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 17595 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17595 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18004 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17616 0funcg 49366 df-termc 49754 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 49831 prsthinc 49745 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 49859 df-mndtc 49859 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 49855 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17639 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 49847 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 49872 oppgoppchom 49871 oppgoppcid 49873 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17709 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17697 invisoinvl 17718 |
| [Adamek] p. 28 | Example 3.13 | idinv 17717 idiso 17716 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17702 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17676 df-iso 17677 dfiso2 17700 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17683 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17734 cicerALT 49327 |
| [Adamek] p. 29 | Definition 3.15 | cic 17727 df-cic 17724 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17786 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17698 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17699 isoco 17705 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17786 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17809 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 49585 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17802 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 49855 discthing 49742 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 49699 prsthinc 49745 thincciso 49734 thincciso2 49736 thincciso3 49737 thinccisod 49735 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 49859 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17816 cofucla 49377 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 49443 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18039 catcisoi 49681 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18094 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17835 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17834 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18094 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17859 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17865 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17864 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18079 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18079 |
| [Adamek] p. 39 | Remark 3.42 | 2oppf 49413 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 49404 funcoppc 17803 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18027 elcatchom 49678 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17853 fthoppf 49445 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17852 fulloppf 49444 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18036 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 49366 df-catc 18027 |
| [Adamek] p. 45 | Exercise 3G | incat 49882 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 49885 nelsubc3 49352 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 49432 imasubc2 49433 imasubc3 49437 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17766 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17767 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 49352 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17778 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17740 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 49441 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 49440 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 49442 ressffth 17868 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 49883 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 17874 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 17895 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 17899 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 17875 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 17901 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 49366 df-inito 17912 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 49366 df-termc 49754 initc 49372 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21438 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 17913 oppctermo 49517 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 17940 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 17944 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 49518 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 17914 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21439 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 17947 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17675 |
| [Adamek] p. 107 | Example 7.20(7) | thincinv 49750 |
| [Adamek] p. 108 | Example 7.25(4) | thincsect2 49749 |
| [Adamek] p. 110 | Example 7.33(9) | thincmon 49714 |
| [Adamek] p. 110 | Proposition 7.35 | sectmon 17710 |
| [Adamek] p. 112 | Proposition 7.42 | sectepi 17712 |
