34 | Proposition 7 | frege7 42559 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 42560 axfrege8 42558 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 90 wl-luk-pm2.04 36326 |
| [Frege1879] p. 35 | Proposition 9 | frege9 42563 |
| [Frege1879] p. 36 | Proposition 10 | frege10 42571 |
| [Frege1879] p. 36 | Proposition 11 | frege11 42565 |
| [Frege1879] p. 37 | Proposition 12 | frege12 42564 |
| [Frege1879] p. 37 | Proposition 13 | frege13 42573 |
| [Frege1879] p. 37 | Proposition 14 | frege14 42574 |
| [Frege1879] p. 38 | Proposition 15 | frege15 42577 |
| [Frege1879] p. 38 | Proposition 16 | frege16 42567 |
| [Frege1879] p. 39 | Proposition 17 | frege17 42572 |
| [Frege1879] p. 39 | Proposition 18 | frege18 42569 |
| [Frege1879] p. 39 | Proposition 19 | frege19 42575 |
| [Frege1879] p. 40 | Proposition 20 | frege20 42579 |
| [Frege1879] p. 40 | Proposition 21 | frege21 42578 |
| [Frege1879] p. 41 | Proposition 22 | frege22 42570 |
| [Frege1879] p. 42 | Proposition 23 | frege23 42576 |
| [Frege1879] p. 42 | Proposition 24 | frege24 42566 |
| [Frege1879] p. 42 | Proposition 25 | frege25 42568 rp-frege25 42556 |
| [Frege1879] p. 42 | Proposition 26 | frege26 42561 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 42581 |
| [Frege1879] p. 43 | Proposition 27 | frege27 42562 |
| [Frege1879] p. 43 | Proposition 28 | con3 153 |
| [Frege1879] p. 43 | Proposition 29 | frege29 42582 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 42585 axfrege31 42584 |
| [Frege1879] p. 44 | Proposition 30 | frege30 42583 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 130 |
| [Frege1879] p. 44 | Proposition 32 | frege32 42586 |
| [Frege1879] p. 44 | Proposition 33 | frege33 42587 |
| [Frege1879] p. 45 | Proposition 34 | frege34 42588 |
| [Frege1879] p. 45 | Proposition 35 | frege35 42589 |
| [Frege1879] p. 45 | Proposition 36 | frege36 42590 |
| [Frege1879] p. 46 | Proposition 37 | frege37 42591 |
| [Frege1879] p. 46 | Proposition 38 | frege38 42592 |
| [Frege1879] p. 46 | Proposition 39 | frege39 42593 |
| [Frege1879] p. 46 | Proposition 40 | frege40 42594 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 42596 axfrege41 42595 |
| [Frege1879] p. 47 | Proposition 41 | notnot 142 |
| [Frege1879] p. 47 | Proposition 42 | frege42 42597 |
| [Frege1879] p. 47 | Proposition 43 | frege43 42598 |
| [Frege1879] p. 47 | Proposition 44 | frege44 42599 |
| [Frege1879] p. 47 | Proposition 45 | frege45 42600 |
| [Frege1879] p. 48 | Proposition 46 | frege46 42601 |
| [Frege1879] p. 48 | Proposition 47 | frege47 42602 |
| [Frege1879] p. 49 | Proposition 48 | frege48 42603 |
| [Frege1879] p. 49 | Proposition 49 | frege49 42604 |
| [Frege1879] p. 49 | Proposition 50 | frege50 42605 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 42608 ax-frege52c 42639 frege52aid 42609 frege52b 42640 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 42613 ax-frege54c 42643 frege54b 42644 |
| [Frege1879] p. 50 | Proposition 51 | frege51 42606 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3780 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 42611 frege53aid 42610 frege53b 42641 frege53c 42665 |
| [Frege1879] p. 50 | Proposition 54 | biid 261 eqid 2733 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 42619 frege55aid 42616 frege55b 42648 frege55c 42669 frege55cor1a 42620 frege55lem2a 42618 frege55lem2b 42647 frege55lem2c 42668 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 42622 frege56aid 42621 frege56b 42649 frege56c 42670 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 42626 ax-frege58b 42652 frege58bid 42653 frege58c 42672 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 42624 frege57aid 42623 frege57b 42650 frege57c 42671 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3791 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 42628 frege59b 42655 frege59c 42673 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 42629 frege60b 42656 frege60c 42674 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 42630 frege61b 42657 frege61c 42675 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 42631 frege62b 42658 frege62c 42676 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 42632 frege63b 42659 frege63c 42677 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 42633 frege64b 42660 frege64c 42678 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 42634 frege65b 42661 frege65c 42679 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 42635 frege66b 42662 frege66c 42680 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 42636 frege67b 42663 frege67c 42681 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 42637 frege68b 42664 frege68c 42682 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 42683 |
| [Frege1879] p. 58 | Proposition 70 | frege70 42684 |
| [Frege1879] p. 59 | Proposition 71 | frege71 42685 |
| [Frege1879] p. 59 | Proposition 72 | frege72 42686 |
| [Frege1879] p. 59 | Proposition 73 | frege73 42687 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 42690 |
| [Frege1879] p. 60 | Proposition 74 | frege74 42688 |
| [Frege1879] p. 60 | Proposition 75 | frege75 42689 |
| [Frege1879] p. 62 | Proposition 77 | frege77 42691 frege77d 42497 |
| [Frege1879] p. 63 | Proposition 78 | frege78 42692 |
| [Frege1879] p. 63 | Proposition 79 | frege79 42693 |
| [Frege1879] p. 63 | Proposition 80 | frege80 42694 |
| [Frege1879] p. 63 | Proposition 81 | frege81 42695 frege81d 42498 |
| [Frege1879] p. 64 | Proposition 82 | frege82 42696 |
| [Frege1879] p. 65 | Proposition 83 | frege83 42697 frege83d 42499 |
| [Frege1879] p. 65 | Proposition 84 | frege84 42698 |
| [Frege1879] p. 66 | Proposition 85 | frege85 42699 |
| [Frege1879] p. 66 | Proposition 86 | frege86 42700 |
| [Frege1879] p. 66 | Proposition 87 | frege87 42701 frege87d 42501 |
| [Frege1879] p. 67 | Proposition 88 | frege88 42702 |
| [Frege1879] p. 68 | Proposition 89 | frege89 42703 |
| [Frege1879] p. 68 | Proposition 90 | frege90 42704 |
| [Frege1879] p. 68 | Proposition 91 | frege91 42705 frege91d 42502 |
| [Frege1879] p. 69 | Proposition 92 | frege92 42706 |
| [Frege1879] p. 70 | Proposition 93 | frege93 42707 |
| [Frege1879] p. 70 | Proposition 94 | frege94 42708 |
| [Frege1879] p. 70 | Proposition 95 | frege95 42709 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 42713 |
| [Frege1879] p. 71 | Proposition 96 | frege96 42710 frege96d 42500 |
| [Frege1879] p. 71 | Proposition 97 | frege97 42711 frege97d 42503 |
| [Frege1879] p. 71 | Proposition 98 | frege98 42712 frege98d 42504 |
| [Frege1879] p. 72 | Proposition 100 | frege100 42714 |
| [Frege1879] p. 72 | Proposition 101 | frege101 42715 |
| [Frege1879] p. 72 | Proposition 102 | frege102 42716 frege102d 42505 |
| [Frege1879] p. 73 | Proposition 103 | frege103 42717 |
| [Frege1879] p. 73 | Proposition 104 | frege104 42718 |
| [Frege1879] p. 73 | Proposition 105 | frege105 42719 |
| [Frege1879] p. 73 | Proposition 106 | frege106 42720 frege106d 42506 |
| [Frege1879] p. 74 | Proposition 107 | frege107 42721 |
| [Frege1879] p. 74 | Proposition 108 | frege108 42722 frege108d 42507 |
| [Frege1879] p. 74 | Proposition 109 | frege109 42723 frege109d 42508 |
| [Frege1879] p. 75 | Proposition 110 | frege110 42724 |
| [Frege1879] p. 75 | Proposition 111 | frege111 42725 frege111d 42510 |
| [Frege1879] p. 76 | Proposition 112 | frege112 42726 |
| [Frege1879] p. 76 | Proposition 113 | frege113 42727 |
| [Frege1879] p. 76 | Proposition 114 | frege114 42728 frege114d 42509 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 42729 |
| [Frege1879] p. 77 | Proposition 116 | frege116 42730 |
| [Frege1879] p. 78 | Proposition 117 | frege117 42731 |
| [Frege1879] p. 78 | Proposition 118 | frege118 42732 |
| [Frege1879] p. 78 | Proposition 119 | frege119 42733 |
| [Frege1879] p. 78 | Proposition 120 | frege120 42734 |
| [Frege1879] p. 79 | Proposition 121 | frege121 42735 |
| [Frege1879] p. 79 | Proposition 122 | frege122 42736 frege122d 42511 |
| [Frege1879] p. 79 | Proposition 123 | frege123 42737 |
| [Frege1879] p. 80 | Proposition 124 | frege124 42738 frege124d 42512 |
| [Frege1879] p. 81 | Proposition 125 | frege125 42739 |
| [Frege1879] p. 81 | Proposition 126 | frege126 42740 frege126d 42513 |
| [Frege1879] p. 82 | Proposition 127 | frege127 42741 |
| [Frege1879] p. 83 | Proposition 128 | frege128 42742 |
| [Frege1879] p. 83 | Proposition 129 | frege129 42743 frege129d 42514 |
| [Frege1879] p. 84 | Proposition 130 | frege130 42744 |
| [Frege1879] p. 85 | Proposition 131 | frege131 42745 frege131d 42515 |
| [Frege1879] p. 86 | Proposition 132 | frege132 42746 |
| [Frege1879] p. 86 | Proposition 133 | frege133 42747 frege133d 42516 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 45029 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 45352 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 45052 |
| [Fremlin1] p. 14 | Definition 112A | ismea 45167 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 45187 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 45178 meadjunre 45192 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 45179 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 45180 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 45176 meaiunle 45185 meaiunlelem 45184 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 45197 meaiuninc2 45198 meaiuninc3 45201 meaiuninc3v 45200 meaiunincf 45199 meaiuninclem 45196 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 45203 meaiininc2 45204 meaiininclem 45202 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 45222 caragendifcl 45230 caratheodory 45244 omelesplit 45234 |
| [Fremlin1] p. 19 | Definition 113A | isome 45210 isomennd 45247 isomenndlem 45246 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 45232 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 45251 voncmpl 45337 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 45214 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 45239 carageniuncllem1 45237 carageniuncllem2 45238 caragenuncl 45229 caragenuncllem 45228 caragenunicl 45240 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 45248 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 45242 caratheodorylem2 45243 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 45251 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 45310 hoidmv1lelem1 45307 hoidmv1lelem2 45308 hoidmv1lelem3 45309 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 45354 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 45310 hoidmvle 45316 hoidmvlelem1 45311 hoidmvlelem2 45312 hoidmvlelem3 45313 hoidmvlelem4 45314 hoidmvlelem5 45315 hsphoidmvle2 45301 hsphoif 45292 hsphoival 45295 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 45264 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 45272 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 45299 hoidmvn0val 45300 hoidmvval 45293 hoidmvval0 45303 hoidmvval0b 45306 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 45304 hsphoidmvle 45302 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 45253 df-voln 45255 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 45320 ovn0 45282 ovn0lem 45281 ovnf 45279 ovnome 45289 ovnssle 45277 ovnsslelem 45276 ovnsupge0 45273 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 45319 ovnhoilem1 45317 ovnhoilem2 45318 vonhoi 45383 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 45336 hoidifhspf 45334 hoidifhspval 45324 hoidifhspval2 45331 hoidifhspval3 45335 hspmbl 45345 hspmbllem1 45342 hspmbllem2 45343 hspmbllem3 45344 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 45337 vonmea 45290 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 45288 ovnsubadd2 45362 ovnsubadd2lem 45361 ovnsubaddlem1 45286 ovnsubaddlem2 45287 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 45347 hoimbl2 45381 hoimbllem 45346 hspdifhsp 45332 opnvonmbl 45350 opnvonmbllem2 45349 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 45352 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 45395 iccvonmbllem 45394 ioovonmbl 45393 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 45401 vonicclem2 45400 vonioo 45398 vonioolem2 45397 vonn0icc 45404 vonn0icc2 45408 vonn0ioo 45403 vonn0ioo2 45406 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 45405 snvonmbl 45402 vonct 45409 vonsn 45407 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 45075 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 45074 subsaliuncllem 45073 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 45441 salpreimalegt 45425 salpreimaltle 45442 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 45444 issmff 45450 issmflem 45443 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 45461 issmflelem 45460 smfpreimale 45470 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 45472 issmfgtlem 45471 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 45412 issmf 45444 issmff 45450 issmfge 45486 issmfgelem 45485 issmfgt 45472 issmfgtlem 45471 issmfle 45461 issmflelem 45460 issmflem 45443 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 45423 salpreimagtlt 45446 salpreimalelt 45445 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 45486 issmfgelem 45485 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 45469 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 45467 cnfsmf 45456 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 45483 decsmflem 45482 incsmf 45458 incsmflem 45457 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 45417 pimconstlt1 45418 smfconst 45465 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 45481 smfaddlem1 45479 smfaddlem2 45480 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 45512 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 45511 smfmullem1 45507 smfmullem2 45508 smfmullem3 45509 smfmullem4 45510 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 45513 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 45516 smfpimbor1lem2 45515 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 45518 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 45506 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 45505 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 45514 smfresal 45504 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 45493 smflim2 45522 smflimlem1 45487 smflimlem2 45488 smflimlem3 45489 smflimlem4 45490 smflimlem5 45491 smflimlem6 45492 smflimmpt 45526 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 45530 smfsuplem1 45527 smfsuplem2 45528 smfsuplem3 45529 smfsupmpt 45531 smfsupxr 45532 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 45534 smfinflem 45533 smfinfmpt 45535 |