| [Adamek] p. 185 | Section 10.67 | updjud 9850 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 49926 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 49926 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 49926 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 49927 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 49927 |
| [Adamek] p. 478 | Item Rng | df-ringc 20583 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 48830 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 48852 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14498 df-pfx 14599 df-substr 14569 df-word 14441 lencl 14460 wrd0 14466 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24656 df-nmoo 30803 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32211 hmopidmchi 32209 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32259 pjcmul2i 32260 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 31976 unoplin 31978 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 31977 unopadj2 31996 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 32071 lnopunii 32070 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32144 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 27909 |
| [Alling] p. 184 | Axiom B | bdayfo 27649 |
| [Alling] p. 184 | Axiom O | sltso 27648 |
| [Alling] p. 184 | Axiom SD | nodense 27664 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27755 |
| [Alling] p. 185 | Theorem | conway 27777 |
| [Alling] p. 185 | Axiom FE | noeta 27715 |
| [Alling] p. 186 | Theorem 4 | slerec 27797 slerecd 27798 |
| [Alling], p. 2 | Definition | rp-brsslt 43700 |
| [Alling], p. 3 | Note | nla0001 43703 nla0002 43701 nla0003 43702 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11321 addcan2d 11341 addcan2i 11331 addcand 11340 addcani 11330 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11374 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11433 negsubd 11502 negsubi 11463 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11435 negnegd 11487 negnegi 11455 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11574 subdid 11597 subdii 11590 subdir 11575 subdird 11598 subdiri 11591 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11316 mul01d 11336 mul01i 11327 mul02 11315 mul02d 11335 mul02i 11326 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11778 mulcan2d 11775 mulcand 11774 mulcani 11780 |
| [Apostol] p. 18 | Theorem I.8 | receu 11786 xreceu 32984 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11816 divrecd 11924 divreci 11890 divreczi 11883 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11842 recreci 11877 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11781 mul0ord 11789 mul0ori 11788 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11580 mul2negd 11596 mul2negi 11589 mulneg1 11577 mulneg1d 11594 mulneg1i 11587 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11860 divadddivd 11965 divadddivi 11907 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11845 divmuldivd 11962 divmuldivi 11905 rdivmuldivd 20353 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11846 divdivdivd 11968 divdivdivi 11908 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 12933 rpaddcld 12968 rpmulcl 12934 rpmulcld 12969 |
| [Apostol] p. 20 | Axiom 8 | rpneg 12943 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 12946 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11263 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11734 ltadd1dd 11752 ltadd1i 11695 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 11995 ltmul1a 11994 ltmul1i 12064 ltmul1ii 12074 ltmul2 11996 ltmul2d 12995 ltmul2dd 13009 ltmul2i 12067 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11661 msqgt0d 11708 msqgt0i 11678 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11663 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11647 lt0neg1d 11710 ltneg 11641 ltnegd 11719 ltnegi 11685 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11626 lt2addd 11764 lt2addi 11703 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 12910 |
| [Apostol] p. 21 | Exercise 4 | recgt0 11991 recgt0d 12080 recgt0i 12051 recgt0ii 12052 |
| [Apostol] p. 22 | Definition of integers | df-z 12493 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12163 |
| [Apostol] p. 22 | Definition of rationals | df-q 12866 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9361 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12401 |
| [Apostol] p. 26 | Theorem I.29 | arch 12402 archd 45442 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12599 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12403 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12864 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12863 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13118 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16270 zneo 12579 zneoALTV 47951 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26699 msqsqrtd 15370 resqrtth 15182 sqrtth 15292 sqrtthi 15298 sqsqrtd 15369 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12152 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12830 |
| [Apostol] p. 361 | Remark | crreczi 14155 |
| [Apostol] p. 363 | Remark | absgt0i 15327 |
| [Apostol] p. 363 | Example | abssubd 15383 abssubi 15331 |
| [ApostolNT] p. 7 | Remark | fmtno0 47822 fmtno1 47823 fmtno2 47832 fmtno3 47833 fmtno4 47834 fmtno5fac 47864 fmtnofz04prm 47859 |
| [ApostolNT] p. 7 | Definition | df-fmtno 47810 |
| [ApostolNT] p. 8 | Definition | df-ppi 27070 |