| [Fremlin1] p. 39 | Remark 121G | smflim 45493 smflim2 45522 smflimmpt 45526 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 45524 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 45554 smfdivdmmbl2 45557 smfinfdmmbl 45565 smfinfdmmbllem 45564 smfsupdmmbl 45561 smfsupdmmbllem 45560 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 45544 smflimsuplem2 45537 smflimsuplem6 45541 smflimsuplem7 45542 smflimsuplem8 45543 smflimsupmpt 45545 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 45547 smfliminflem 45546 smfliminfmpt 45548 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 45412 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 45558 fsupdm2 45559 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 45549 adddmmbl2 45550 finfdm 45562 finfdm2 45563 fsupdm 45558 fsupdm2 45559 muldmmbl 45551 muldmmbl2 45552 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 45562 finfdm2 45563 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25053 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25096 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25106 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 36566 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 36569 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9633 inf1 9617 inf2 9618 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10906 enqer 10916 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10911 df-nq 10907 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10903 df-plq 10909 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7644 df-mpq 10904 df-mq 10910 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10912 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10970 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10971 ltbtwnnq 10973 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10966 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10967 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10974 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10976 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 10988 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 10990 |
| [Gleason] p. 122 | Definition | df-1p 10977 |
| [Gleason] p. 122 | Remark (1) | prub 10989 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 11028 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10980 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 11027 psslinpr 11026 supexpr 11049 suplem1pr 11047 suplem2pr 11048 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 11013 addclprlem1 11011 addclprlem2 11012 df-plp 10978 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 11017 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 11016 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 11029 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 11038 ltexprlem1 11031 ltexprlem2 11032 ltexprlem3 11033 ltexprlem4 11034 ltexprlem5 11035 ltexprlem6 11036 ltexprlem7 11037 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 11040 ltaprlem 11039 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 11041 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 11042 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10979 mulclpr 11015 mulclprlem 11014 reclem2pr 11043 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 11024 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 11019 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 11018 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 11023 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 11046 reclem3pr 11044 reclem4pr 11045 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 11050 enrer 11058 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 11055 df-1r 11056 df-nr 11051 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 11053 df-plr 11052 negexsr 11097 recexsr 11102 recexsrlem 11098 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 11054 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12207 creur 12206 cru 12204 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11183 axcnre 11159 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15062 crimd 15179 crimi 15140 crre 15061 crred 15178 crrei 15139 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15064 remimd 15145 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15231 absval2d 15392 absval2i 15344 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15088 cjaddd 15167 cjaddi 15135 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15089 cjmuld 15168 cjmuli 15136 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15087 cjcjd 15146 cjcji 15118 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15086 cjreb 15070 cjrebd 15149 cjrebi 15121 cjred 15173 rere 15069 rereb 15067 rerebd 15148 rerebi 15120 rered 15171 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15095 addcjd 15159 addcji 15130 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15185 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15226 abscjd 15397 abscji 15348 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15236 abs00d 15393 abs00i 15345 absne0d 15394 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15268 releabsd 15398 releabsi 15349 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15241 absmuld 15401 absmuli 15351 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15229 sqabsaddi 15352 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15277 abstrid 15403 abstrii 15355 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14028 exp0 14031 expp1 14034 expp1d 14112 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26187 cxpaddd 26225 expadd 14070 expaddd 14113 expaddz 14072 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26196 cxpmuld 26245 expmul 14073 expmuld 14114 expmulz 14074 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26193 mulcxpd 26236 mulexp 14067 mulexpd 14126 mulexpz 14068 |
| [Gleason] p. 140 | Exercise 1 | znnen 16155 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13486 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15576 rlimadd 15587 rlimdiv 15592 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15578 rlimsub 15589 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15577 rlimmul 15590 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15581 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15527 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15548 climcj 15549 climim 15551 climre 15550 rlimabs 15553 rlimcj 15554 rlimim 15556 rlimre 15555 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11253 df-xr 11252 ltxr 13095 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15415 limsupval 15418 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15616 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15625 caucvgb 15626 caucvgbf 44200 caucvgr 15622 climcau 15617 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15762 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15829 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15282 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13793 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 20938 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 23849 xmet0 23848 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 23865 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 23856 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 23858 mstri 23975 xmettri 23857 xmstri 23974 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 23888 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23152 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 24827 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24049 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24381 addcn2 15538 mulcn 24383 mulcn2 15540 subcn 24382 subcn2 15539 |
| [Gleason] p. 295 | Remark | bcval3 14266 bcval4 14267 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14281 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14264 df-bc 14263 |
| [Gleason] p. 296 | Remark | bcn0 14270 bcnn 14272 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15776 |
| [Gleason] p. 308 | Equation 2 | ef0 16034 |
| [Gleason] p. 308 | Equation 3 | efcj 16035 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16040 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16044 |
| [Gleason] p. 310 | Equation 14 | sinadd 16107 |
| [Gleason] p. 310 | Equation 15 | cosadd 16108 |
| [Gleason] p. 311 | Equation 17 | sincossq 16119 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16124 sinbnd 16123 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14180 sqeqori 14178 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16016 |
| [Godowski] p. 730 | Equation SF | goeqi 31526 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 30921 |
| [Golan] p. 1 | Remark | srgisid 20032 |
| [Golan] p. 1 | Definition | df-srg 20010 |
| [Golan] p. 149 | Definition | df-slmd 32346 |
| [Gonshor] p. 7 | Definition | df-scut 27285 |
| [Gonshor] p. 9 | Theorem 2.5 | slerec 27320 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 27407 cofcut1d 27408 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 27409 cofcut2d 27410 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 27411 cofcutr1d 27412 cofcutr2d 27413 |
| [Gonshor] p. 13 | Definition | df-adds 27444 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 27460 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 27485 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 27586 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 27605 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 35131 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17530 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17532 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 46598 df-cllaw 46596 df-comlaw 46597 |
| [Hall] p. 2 | Section 1.2 | df-clintop 46610 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 46631 |
| [Halmos] p. 28 | Partition ` ` | df-parts 37635 dfmembpart2 37640 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 31318 riesz2 31319 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 31194 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 31426 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 31438 elpjidm 31437 pjnmopi 31401 |
| [Halmos] p. 44 | Remark | pjinormi 30940 pjinormii 30929 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 31442 pjrn 30960 pjrni 30955 pjvec 30949 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 30980 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 31407 hmopidmpji 31405 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 31444 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 31433 pjocvec 30950 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 31422 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 31425 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 31428 pjssdif2i 31427 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 31108 |
| [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 24508 df-phtpy 24487 |
| [Hatcher] p. 26 | Definition | df-pco 24521 df-pi1 24524 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 24511 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 24566 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 21992 df-dmatalt 47079 |
| [Helfgott] p. 2 | Theorem | tgoldbach 46485 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 46470 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 46482 bgoldbtbnd 46477 bgoldbtbnd 46477 tgblthelfgott 46483 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 33654 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 33655 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 33669 hgt750lemb 33668 hgt750leme 33670 hgt750lemf 33665 hgt750lemg 33666 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 46479 tgoldbachgt 33675 tgoldbachgtALTV 46480 tgoldbachgtd 33674 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 33656 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 29746 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 18830 grpoideu 29762 mndideu 18636 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 18859 grpoinveu 29772 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 18890 grpo2inv 29784 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 18901 grpoinvop 29786 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 18923 |
| [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 31673 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 31686 cdj3i 31694 cdj3lem1 31687 cdjreui 31685 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 31684 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 40836 |
| [Holland95] p. 14 | Line 15 | hgmapvs 40762 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 40784 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 40785 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 40782 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 40788 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 40707 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 40802 |
| [Holland95] p. 204 | Definition of involution | df-srng 20454 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 38374 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 40399 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 40352 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 38804 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 40248 poml4N 38824 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 40339 pexmidALTN 38849 pexmidN 38840 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 40404 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 37994 ldualset 37995 |
| [Holland95] p. 222 | Item 1 | df-lines 38372 df-pointsN 38373 |
| [Holland95] p. 222 | Item 2 | df-polarityN 38774 |
| [Holland95] p. 223 | Remark | ispsubcl2N 38818 omllaw4 38116 pol1N 38781 polcon3N 38788 |
| [Holland95] p. 223 | Definition | df-psubclN 38806 |
| [Holland95] p. 223 | Equation for polarity | polval2N 38777 |
| [Holmes] p. 40 | Definition | df-xrn 37241 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 30337 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 31435 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 31216 eigre 31088 eigrei 31087 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 31217 eigorth 31091 eigorthi 31090 |
| [Hughes] p. 137 | Remark (ii) | eigposi 31089 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 29562 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 29558 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 29559 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 29560 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 29578 frgrregorufr0 29577 frgrregorufrg 29579 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 29585 frrusgrord 29594 frrusgrord0 29593 |
| [Huneke] p. 2 | Statement | df-clwwlknon 29341 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 29568 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 29571 frgrwopreg2 29572 frgrwopregasn 29569 frgrwopregbsn 29570 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 29574 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 29588 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 29591 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 29339 numclwlk1 29624 numclwlk1lem1 29622 numclwlk1lem2 29623 numclwwlk1 29614 numclwwlk8 29645 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 29565 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 29028 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 29600 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 29626 numclwwlkovh0 29625 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 29634 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 29231 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 29638 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 29641 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 29644 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 29656 natded 29656 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 29656 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 29656 natded 29656 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 29656 |