| [ApostolNT] p. 14 | Definition | df-dvds 16184 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16200 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16225 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16220 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16213 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16215 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16201 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16202 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16207 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16242 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16244 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16246 |
| [ApostolNT] p. 15 | Definition | df-gcd 16426 dfgcd2 16477 |
| [ApostolNT] p. 16 | Definition | isprm2 16613 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16584 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16847 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16444 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16478 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16480 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16459 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16451 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16642 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16644 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16860 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16854 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16334 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16518 |
| [ApostolNT] p. 24 | Definition | df-mu 27071 |
| [ApostolNT] p. 25 | Definition | df-phi 16697 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27161 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16722 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16707 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16711 |
| [ApostolNT] p. 32 | Definition | df-vma 27068 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27163 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27187 |
| [ApostolNT] p. 38 | Remark | df-sgm 27072 |
| [ApostolNT] p. 38 | Definition | df-sgm 27072 |
| [ApostolNT] p. 75 | Definition | df-chp 27069 df-cht 27067 |
| [ApostolNT] p. 104 | Definition | congr 16595 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16187 |
| [ApostolNT] p. 106 | Definition | moddvds 16194 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16277 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16278 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13812 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13852 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14165 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16219 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16598 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17006 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16600 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16714 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16733 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16715 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27042 |
| [ApostolNT] p. 179 | Definition | df-lgs 27266 lgsprme0 27310 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27311 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27287 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27302 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27359 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27378 2lgsoddprm 27387 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27345 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27354 |
| [ApostolNT] p. 188 | Definition | df-lgs 27266 lgs1 27312 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27303 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27305 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27313 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27314 |
| [Baer] p. 40 | Property (b) | mapdord 41935 |
| [Baer] p. 40 | Property (c) | mapd11 41936 |
| [Baer] p. 40 | Property (e) | mapdin 41959 mapdlsm 41961 |
| [Baer] p. 40 | Property (f) | mapd0 41962 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 41922 mapd1o 41945 |
| [Baer] p. 41 | Property (g) | mapdat 41964 |
| [Baer] p. 44 | Part (1) | mapdpg 42003 |
| [Baer] p. 45 | Part (2) | hdmap1eq 42098 mapdheq 42025 mapdheq2 42026 mapdheq2biN 42027 |
| [Baer] p. 45 | Part (3) | baerlem3 42010 |
| [Baer] p. 46 | Part (4) | mapdheq4 42029 mapdheq4lem 42028 |
| [Baer] p. 46 | Part (5) | baerlem5a 42011 baerlem5abmN 42015 baerlem5amN 42013 baerlem5b 42012 baerlem5bmN 42014 |
| [Baer] p. 47 | Part (6) | hdmap1l6 42118 hdmap1l6a 42106 hdmap1l6e 42111 hdmap1l6f 42112 hdmap1l6g 42113 hdmap1l6lem1 42104 hdmap1l6lem2 42105 mapdh6N 42044 mapdh6aN 42032 mapdh6eN 42037 mapdh6fN 42038 mapdh6gN 42039 mapdh6lem1N 42030 mapdh6lem2N 42031 |
| [Baer] p. 48 | Part 9 | hdmapval 42125 |
| [Baer] p. 48 | Part 10 | hdmap10 42137 |
| [Baer] p. 48 | Part 11 | hdmapadd 42140 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 42114 mapdh6hN 42040 |
| [Baer] p. 48 | Part (7) | mapdh75cN 42050 mapdh75d 42051 mapdh75e 42049 mapdh75fN 42052 mapdh7cN 42046 mapdh7dN 42047 mapdh7eN 42045 mapdh7fN 42048 |
| [Baer] p. 48 | Part (8) | mapdh8 42085 mapdh8a 42072 mapdh8aa 42073 mapdh8ab 42074 mapdh8ac 42075 mapdh8ad 42076 mapdh8b 42077 mapdh8c 42078 mapdh8d 42080 mapdh8d0N 42079 mapdh8e 42081 mapdh8g 42082 mapdh8i 42083 mapdh8j 42084 |
| [Baer] p. 48 | Part (9) | mapdh9a 42086 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 42066 |
| [Baer] p. 49 | Part 12 | hdmap11 42145 hdmapeq0 42141 hdmapf1oN 42162 hdmapneg 42143 hdmaprnN 42161 hdmaprnlem1N 42146 hdmaprnlem3N 42147 hdmaprnlem3uN 42148 hdmaprnlem4N 42150 hdmaprnlem6N 42151 hdmaprnlem7N 42152 hdmaprnlem8N 42153 hdmaprnlem9N 42154 hdmapsub 42144 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 42165 hdmap14lem10 42174 hdmap14lem1a 42163 hdmap14lem2N 42166 hdmap14lem2a 42164 hdmap14lem3 42167 hdmap14lem8 42172 hdmap14lem9 42173 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 42175 hdmap14lem12 42176 hdmap14lem13 42177 hdmap14lem14 42178 hdmap14lem15 42179 hgmapval 42184 |
| [Baer] p. 50 | Part 15 | hgmapadd 42191 hgmapmul 42192 hgmaprnlem2N 42194 hgmapvs 42188 |
| [Baer] p. 50 | Part 16 | hgmaprnN 42198 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 42214 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 42215 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 42216 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 42217 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 42219 hgmapvv 42223 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 42218 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 42220 |
| [Baer] p. 111 | Line 15 | hdmapg 42227 hdmapglem7 42226 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26700 2irrexpqALT 26770 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 23 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2570 |
| [BellMachover] p. 460 | Notation | df-mo 2540 |
| [BellMachover] p. 460 | Definition | mo3 2565 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2709 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2713 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5233 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5242 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37240 sepex 5246 |
| [BellMachover] p. 466 | Problem | axpow2 5313 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5314 |
| [BellMachover] p. 466 | Axiom Union | axun2 7684 |
| [BellMachover] p. 468 | Definition | df-ord 6321 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6336 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6343 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6338 |
| [BellMachover] p. 471 | Definition of N | df-om 7811 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7748 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6323 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9555 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7826 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9680 |
| [BellMachover] p. 478 | Definition | rankval2 9734 rankval2b 35236 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9698 r1ord3g 9695 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9505 |
| [BellMachover] p. 488 | Axiom AC | ac5 10391 dfac4 10036 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10024 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 39616 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32411 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32453 chirredi 32452 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32441 |
| [Beran] p. 3 | Definition of join | sshjval3 31412 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 31674 cmcm2i 31651 cmcm2ii 31656 cmt2N 39547 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 31675 lecmi 31660 lecmii 31661 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 31649 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 31678 cm2ji 31683 cm2mi 31684 |
| [Beran] p. 95 | Definition | df-sh 31265 issh2 31267 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31144 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31157 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31148 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 31886 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 31888 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 31887 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 31889 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31140 his1i 31158 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31141 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31142 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31143 |
| [Beran] p. 96 | Definition of norm | df-hnorm 31026 dfhnorm2 31180 normval 31182 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31242 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 31031 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31299 |
| [Beran] p. 96 | Definition of converge | df-hlim 31030 hlimi 31246 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31191 norm-i 31187 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31195 norm-ii 31196 normlem0 31167 normlem1 31168 normlem2 31169 normlem3 31170 normlem4 31171 normlem5 31172 normlem6 31173 normlem7 31174 normlem7tALT 31177 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31197 norm-iii 31198 |
| [Beran] p. 98 | Remark 3.4 | bcs 31239 bcsiALT 31237 bcsiHIL 31238 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31179 normpar 31213 normpari 31212 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31204 normpyth 31203 normpythi 31200 |