| [Jech] p. 4 | Definition of class | cv 1541 cvjust 2727 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10574 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10572 alephmul 10573 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10571 infmap2 10213 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9809 |
| [Jech] p. 72 | Equation 9.3 | scott0 9881 scottex 9880 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9862 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9886 |
| [Jech] p. 78 | Note | opthprc 5741 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 41654 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 41742 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 41743 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 41666 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 41670 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 41671 rmyp1 41672 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 41673 rmym1 41674 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 41664 rmx1 41665 rmxluc 41675 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 41668 rmy1 41669 rmyluc 41676 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 41678 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 41679 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 41699 jm2.17b 41700 jm2.17c 41701 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 41732 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 41736 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 41727 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 41702 jm2.24nn 41698 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 41741 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 41747 rmygeid 41703 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 41759 |
| [Juillerat] p. 11 | Section *5 | etransc 44999 etransclem47 44997 etransclem48 44998 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 44994 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 44996 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 44982 |
| [Juillerat] p. 13 | Proof | etransclem35 44985 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 44988 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 44974 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 44991 |
| [Juillerat] p. 14 | Proof | etransclem23 44973 |
| [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 36382 wl-motae 36384 wl-moteq 36383 |
| [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 30769 chabs1i 30771 chabs2 30770 chabs2i 30772 chjass 30786 chjassi 30739 latabs1 18428 latabs2 18429 |
| [Kalmbach] p. 15 | Definition of atom | df-at 31591 ela 31592 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 31536 cvrval2 38144 |
| [Kalmbach] p. 16 | Definition | df-ol 38048 df-oml 38049 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 30837 cmbri 30843 cmtvalN 38081 df-cm 30836 df-cmtN 38047 |
| [Kalmbach] p. 22 | Remark | omllaw5N 38117 pjoml5 30866 pjoml5i 30841 |
| [Kalmbach] p. 22 | Definition | pjoml2 30864 pjoml2i 30838 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 30867 cmcmi 30845 cmcmii 30850 cmtcomN 38119 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 38115 omlsi 30657 pjoml 30689 pjomli 30688 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 38114 |
| [Kalmbach] p. 23 | Remark | cmbr2i 30849 cmcm3 30868 cmcm3i 30847 cmcm3ii 30852 cmcm4i 30848 cmt3N 38121 cmt4N 38122 cmtbr2N 38123 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 30861 cmbr3i 30853 cmtbr3N 38124 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 30871 fh1i 30874 fh2 30872 fh2i 30875 omlfh1N 38128 |
| [Kalmbach] p. 65 | Remark | chjatom 31610 chslej 30751 chsleji 30711 shslej 30633 shsleji 30623 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 30748 chocini 30707 chsupcl 30593 chsupval2 30663 h0elch 30508 helch 30496 hsupval2 30662 ocin 30549 ococss 30546 shococss 30547 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 30565 |
| [Kalmbach] p. 66 | Remark | df-pjh 30648 pjssmi 31418 pjssmii 30934 |
| [Kalmbach] p. 67 | Lemma 3 | osum 30898 osumi 30895 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 31453 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 31653 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 31563 |
| [Kalmbach] p. 140 | Remark | hatomic 31613 hatomici 31612 hatomistici 31615 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 38189 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 31634 lsatexch 37913 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 31608 cvlcvr1 38209 cvr1 38281 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 31627 cvexchi 31622 cvrexch 38291 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 31617 hlrelat 38273 hlrelat5N 38272 lrelat 37884 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 20754 lsmsatcv 37880 spansncv 30906 spansncvi 30905 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 37899 spansncv2 31546 |
| [Kalmbach] p. 266 | Definition | df-st 31464 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 31102 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10641 fpwwe2 10638 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10642 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10649 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10644 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10646 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10659 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10663 gchxpidm 10664 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10675 gchhar 10674 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10211 unxpwdom 9584 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10665 |
| [Kreyszig] p. 3 | Property M1 | metcl 23838 xmetcl 23837 |
| [Kreyszig] p. 4 | Property M2 | meteq0 23845 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24081 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11931 muleqadd 11858 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 23944 |
| [Kreyszig] p. 19 | Remark | mopntopon 23945 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24007 mopnm 23950 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24005 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24010 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24051 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 22762 lmmbr 24775 lmmbr2 24776 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 22884 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 24830 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 24793 iscmet2 24811 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 24833 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 22965 metelcls 24822 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 24823 metcld2 24824 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 24615 lmodvneg1 20515 nvinv 29892 vcm 29829 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 24611 lmod0vs 20505 slmd0vs 32369 vc0 29827 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20506 slmdvs0 32370 vcz 29828 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 29944 ngpmet 24112 nrmmetd 24083 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 29939 imsdval2 29940 ncvspds 24678 ngpds 24113 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24098 nvnd 29941 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24127 nmge0 24126 nvge0 29926 nvz 29922 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24133 nvabs 29925 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 30054 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 29998 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 30060 blocni 30058 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 30059 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 24721 ipeq0 21191 ipz 29972 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 24733 pythi 30103 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 30107 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 24755 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15802 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 24953 minveco 30137 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 30003 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 24846 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 30126 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 31376 leopg 31375 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 31394 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 30171 |
| [Kulpa] p. 547 | Theorem | poimir 36521 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 36520 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 36519 |
| [Kulpa] p. 548 | Theorem | broucube 36522 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 36514 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 36515 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2383 axnul 5306 |
| [Kunen] p. 11 | Axiom 3 | axnul 5306 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 7941 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8832 mapvalg 8830 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10517 |
| [Kunen] p. 31 | Definition 10.24 | mapex 8826 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9759 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9801 r1elssi 9800 |
| [Kunen] p. 107 | Exercise 4 | rankop 9853 rankopb 9847 rankuni 9858 rankxplim 9874 rankxpsuc 9877 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 5010 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 32741 |
| [Lang] p. | Definition | df-rn 5688 |
| [Lang] p. 3 | Statement | lidrideqd 18588 mndbn0 18641 |
| [Lang] p. 3 | Definition | df-mnd 18626 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18606 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18722 |
| [Lang] p. 5 | Equation | gsumreidx 19785 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 46592 |
| [Lang] p. 6 | Example | nn0mnd 46589 |
| [Lang] p. 6 | Equation | gsumxp2 19848 |
| [Lang] p. 6 | Statement | cycsubm 19079 |
| [Lang] p. 6 | Definition | mulgnn0gsum 18960 |
| [Lang] p. 6 | Observation | mndlsmidm 19538 |
| [Lang] p. 7 | Definition | dfgrp2e 18848 |
| [Lang] p. 30 | Definition | df-tocyc 32266 |
| [Lang] p. 32 | Property (a) | cyc3genpm 32311 |
| [Lang] p. 32 | Property (b) | cyc3conja 32316 cycpmconjv 32301 |
| [Lang] p. 53 | Definition | df-cat 17612 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18047 cat1lem 18046 |
| [Lang] p. 54 | Definition | df-iso 17696 |
| [Lang] p. 57 | Definition | df-inito 17934 df-termo 17935 |
| [Lang] p. 58 | Example | irinitoringc 46967 |
| [Lang] p. 58 | Statement | initoeu1 17961 termoeu1 17968 |
| [Lang] p. 62 | Definition | df-func 17808 |
| [Lang] p. 65 | Definition | df-nat 17894 |
| [Lang] p. 91 | Note | df-ringc 46903 |
| [Lang] p. 92 | Statement | mxidlprm 32586 |
| [Lang] p. 92 | Definition | isprmidlc 32566 |
| [Lang] p. 128 | Remark | dsmmlmod 21300 |
| [Lang] p. 129 | Proof | lincscm 47111 lincscmcl 47113 lincsum 47110 lincsumcl 47112 |
| [Lang] p. 129 | Statement | lincolss 47115 |
| [Lang] p. 129 | Observation | dsmmfi 21293 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 32712 qusdimsum 32713 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 32692 |
| [Lang] p. 147 | Definition | snlindsntor 47152 |
| [Lang] p. 504 | Statement | mat1 21949 matring 21945 |
| [Lang] p. 504 | Definition | df-mamu 21886 |
| [Lang] p. 505 | Statement | mamuass 21902 mamutpos 21960 matassa 21946 mattposvs 21957 tposmap 21959 |
| [Lang] p. 513 | Definition | mdet1 22103 mdetf 22097 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22193 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22089 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22113 |
| [Lang] p. 515 | Definition | df-minmar1 22137 smadiadetr 22177 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22112 mdetralt 22110 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22125 |
| [Lang] p. 518 | Definition | df-madu 22136 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22147 madurid 22146 matinv 22179 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 22392 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 32740 fedgmul 32716 |
| [Lang], p. 561 | Remark | chpmatply1 22334 |
| [Lang], p. 561 | Definition | df-chpmat 22329 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 43093 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 43088 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 43094 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5306 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2711 |
| [Levy] p. 59 | Definition | df-ttrcl 9703 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9746 |
| [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 10381 |
| [Levy58] p. 2 | Definition II | df-fin2 10281 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10280 |
| [Levy58] p. 2 | Definition III | df-fin3 10283 |
| [Levy58] p. 3 | Definition V | df-fin5 10284 |
| [Levy58] p. 3 | Definition IV | df-fin4 10282 |
| [Levy58] p. 4 | Definition VI | df-fin6 10285 |
| [Levy58] p. 4 | Definition VII | df-fin7 10286 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10410 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27189 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27200 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27232 nosupbnd1 27217 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27234 nosupbnd2 27219 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27238 noetasuplem4 27239 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27235 |
| [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 31661 |
| [Maeda] p. 168 | Lemma 5 | mdsym 31665 mdsymi 31664 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 31659 mdsymlem6 31661 mdsymlem7 31662 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 31663 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 31566 ssdmd2 31567 ssmd1 31564 ssmd2 31565 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 31562 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 31534 df-md 31533 mdbr 31547 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 31584 mdslj1i 31572 mdslj2i 31573 mdslle1i 31570 mdslle2i 31571 mdslmd1i 31582 mdslmd2i 31583 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 31574 mdsl2bi 31576 mdsl2i 31575 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 31588 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 31585 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 31586 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 31563 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 31568 mdsl3 31569 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 31587 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 31682 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 38191 hlrelat1 38271 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 37909 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 31589 cvmdi 31577 cvnbtwn4 31542 cvrnbtwn4 38149 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 31590 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 38210 cvp 31628 cvrp 38287 lcvp 37910 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 31652 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 31651 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 38203 hlexch4N 38263 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 31654 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 38314 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 38620 atpsubN 38624 df-pointsN 38373 pointpsubN 38622 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 38375 pmap11 38633 pmaple 38632 pmapsub 38639 pmapval 38628 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 38636 pmap1N 38638 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 38641 pmapglb2N 38642 pmapglb2xN 38643 pmapglbx 38640 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 38723 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 38348 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 38667 paddclN 38713 paddidm 38712 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 38349 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 38709 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 38348 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 38349 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19543 lsmmod2 19544 lssats 37882 shatomici 31611 shatomistici 31614 shmodi 30643 shmodsi 30642 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 31553 mdsymlem7 31662 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 30842 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 30746 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 31668 |
| [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 29653 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 43676 |
| [Margaris] p. 60 | Theorem 8 | jcn 162 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 43677 |
| [Margaris] p. 79 | Rule C | exinst01 43386 exinst11 43387 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1981 19.2g 2182 r19.2z 4495 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2196 rr19.3v 3658 |
| [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 29654 conventions-labels 29654 conventions-labels 29654 conventions-labels 29654 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1830 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 43137 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 43139 exbi 1850 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2223 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 43136 2alimdv 1922 alimd 2206 alimdh 1820 alimdv 1920 ax-4 1812 ralimdaa 3258 ralimdv 3170 ralimdva 3168 ralimdvva 3205 sbcimdv 3852 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2201 19.21h 2284 19.21t 2200 19.21vv 43135 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 43138 2eximdv 1923 exim 1837 eximd 2210 eximdh 1868 eximdv 1921 rexim 3088 reximd2a 3267 reximdai 3259 reximdd 43841 reximddv 3172 reximddv2 3213 reximddv3 43840 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 43285 exlimiv 1934 exlimivv 1936 rexlimd3 43833 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 4505 r19.27zv 4506 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2222 19.28vv 43145 r19.28z 4498 r19.28zf 43853 r19.28zv 4501 rr19.28v 3659 |
| [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 43143 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2227 r19.32 45806 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 43141 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 43142 r19.36zv 4507 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2226 19.37vv 43144 r19.37zv 4502 |
| [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 43311 |
| [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 4504 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2232 r19.45zv 4503 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2607 |
| [Mayet] p. 370 | Remark | jpi 31523 largei 31520 stri 31510 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 31465 ishst 31467 |
| [Mayet3] p. 10 | Theorem | hstrbi 31519 hstri 31518 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 30981 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 30982 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 31531 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 30585 chsupcl 30593 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 31613 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 31607 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 31634 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 38854 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18440 latj32 18438 latjass 18436 |
| [Megill] p. 444 | Axiom C5 | ax-5 1914 ax5ALT 37777 |
| [Megill] p. 444 | Section 7 | conventions 29653 |
| [Megill] p. 445 | Lemma L12 | aecom-o 37771 ax-c11n 37758 axc11n 2426 |
| [Megill] p. 446 | Lemma L17 | equtrr 2026 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 37766 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 37798 hbnae 2432 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2481 sbid 2248 sbidd-misc 47764 sbidd 47763 |
| [Megill] p. 448 | Remark 9.6 | axc14 2463 |
| [Megill] p. 448 | Scheme C4' | ax-c4 37754 |
| [Megill] p. 448 | Scheme C5' | ax-c5 37753 sp 2177 |
| [Megill] p. 448 | Scheme C6' | ax-11 2155 |
| [Megill] p. 448 | Scheme C7' | ax-c7 37755 |
| [Megill] p. 448 | Scheme C8' | ax-7 2012 |
| [Megill] p. 448 | Scheme C9' | ax-c9 37760 |
| [Megill] p. 448 | Scheme C10' | ax-6 1972 ax-c10 37756 |
| [Megill] p. 448 | Scheme C11' | ax-c11 37757 |
| [Megill] p. 448 | Scheme C12' | ax-8 2109 |
| [Megill] p. 448 | Scheme C13' | ax-9 2117 |
| [Megill] p. 448 | Scheme C14' | ax-c14 37761 |
| [Megill] p. 448 | Scheme C15' | ax-c15 37759 |
| [Megill] p. 448 | Scheme C16' | ax-c16 37762 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 37774 dral1 2439 dral2-o 37800 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 37767 hba1 2290 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 45602 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 23 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3874 rspsbca 3875 stdpc4 2072 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 37754 ra4 3881 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 3777 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5515 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4395 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4396 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4267 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4324 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4268 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4137 |
| [Mendelson] p. 231 | Definition of union | dfun3 4266 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5452 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4906 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5571 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4621 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5572 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4936 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5827 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6268 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7762 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6371 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8595 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9140 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 9055 xpsneng 9056 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9063 xpcomeng 9064 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9066 |
| [Mendelson] p. 255 | Definition | brsdom 8971 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9058 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8824 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 9037 mapsnend 9036 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9146 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9145 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8876 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 9040 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9059 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10173 djucomen 10172 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10177 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10171 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8531 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8558 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10554 |
| [Mendelson] p. 281 | Definition | df-r1 9759 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9808 |
| [Mendelson] p. 287 | Axiom system MK | ru 3777 |
| [MertziosUnger] p. 152 | Definition | df-frgr 29512 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 29547 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 29549 vdgn1frgrv3 29550 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 29551 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 29544 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 29537 2pthfrgrrn 29535 2pthfrgrrn2 29536 |
| [Mittelstaedt] p. 9 | Definition | df-oc 30505 |
| [Monk1] p. 22 | Remark | conventions 29653 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 29653 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4231 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5783 ssrelf 31844 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5785 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5212 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6262 coi2 6263 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5921 rn0 5926 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 6142 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5695 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5929 rnxp 6170 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5775 xp0 6158 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6077 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6074 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7907 imaexALTV 37199 imaexg 7906 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6071 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7078 funfvop 7052 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6948 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6958 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6595 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7254 dff13f 7255 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7221 funrnex 7940 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7246 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6227 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4969 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 7992 df-1st 7975 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 7993 df-2nd 7976 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9849 ranksnb 9822 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9850 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9851 rankunb 9845 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9833 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9759 r1val2 9832 |
| [Monk1] p. 117 | Lemma | zorn2 10501 zorn2g 10498 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9981 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10556 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9976 |
| [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 37759 ax12v2 2174 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 37754 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2155 |
| [Monk2] p. 109 | Lemma 15 | equvini 2455 equvinv 2033 eqvinop 5488 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1914 ax5ALT 37777 |
| [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 37767 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 17530 |
| [Munkres] p. 77 | Example 2 | distop 22498 indistop 22505 indistopon 22504 |
| [Munkres] p. 77 | Example 3 | fctop 22507 fctop2 22508 |
| [Munkres] p. 77 | Example 4 | cctop 22509 |
| [Munkres] p. 78 | Definition of basis | df-bases 22449 isbasis3g 22452 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17389 tgval2 22459 |
| [Munkres] p. 79 | Remark | tgcl 22472 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 22466 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 22490 tgss3 22489 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 22491 basgen2 22492 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 36230 topdifinfeq 36231 topdifinffin 36229 topdifinfindis 36227 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 22664 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 22542 topcld 22539 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 22543 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 22545 |
| [Munkres] p. 94 | Definition of closure | clsval 22541 |
| [Munkres] p. 94 | Definition of interior | ntrval 22540 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 22579 elcls 22577 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 22587 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 22652 neindisj 22621 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 22654 |
| [Munkres] p. 97 | Definition of limit point | islp2 22649 lpval 22643 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 22819 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 22731 iscn 22739 iscn2 22742 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 22784 cncnp2 22785 cncnpi 22782 df-cnp 22732 iscnp 22741 iscnp2 22743 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24052 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 24828 |
| [Nathanson] p. 123 | Remark | reprgt 33633 reprinfz1 33634 reprlt 33631 |
| [Nathanson] p. 123 | Definition | df-repr 33621 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 33653 |
| [Nathanson] p. 123 | Proposition | breprexp 33645 breprexpnat 33646 itgexpif 33618 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 31357 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 46478 |
| [Pfenning] p. 17 | Definition XM | natded 29656 |
| [Pfenning] p. 17 | Definition NNC | natded 29656 notnotrd 133 |
| [Pfenning] p. 17 | Definition ` `C | natded 29656 |
| [Pfenning] p. 18 | Rule" | natded 29656 |
| [Pfenning] p. 18 | Definition /\I | natded 29656 |
| [Pfenning] p. 18 | Definition ` `E | natded 29656 natded 29656 natded 29656 natded 29656 natded 29656 |
| [Pfenning] p. 18 | Definition ` `I | natded 29656 natded 29656 natded 29656 natded 29656 natded 29656 |
| [Pfenning] p. 18 | Definition ` `EL | natded 29656 |
| [Pfenning] p. 18 | Definition ` `ER | natded 29656 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 29656 |
| [Pfenning] p. 18 | Definition ` `IR | natded 29656 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 29656 |
| [Pfenning] p. 127 | Definition =E | natded 29656 |
| [Pfenning] p. 127 | Definition =I | natded 29656 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 24719 df-dip 29954 dip0l 29971 ip0l 21189 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 24760 ipval 29956 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 29967 ipcj 21187 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 24722 dipdir 30095 ipdir 21192 ipdiri 30083 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 29963 nmsq 24711 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 30078 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 30080 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 30081 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 24728 dipass 30098 ipass 21198 ipassi 30094 |