| [Beran] p. 99 | Remark | lnfn0 32105 lnfn0i 32100 lnop0 32024 lnop0i 32028 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32084 nmcfnex 32111 nmcfnexi 32109 nmcopex 32087 nmcopexi 32085 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32112 nmcfnlbi 32110 nmcoplb 32088 nmcoplbi 32086 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32114 lnfnconi 32113 lnopcon 32093 lnopconi 32092 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31214 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31211 norm3adifii 31206 norm3dif 31208 norm3difi 31205 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31359 pjhth 31451 pjhtheu 31452 pjpjhth 31483 pjpjhthi 31484 pjth 25399 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31464 ococi 31463 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32119 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32120 riesz4 32122 riesz4i 32121 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32137 cnlnadjeu 32136 cnlnadjeui 32135 cnlnadji 32134 cnlnadjlem1 32125 nmopadjlei 32146 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32149 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32148 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32150 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 31994 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32160 nmopcoadji 32159 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32151 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32161 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32158 pjadj2coi 32262 pjadjcoi 32219 |
| [Beran] p. 107 | Definition | df-ch 31279 isch2 31281 |
| [Beran] p. 107 | Remark 3.12 | choccl 31364 isch3 31299 occl 31362 ocsh 31341 shoccl 31363 shocsh 31342 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31466 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31390 |
| [Beran] p. 109 | Property (i) | pjadj2 32245 pjadj3 32246 pjadji 31743 pjadjii 31732 |
| [Beran] p. 109 | Property (ii) | pjidmco 32239 pjidmcoi 32235 pjidmi 31731 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32231 |
| [Beran] p. 111 | Remark | ho0val 31808 pjch1 31728 |
| [Beran] p. 111 | Definition | df-hfmul 31792 df-hfsum 31791 df-hodif 31790 df-homul 31789 df-hosum 31788 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 31729 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 31752 pjchi 31490 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31497 pjoc2i 31496 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 31738 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32223 pjssmii 31739 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32222 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32221 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32226 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32224 pjssge0ii 31740 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32225 pjdifnormii 31741 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1778 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1776 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1779 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1774 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34430 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34438 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34436 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34440 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34460 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34491 df-sitm 34469 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34491 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34468 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29104 isuhgrop 29126 isusgrop 29218 isuspgrop 29217 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 48143 df-subgr 29324 uhgrspan1 29359 uhgrspansubgr 29347 |
| [Bollobas] p. 3 | Definition | df-gric 48163 gricuspgr 48200 isuspgrim 48178 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29511 df-clnbgr 48101 df-cusgr 29468 df-nbgr 29389 fusgrmaxsize 29521 |
| [Bollobas] p. 4 | Definition | df-upwlks 48416 df-wlks 29656 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 29607 finsumvtxdgeven 29609 fusgr1th 29608 fusgrvtxdgonume 29611 vtxdgoddnumeven 29610 |
| [Bollobas] p. 5 | Notation | df-pths 29770 |
| [Bollobas] p. 5 | Definition | df-crcts 29842 df-cycls 29843 df-trls 29747 df-wlkson 29657 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29115 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 48482 df-cllaw 48468 df-mgm 18569 df-mgm2 48501 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 48483 df-asslaw 48470 df-sgrp 18648 df-sgrp2 48503 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 48502 df-comlaw 48469 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18664 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33089 mndlactf1o 33093 mndractf1 33091 mndractf1o 33094 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20174 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20092 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 33771 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 33775 assarrginv 33774 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 33816 fldextrspunfld 33814 fldextrspunlem1 33813 fldextrspunlem2 33815 fldextrspunlsp 33812 fldextrspunlsplem 33811 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 33599 dfufd2 33612 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7235 fcofo 7236 |
| [BourbakiTop1] p. | Remark | xnegmnf 13129 xnegpnf 13128 |
| [BourbakiTop1] p. | Remark | rexneg 13130 |
| [BourbakiTop1] p. | Remark 3 | ust0 24168 ustfilxp 24161 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24038 |
| [BourbakiTop1] p. | Criterion | ishmeo 23707 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24231 iducn 24230 snfil 23812 |
| [BourbakiTop1] p. | Example 2 | neifil 23828 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 24015 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24251 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 34095 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23811 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24223 df-ust 24149 filintn0 23809 filn0 23810 istgp 24025 ucnprima 24229 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24234 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24245 df-usp 24205 df-utop 24179 trust 24177 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 33994 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23064 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23217 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24154 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24157 |
| [BourbakiTop1] p. | Property V_ii | innei 23073 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23081 neissex 23075 |
| [BourbakiTop1] p. | Proposition 1 | neips 23061 neiss 23057 ucncn 24232 ustund 24170 ustuqtop 24194 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23215 neiptopreu 23081 utop2nei 24198 utop3cls 24199 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24239 uspreg 24221 utopreg 24200 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23639 imasncls 23640 imasnopn 23638 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 23948 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24156 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24158 |
| [BourbakiTop1] p. | Property V_iii | elnei 23059 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24250 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24155 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24159 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23335 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23794 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 22842 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 33991 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 46342 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 46344 stoweid 46343 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 46281 stoweidlem10 46290 stoweidlem14 46294 stoweidlem15 46295 stoweidlem35 46315 stoweidlem36 46316 stoweidlem37 46317 stoweidlem38 46318 stoweidlem40 46320 stoweidlem41 46321 stoweidlem43 46323 stoweidlem44 46324 stoweidlem46 46326 stoweidlem5 46285 stoweidlem50 46330 stoweidlem52 46332 stoweidlem53 46333 stoweidlem55 46335 stoweidlem56 46336 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 46303 stoweidlem24 46304 stoweidlem27 46307 stoweidlem28 46308 stoweidlem30 46310 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 46314 stoweidlem59 46339 stoweidlem60 46340 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 46325 stoweidlem49 46329 stoweidlem7 46287 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 46311 stoweidlem39 46319 stoweidlem42 46322 stoweidlem48 46328 stoweidlem51 46331 stoweidlem54 46334 stoweidlem57 46337 stoweidlem58 46338 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 46305 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 46297 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 46291 stoweidlem13 46293 stoweidlem26 46306 stoweidlem61 46341 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 46298 |
| [Bruck] p. 1 | Section I.1 | df-clintop 48482 df-mgm 18569 df-mgm2 48501 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18648 df-sgrp2 48503 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 18973 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5181 |
| [Church] p. 129 | Section II.24 | df-ifp 1064 dfifp2 1065 |
| [Clemente] p. 10 | Definition IT | natded 30461 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30461 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30461 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30461 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30461 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30461 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30461 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30461 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30461 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30461 |
| [Clemente] p. 14 | Proof 5.11 | natded 30461 |
| [Clemente] p. 14 | Definition E` `n | natded 30461 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30463 ex-natded5.2 30462 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30466 ex-natded5.3 30465 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30468 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30470 ex-natded5.7 30469 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30472 ex-natded5.8 30471 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30474 ex-natded5.13 30473 |