| [Prugovecki] p. 186 | Definition of bra | braval 31197 df-bra 31103 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 31104 kbval 31207 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 31635 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 38759 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 31649 atcvat4i 31650 cvrat3 38313 cvrat4 38314 lsatcvat3 37922 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 31535 cvrval 38139 df-cv 31532 df-lcv 37889 lspsncv0 20759 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 38771 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 38772 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2711 rabid 3453 rabidd 43849 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2276 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2725 |
| [Quine] p. 19 | Definition 2.9 | conventions 29653 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 29720 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2740 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3779 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3780 dfsbcq2 3781 |
| [Quine] p. 43 | Theorem 6.8 | vex 3479 |
| [Quine] p. 43 | Theorem 6.9 | isset 3488 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3582 spcgv 3587 spcimgf 3580 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3791 spsbcd 3792 |
| [Quine] p. 44 | Theorem 6.12 | elex 3493 |
| [Quine] p. 44 | Theorem 6.13 | elab 3669 elabg 3667 elabgf 3665 |
| [Quine] p. 44 | Theorem 6.14 | noel 4331 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4722 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4632 df-sn 4630 |
| [Quine] p. 49 | Theorem 7.4 | snss 4790 snssg 4788 |
| [Quine] p. 49 | Theorem 7.5 | prss 4824 prssg 4823 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4767 prid1g 4765 prid2 4768 prid2g 4766 snid 4665 snidg 4663 |
| [Quine] p. 51 | Theorem 7.12 | snex 5432 |
| [Quine] p. 51 | Theorem 7.13 | prex 5433 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4931 unisnALT 43687 unisng 4930 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4935 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4942 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4940 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6511 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 45794 dfiota2 6497 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 45803 iotaval 6515 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6522 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6517 |
| [Quine] p. 58 | Definition 9.1 | df-op 4636 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5526 opabidw 5525 opelopab 5543 opelopaba 5537 opelopabaf 5545 opelopabf 5546 opelopabg 5539 opelopabga 5534 opelopabgf 5541 oprabid 7441 oprabidw 7440 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5683 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5685 |
| [Quine] p. 64 | Definition 9.15 | df-id 5575 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6614 |
| [Quine] p. 65 | Theorem 10.4 | funi 6581 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6602 funsng 6600 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6546 |
| [Quine] p. 65 | Definition 10.2 | args 6092 dffv4 6889 |
| [Quine] p. 68 | Definition 10.11 | conventions 29653 df-fv 6552 fv2 6887 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14232 nn0opth2i 14231 nn0opthi 14230 omopthi 8660 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8410 |
| [Quine] p. 232 | Equation i | carddom 10549 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6637 funimaexg 6635 |
| [Quine] p. 331 | Axiom system NF | ru 3777 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 30337 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 29954 polid 30412 polid2i 30410 polidi 30411 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 30066 |
| [ReedSimon] p. 195 | Remark | lnophm 31272 lnophmi 31271 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 31385 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 31387 leopmuli 31386 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 31390 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 31105 leoppos 31379 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 31389 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 31378 |
| [Roman] p. 4 | Definition | df-dmat 21992 df-dmatalt 47079 |
| [Roman] p. 18 | Part Preliminaries | df-rng 46649 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20058 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 47166 |
| [Roman] p. 112 | Note | isldepslvec2 47166 ldepsnlinc 47189 zlmodzxznm 47178 |
| [Roman] p. 112 | Example | zlmodzxzequa 47177 zlmodzxzequap 47180 zlmodzxzldep 47185 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 22392 |
| [Rosenlicht] p. 80 | Theorem | heicant 36523 |
| [Rosser] p. 281 | Definition | df-op 4636 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 33657 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 33658 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 47042 pmtr3ncom 19343 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19339 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19282 cayleyth 19283 |
| [Rudin] p. 164 | Equation 27 | efcan 16039 |
| [Rudin] p. 164 | Equation 30 | efzval 16045 |
| [Rudin] p. 167 | Equation 48 | absefi 16139 |
| [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 6117 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6120 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6114 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6112 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17530 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17531 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17531 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17533 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10131 |
| [Schechter] p. 141 | Definition (MC) | dfac11 41804 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10441 axdc3 10449 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20060 isrngo 36765 |
| [Schechter] p. 276 | Remark 11.6.e | span0 30795 |
| [Schechter] p. 276 | Definition of span | df-span 30562 spanval 30586 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 22496 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6390 onelord 42000 ordelon 6389 ordelord 6387 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 42001 sucidg 6446 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6419 onsuc 7799 ord0 6418 ordsuci 7796 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 42002 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5270 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 41767 elon2 6376 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6371 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5584 epelg 5582 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9592 epirron 42003 ordirr 6383 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 42005 oneptr 42004 ontr1 6411 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 42007 oneptri 42006 ordtri3or 6397 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8501 ord0eln0 6420 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6432 onsucss 42016 trsucss 6453 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7806 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6459 ordnbtwn 6458 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 42018 ordnexbtwnsuc 42017 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10396 onsucf1lem 42019 onsucf1o 42022 onsucf1olem 42020 onsucrn 42021 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 42023 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7834 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 42012 ordne0gt0 42011 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 42014 limnsuc 42015 onsucelab 42013 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9638 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7849 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9641 ordom 7865 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9642 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8639 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7767 ssorduni 7766 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8531 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9645 limom 7871 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8466 df1o2 8473 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8516 oa0suclim 42025 oalim 8532 oasuc 8524 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8517 om0suclim 42026 omlim 8533 omsuc 8526 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8522 oe0m1 8521 oe0suclim 42027 oelim 8534 oesuc 8527 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 41978 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 42029 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 42030 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 42031 limexissupab 42033 limiun 42032 limuni 6426 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8538 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8542 om1om1r 42034 om1r 8543 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8535 oaomoecl 42028 oecl 8537 omcl 8536 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 41980 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8544 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8545 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 42035 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 42036 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8611 nnamecl 42037 nnecl 8613 nnmcl 8612 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 42038 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8552 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8553 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8560 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 42040 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 42041 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 42043 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8559 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 42047 omword1 8573 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 42046 oaordnrex 42045 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 42042 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 42048 omword2 8574 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 42049 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 42050 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 42051 omordi 8566 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8568 omord2com 42052 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 42053 df-2o 8467 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 42056 oewordi 8591 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 42057 oeworde 8593 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 42058 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 42059 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 42055 omnord1ex 42054 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 42060 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 42062 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 42066 oenord1ex 42065 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 42067 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8561 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 42061 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8579 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8580 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 42069 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8597 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 42070 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 42071 cantnfub2 42072 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 42075 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 28172 axtgcgrrflx 27713 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 28173 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 28174 axtgcgrid 27714 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 27699 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 28185 axtgsegcon 27715 df-trkgcb 27701 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 28196 axtg5seg 27716 df-trkgcb 27701 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 28197 axtgbtwnid 27717 df-trkgb 27700 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 28199 axtgpasch 27718 df-trkgb 27700 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 28218 df-trkg2d 33677 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 27721 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 27722 df-trkg2d 33677 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 28221 axtgeucl 27723 df-trkge 27702 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 28234 axtgcont 27720 axtgcont1 27719 df-trkgb 27700 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 34959 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 34961 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 34964 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 34968 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 34969 tgcgrcomimp 27728 tgcgrcoml 27730 tgcgrcomr 27729 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 34974 tgcgrtriv 27735 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 34978 tg5segofs 33685 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 33682 df-ofs 34955 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 34980 tgcgrextend 27736 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 34982 tgsegconeq 27737 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 34994 btwntriv2 34984 tgbtwntriv2 27738 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 34985 tgbtwncom 27739 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 34988 tgbtwntriv1 27742 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 34989 tgbtwnswapid 27743 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 34995 btwnintr 34991 tgbtwnexch2 27747 tgbtwnintr 27744 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 34997 btwnexch3 34992 tgbtwnexch 27749 tgbtwnexch3 27745 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 34996 tgbtwnouttr 27748 tgbtwnouttr2 27746 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 28217 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 34999 tgbtwndiff 27757 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 27750 trisegint 35000 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 35016 tgifscgr 27759 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 27809 colrot1 27810 colrot2 27811 lncom 27873 lnrot1 27874 lnrot2 27875 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 35012 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 35017 tgcgrsub 27760 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 35027 tgcgrxfr 27769 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 27768 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 35013 df-cgrg 27762 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 27762 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 35028 tgbtwnxfr 27781 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 35034 colinearperm2 35036 colinearperm3 35035 colinearperm4 35037 colinearperm5 35038 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 27784 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 35011 tgellng 27804 tglng 27797 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 35039 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 35047 lnxfr 27817 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 35048 lnext 27818 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 35052 tgfscgr 27819 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 35053 lncgr 27820 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 35014 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 35055 lnid 27821 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 35056 tgidinside 27822 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 35073 tgbtwnconn1 27826 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 35074 tgbtwnconn2 27827 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 35075 tgbtwnconn3 27828 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 35081 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 35079 legov 27836 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 27837 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 27850 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 35082 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 35084 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 35086 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 35087 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 35088 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 35085 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 35090 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 27838 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 27840 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 27841 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 27842 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 27843 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 35097 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 35098 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 35093 df-outsideof 35092 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 35094 ishlg 27853 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 27858 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 27860 outsideofrflx 35099 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 27854 hlcomd 27855 outsideofcom 35100 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 27861 outsideoftr 35101 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 27869 outsideofeu 35103 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 35110 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 35111 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 35104 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 35119 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 35120 tglineelsb2 27883 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 35122 linerflx1 35121 linerflx2 35123 tglinecom 27886 tglinerflx1 27884 tglinerflx2 27885 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 35125 tglinethru 27887 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 35109 tglng 27797 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 27845 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 35128 tglinethrueu 27890 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 35129 tglineineq 27894 tglineinteq 27896 tglineintmo 27893 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 27900 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 27901 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 27902 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 27917 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 27913 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 27905 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 27904 ismir 27910 mirbtwn 27909 mircgr 27908 mirfv 27907 mirval 27906 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 27915 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 27916 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 27917 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 27920 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 27921 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 27926 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 27923 mirbtwni 27922 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 27924 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 27936 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 27940 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 27937 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 27938 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 27939 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 27942 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 27943 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 27949 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 27945 israg 27948 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 27950 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 27951 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 27953 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 27954 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 27955 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 27956 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 27957 ragncol 27960 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 27958 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 27964 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 27968 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 27965 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 27947 isperp 27963 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 27966 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 27973 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 27981 colperpexlem2 27982 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 27984 colperpexlem3 27983 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 27989 midex 27988 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 27986 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 27995 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 27990 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 27999 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 28002 opphllem6 28003 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 28005 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 27718 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 28006 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 28014 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 28009 hpgbr 28011 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 28016 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 28015 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 28017 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 28018 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 28019 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 28020 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 28021 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 28035 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 28025 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 28039 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 28040 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 28041 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 28042 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 28043 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 28046 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 28048 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 28026 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 28049 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 28052 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 28053 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 28054 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 28055 trgcopyeu 28057 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 28081 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 28060 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 28069 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 28067 cgrahl2 28068 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 28070 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 28071 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 28073 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 28074 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 28077 cgrahl 28078 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 28082 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 28083 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 28084 acopyeu 28085 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 28092 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 28096 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 28089 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 28104 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 28097 isleag 28098 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 28106 tgsas1 28105 tgsas2 28107 tgsas3 28108 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 28110 tgasa1 28109 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 28111 tgsss2 28112 tgsss3 28113 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 26774 dchrsum 26772 dchrsum2 26771 sumdchr 26775 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 26776 sum2dchr 26777 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 19936 ablfacrp2 19937 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 26719 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 26720 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 26727 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 26985 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 26988 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27042 vmalogdivsum2 27041 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27032 dirith2 27031 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27030 rpvmasum 27029 rpvmasum2 27015 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 26990 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27028 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 26995 dchrisumlem1 26992 dchrisumlem2 26993 dchrisumlem3 26994 dchrisumlema 26991 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 26998 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27027 dchrmusumlem 27025 dchrvmasumlem 27026 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 26997 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 26999 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27023 dchrisum0re 27016 dchrisumn0 27024 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27009 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27013 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27014 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27069 pntrsumbnd2 27070 pntrsumo1 27068 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27033 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27035 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27037 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27040 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27045 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27046 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27051 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27053 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27054 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27062 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27063 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27060 selberg3lem2 27061 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27064 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27058 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27071 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27072 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27073 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27087 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27099 pntlemb 27100 pntlemc 27098 pntlemd 27097 pntlemg 27101 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27099 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27091 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27096 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27099 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27112 pntleml 27114 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4297 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4402 dif0 4373 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4492 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4475 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4288 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4289 |
| [Stoll] p. 20 | Remark | invdif 4269 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4638 |
| [Stoll] p. 43 | Definition | uniiun 5062 |
| [Stoll] p. 44 | Definition | intiin 5063 |
| [Stoll] p. 45 | Definition | df-iin 5001 |
| [Stoll] p. 45 | Definition indexed union | df-iun 5000 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 403 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4297 |
| [Strang] p. 242 | Section 6.3 | expgrowth 43094 |
| [Suppes] p. 22 | Theorem 2 | eq0 4344 eq0f 4341 |
| [Suppes] p. 22 | Theorem 4 | eqss 3998 eqssd 4000 eqssi 3999 |
| [Suppes] p. 23 | Theorem 5 | ss0 4399 ss0b 4398 |
| [Suppes] p. 23 | Theorem 6 | sstr 3991 sstrALT2 43596 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4101 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4102 |
| [Suppes] p. 23 | Theorem 9 | psstr 4105 |
| [Suppes] p. 23 | Theorem 10 | pssss 4096 |
| [Suppes] p. 25 | Theorem 12 | elin 3965 elun 4149 |
| [Suppes] p. 26 | Theorem 15 | inidm 4219 |
| [Suppes] p. 26 | Theorem 16 | in0 4392 |
| [Suppes] p. 27 | Theorem 23 | unidm 4153 |
| [Suppes] p. 27 | Theorem 24 | un0 4391 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4173 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4181 |
| [Suppes] p. 27 | Theorem 27 | unss 4185 |
| [Suppes] p. 27 | Theorem 28 | indir 4276 |
| [Suppes] p. 27 | Theorem 29 | undir 4277 |
| [Suppes] p. 28 | Theorem 32 | difid 4371 |
| [Suppes] p. 29 | Theorem 33 | difin 4262 |
| [Suppes] p. 29 | Theorem 34 | indif 4270 |
| [Suppes] p. 29 | Theorem 35 | undif1 4476 |
| [Suppes] p. 29 | Theorem 36 | difun2 4481 |
| [Suppes] p. 29 | Theorem 37 | difin0 4474 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4472 |
| [Suppes] p. 29 | Theorem 39 | difundi 4280 |
| [Suppes] p. 29 | Theorem 40 | difindi 4282 |
| [Suppes] p. 30 | Theorem 41 | nalset 5314 |
| [Suppes] p. 39 | Theorem 61 | uniss 4917 |
| [Suppes] p. 39 | Theorem 65 | uniop 5516 |
| [Suppes] p. 41 | Theorem 70 | intsn 4991 |
| [Suppes] p. 42 | Theorem 71 | intpr 4987 intprg 4986 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5472 |
| [Suppes] p. 42 | Theorem 78 | intun 4985 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 5037 dfiun2g 5034 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 5038 |
| [Suppes] p. 47 | Theorem 86 | elpw 4607 elpw2 5346 elpw2g 5345 elpwg 4606 elpwgdedVD 43678 |
| [Suppes] p. 47 | Theorem 87 | pwid 4625 |
| [Suppes] p. 47 | Theorem 89 | pw0 4816 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4817 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5692 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5834 xpindir 5835 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5745 xpundir 5746 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9591 |
| [Suppes] p. 58 | Theorem 2 | relss 5782 |
| [Suppes] p. 59 | Theorem 4 | eldm 5901 eldm2 5902 eldm2g 5900 eldmg 5899 |
| [Suppes] p. 59 | Definition 3 | df-dm 5687 |
| [Suppes] p. 60 | Theorem 6 | dmin 5912 |
| [Suppes] p. 60 | Theorem 8 | rnun 6146 |
| [Suppes] p. 60 | Theorem 9 | rnin 6147 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5889 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5883 brcnvg 5880 |
| [Suppes] p. 62 | Equation 5 | elcnv 5877 elcnv2 5878 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6104 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6145 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6143 |
| [Suppes] p. 63 | Definition | dftrrels2 37445 |
| [Suppes] p. 63 | Theorem 20 | co02 6260 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5971 |
| [Suppes] p. 63 | Definition 7 | df-co 5686 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5886 |
| [Suppes] p. 64 | Theorem 27 | coass 6265 |
| [Suppes] p. 65 | Theorem 31 | resundi 5996 |
| [Suppes] p. 65 | Theorem 34 | elima 6065 elima2 6066 elima3 6067 elimag 6064 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6150 |
| [Suppes] p. 66 | Theorem 40 | dminss 6153 |
| [Suppes] p. 66 | Theorem 41 | imainss 6154 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6157 |
| [Suppes] p. 81 | Definition 34 | dfec2 8706 |
| [Suppes] p. 82 | Theorem 72 | elec 8747 elecALTV 37134 elecg 8746 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 37481 erth 8752 erth2 8753 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 37484 erdisj 8755 |
| [Suppes] p. 83 | Definition 35, | df-parts 37635 dfmembpart2 37640 |
| [Suppes] p. 89 | Theorem 96 | map0b 8877 |
| [Suppes] p. 89 | Theorem 97 | map0 8881 map0g 8878 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8882 mapsnd 8880 |
| [Suppes] p. 89 | Theorem 99 | mapss 8883 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 10063 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 10062 |
| [Suppes] p. 92 | Theorem 1 | enref 8981 enrefg 8980 |
| [Suppes] p. 92 | Theorem 2 | ensym 8999 ensymb 8998 ensymi 9000 |
| [Suppes] p. 92 | Theorem 3 | entr 9002 |
| [Suppes] p. 92 | Theorem 4 | unen 9046 |
| [Suppes] p. 94 | Theorem 15 | endom 8975 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 8996 |
| [Suppes] p. 94 | Theorem 17 | domtr 9003 |
| [Suppes] p. 95 | Theorem 18 | sbth 9093 |
| [Suppes] p. 97 | Theorem 23 | canth2 9130 canth2g 9131 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9097 df-sdom 8942 dfsdom2 9096 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9114 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9099 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9098 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9112 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8978 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9115 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9110 |
| [Suppes] p. 98 | Exercise 4 | fundmen 9031 fundmeng 9032 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9070 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9111 |
| [Suppes] p. 104 | Theorem 37 | fofi 9338 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9178 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9178 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10546 |
| [Suppes] p. 130 | Definition 3 | df-tr 5267 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7767 |
| [Suppes] p. 134 | Definition 6 | df-suc 6371 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7893 finds 7889 finds1 7892 finds2 7891 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9647 isfinite2 9301 isfiniteg 9304 unbnn 9299 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10913 df-ltpq 10905 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7852 tfinds 7849 tfinds2 7853 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8551 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8553 |
| [Suppes] p. 211 | Theorem 25 | oaass 8561 |
| [Suppes] p. 225 | Definition 8 | iscard2 9971 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10558 |
| [Suppes] p. 228 | Theorem 59 | harcard 9973 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 10061 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6416 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7781 onminsb 7782 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10567 |
| [Suppes] p. 229 | Theorem 65 | alephcard 10065 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 10072 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 10066 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9935 |
| [Suppes] p. 242 | Theorem 6 | weth 10490 |
| [Suppes] p. 242 | Theorem 8 | entric 10552 |
| [Suppes] p. 242 | Theorem 9 | carden 10546 |
| [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 7413 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3777 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5420 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4652 elpr2 4654 elpr2g 4653 elprg 4650 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4644 elsn2 4668 elsn2g 4667 elsng 4643 velsn 4645 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5468 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4639 sneqr 4842 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4648 dfsn2 4642 dfsn2ALT 4649 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7731 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5477 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5465 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5449 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7733 unexg 7736 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4694 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4910 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3956 df-un 3954 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4927 uniprg 4926 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5376 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4693 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6435 elsucg 6433 sstr2 3990 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4154 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4202 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4167 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4220 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4274 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4275 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3968 dfss2 3969 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4605 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4182 |
| [TakeutiZaring] p. 18 | Exercise 9 | df-ss 3966 sseqin2 4216 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 4005 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4229 inss2 4230 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 4047 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4920 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5450 sspwimp 43679 sspwimpALT 43686 sspwimpALT2 43689 sspwimpcf 43681 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5457 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5286 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3434 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5308 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3952 |
| [TakeutiZaring] p. 20 | Definition 5.14 | dfnul2 4326 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4371 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4347 n0f 4343 neq0 4346 neq0f 4342 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9590 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9727 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9729 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3477 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5316 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4397 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5322 ssexg 5324 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5318 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9597 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9592 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4364 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4131 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4291 undif3VD 43643 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4132 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4139 |
| [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 7740 xpexg 7737 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5684 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6620 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6798 fun11 6623 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6560 svrelfun 6621 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5888 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5890 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5689 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5690 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5686 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6194 dfrel2 6189 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5693 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5812 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5819 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5833 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 6011 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5988 opelresi 5990 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 6004 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 6007 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 6012 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6591 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6108 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6589 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6800 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2606 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 29653 df-fv 6552 fv3 6910 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7916 cnvexg 7915 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7902 dmexg 7894 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7903 rnexg 7895 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 43213 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7911 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6905 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 45882 tz6.12-1-afv2 45949 tz6.12-1 6915 tz6.12-afv 45881 tz6.12-afv2 45948 tz6.12 6917 tz6.12c-afv2 45950 tz6.12c 6914 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 45945 tz6.12-2 6880 tz6.12i-afv2 45951 tz6.12i 6920 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6547 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6548 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6550 wfo 6542 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6549 wf1 6541 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6551 wf1o 6543 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 7033 eqfnfv2 7034 eqfnfv2f 7037 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6990 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7219 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7217 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6637 funimaexg 6635 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5150 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5590 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5641 dffr3 6099 eliniseg 6094 iniseg 6097 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5581 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5655 fr3nr 7759 frirr 5654 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5632 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7761 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5644 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5664 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6349 tz6.26i 6351 wefrc 5671 wereu2 5674 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6352 wfii 6354 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6553 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7326 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7327 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7333 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7334 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7335 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7339 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7346 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7348 |
| [TakeutiZaring] p. 35 | Notation | wtr 5266 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 43214 tz7.2 5661 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5272 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6378 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6386 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6387 ordelordALT 43298 ordelordALTVD 43628 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6393 ordelssne 6392 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6391 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6395 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7769 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7770 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6369 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6397 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 43310 ordon 7764 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7765 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7842 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6412 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5268 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7780 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7819 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6469 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6468 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7766 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4942 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6371 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6445 sucidg 6446 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7799 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6459 ordnbtwn 6458 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7816 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6370 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7870 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7875 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7830 ordelsuc 7808 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7810 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7840 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7857 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7879 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7881 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7882 |
| [TakeutiZaring] p. 43 | Remark | omon 7867 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9630 omex 9638 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7865 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7887 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7883 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7884 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7860 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4967 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5285 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4968 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5338 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7783 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6415 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4952 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9655 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7778 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8376 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8397 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8398 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8399 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8406 tz7.44-2 8407 tz7.44-3 8408 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8367 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8362 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8346 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8445 tz7.49c 8446 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8443 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8442 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8444 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2652 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 10006 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 10007 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8532 oasuc 8524 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7850 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8535 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8516 oa0r 8538 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8536 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8548 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8619 nnaordi 8618 oaord 8547 oaordi 8546 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5053 uniss2 4946 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8550 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8555 oawordex 8557 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8611 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8647 |
| [TakeutiZaring] p. 60 | Remark | oancom 9646 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8560 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8616 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8552 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8519 omlim 8533 omsuc 8526 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8517 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8613 nnmcl 8612 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8632 nnmordi 8631 omord 8568 omordi 8566 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8569 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8636 omwordri 8572 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8539 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8542 om1r 8543 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8575 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8577 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8578 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8579 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8580 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8608 oe0 8522 oelim 8534 oesuc 8527 onesuc 8530 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8520 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8586 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8587 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8521 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8545 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8588 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8594 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8592 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8593 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8597 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8599 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9723 tz9.1 9724 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9759 r10 9763 r1lim 9767 r1limg 9766 r1suc 9765 r1sucg 9764 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9775 r1ord2 9776 r1ordg 9773 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9785 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9810 tz9.13 9786 tz9.13g 9787 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9760 rankval 9811 rankvalb 9792 rankvalg 9812 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9834 rankelb 9819 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9848 rankval3 9835 rankval3b 9821 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9824 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9790 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9829 rankr1c 9816 rankr1g 9827 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9830 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9844 rankssb 9843 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9837 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9836 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10470 dfac3 10116 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 10025 numth 10467 numth2 10466 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10541 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10542 cardid2 9948 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9955 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10546 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9954 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9939 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9960 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9952 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9150 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 9013 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9155 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9074 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9958 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10093 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9209 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9228 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10094 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9214 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10083 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 10061 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9967 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10212 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9321 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8943 isfi 8972 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9230 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10529 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9067 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10521 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10180 unxpdom 9253 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9969 cardsdomelir 9968 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9255 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 10009 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8822 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10557 infxpidm2 10012 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10203 infxp 10210 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9079 pw2f1o 9077 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9143 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10482 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10477 ac6s5 10486 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10538 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10539 uniimadomf 10540 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10269 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10264 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10249 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10246 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10252 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10259 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10268 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10577 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10247 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10271 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10092 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10091 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10103 alephfp2 10104 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10694 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10107 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10564 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10578 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10579 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 37753 |
| [Tarski] p. 67 | Scheme B5 | sp 2177 |
| [Tarski] p. 68 | Lemma 6 | avril1 29716 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 37759 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 37777 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2012 ax-8 2109 ax-9 2117 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 27715 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 27716 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 27718 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 27718 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 27719 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16186 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 36527 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 36529 |
| [Weierstrass] p. 272 | Definition | df-mdet 22087 mdetuni 22124 |
| [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 36326 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 42551 imim2 58 wl-luk-imim2 36321 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 45729 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 36324 |
| [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 43688 wl-luk-notnotr 36325 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 146 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 42581 axfrege28 42580 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 36318 |
| [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 29654 pm2.27 42 wl-luk-pm2.27 36316 |
| [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 37232 |
| [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 43117 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 43118 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1874 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 43119 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 43120 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 43121 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1897 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 43122 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 43123 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 43124 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 43125 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 43126 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 43128 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 43129 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 43130 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 43127 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2094 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 43133 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 43134 |
| [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 43135 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 43136 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 43137 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 43138 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 43140 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 43139 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1891 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 43142 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 43143 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 43141 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1831 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 43144 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 43145 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1849 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 43146 |
| [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 43151 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 43147 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 43148 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 43149 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 43150 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 43155 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 43152 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 43153 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 43154 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 43156 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2564 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 43166 pm13.13b 43167 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 43168 |
| [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 3657 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 43174 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 43175 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 43169 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 43313 pm13.193 43170 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 43171 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 43172 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 43173 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 43180 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 43179 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 43178 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3846 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 43181 pm14.122b 43182 pm14.122c 43183 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 43184 pm14.123b 43185 pm14.123c 43186 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 43188 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 43187 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 43189 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6525 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 43190 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6526 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 43191 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 43193 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2630 eupickbi 2633 sbaniota 43194 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 43192 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2579 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 43196 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 29653 df-fv 6552 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 9996 pm54.43lem 9995 |
| [Young] p. 141 | Definition of operator ordering | leop2 31377 |
| [Young] p. 142 | Example 12.2(i) | 0leop 31383 idleop 31384 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 41566 |
| [vandenDries] p. 43 | Theorem 62 | pellex 41573 pellexlem1 41567 |