| [Clemente] p. 32 | Definition I` `n | natded 30461 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30461 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30461 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30461 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30475 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30476 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30478 ex-natded9.26 30477 |
| [Cohen] p. 301 | Remark | relogoprlem 26560 |
| [Cohen] p. 301 | Property 2 | relogmul 26561 relogmuld 26594 |
| [Cohen] p. 301 | Property 3 | relogdiv 26562 relogdivd 26595 |
| [Cohen] p. 301 | Property 4 | relogexp 26565 |
| [Cohen] p. 301 | Property 1a | log1 26554 |
| [Cohen] p. 301 | Property 1b | loge 26555 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26757 |
| [Cohen4] p. 349 | Property | relogbf 26761 |
| [Cohen4] p. 352 | Definition | elogb 26740 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26747 |
| [Cohen4] p. 361 | Property 3 | logbrec 26752 relogbdiv 26749 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26745 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26750 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26738 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26739 |
| [Cohen4] p. 367 | Property | logbchbase 26741 |
| [Cohen4] p. 377 | Property 2 | logblt 26754 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34423 sxbrsigalem4 34425 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18484 acsinfd 18483 acsinfdimd 18485 acsmap2d 18482 acsmapd 18481 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34428 |
| [Connell] p. 57 | Definition | df-scmat 22439 df-scmatalt 48681 |
| [Conway] p. 4 | Definition | slerec 27797 slerecd 27798 |
| [Conway] p. 5 | Definition | addsval 27944 addsval2 27945 df-adds 27942 df-muls 28089 df-negs 28003 |
| [Conway] p. 7 | Theorem | 0slt1s 27810 |
| [Conway] p. 12 | Theorem 12 | pw2cut2 28441 |
| [Conway] p. 16 | Theorem 0(i) | ssltright 27853 |
| [Conway] p. 16 | Theorem 0(ii) | ssltleft 27852 |
| [Conway] p. 16 | Theorem 0(iii) | slerflex 27739 |
| [Conway] p. 17 | Theorem 3 | addsass 27987 addsassd 27988 addscom 27948 addscomd 27949 addsrid 27946 addsridd 27947 |
| [Conway] p. 17 | Definition | df-0s 27805 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 28026 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 28023 negsidd 28024 |
| [Conway] p. 18 | Theorem 5 | sleadd1 27971 sleadd1d 27977 |
| [Conway] p. 18 | Definition | df-1s 27806 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 28018 negscld 28019 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 27962 |
| [Conway] p. 19 | Note | mulsunif2 28152 |
| [Conway] p. 19 | Theorem 7 | addsdi 28137 addsdid 28138 addsdird 28139 mulnegs1d 28142 mulnegs2d 28143 mulsass 28148 mulsassd 28149 mulscom 28121 mulscomd 28122 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28116 mulscld 28117 |
| [Conway] p. 19 | Theorem 8(iii) | slemuld 28120 sltmul 28118 sltmuld 28119 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28126 mulsgt0d 28127 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28199 |
| [Conway] p. 23 | Theorem 11 | eqscut3 27802 |
| [Conway] p. 24 | Definition | df-reno 28469 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28478 remulscl 28481 renegscl 28477 |
| [Conway] p. 27 | Definition | df-ons 28233 elons2 28239 |
| [Conway] p. 27 | Theorem 14 | sltonex 28243 |
| [Conway] p. 28 | Theorem 15 | onscutlt 28245 onswe 28253 |
| [Conway] p. 29 | Remark | madebday 27882 newbday 27884 oldbday 27883 |
| [Conway] p. 29 | Definition | df-made 27825 df-new 27827 df-old 27826 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13785 |
| [Crawley] p. 1 | Definition of poset | df-poset 18240 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 39683 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 40487 dalaw 40183 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 42258 |
| [Crawley] p. 111 | Definition of set W | df-watsN 40287 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 40403 df-ldil 40401 isldil 40407 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 40402 df-trnN 40404 isltrn 40416 ltrnu 40418 |
| [Crawley] p. 112 | Lemma A | cdlema1N 40088 cdlema2N 40089 exatleN 39701 |
| [Crawley] p. 112 | Lemma B | 1cvrat 39773 cdlemb 40091 cdlemb2 40338 cdlemb3 40903 idltrn 40447 l1cvat 39352 lhpat 40340 lhpat2 40342 lshpat 39353 ltrnel 40436 ltrnmw 40448 |
| [Crawley] p. 112 | Lemma C | cdlemc1 40488 cdlemc2 40489 ltrnnidn 40471 trlat 40466 trljat1 40463 trljat2 40464 trljat3 40465 trlne 40482 trlnidat 40470 trlnle 40483 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 40288 |
| [Crawley] p. 113 | Lemma C | cdlemc 40494 cdlemc3 40490 cdlemc4 40491 |
| [Crawley] p. 113 | Lemma D | cdlemd 40504 cdlemd1 40495 cdlemd2 40496 cdlemd3 40497 cdlemd4 40498 cdlemd5 40499 cdlemd6 40500 cdlemd7 40501 cdlemd8 40502 cdlemd9 40503 cdleme31sde 40682 cdleme31se 40679 cdleme31se2 40680 cdleme31snd 40683 cdleme32a 40738 cdleme32b 40739 cdleme32c 40740 cdleme32d 40741 cdleme32e 40742 cdleme32f 40743 cdleme32fva 40734 cdleme32fva1 40735 cdleme32fvcl 40737 cdleme32le 40744 cdleme48fv 40796 cdleme4gfv 40804 cdleme50eq 40838 cdleme50f 40839 cdleme50f1 40840 cdleme50f1o 40843 cdleme50laut 40844 cdleme50ldil 40845 cdleme50lebi 40837 cdleme50rn 40842 cdleme50rnlem 40841 cdlemeg49le 40808 cdlemeg49lebilem 40836 |
| [Crawley] p. 113 | Lemma E | cdleme 40857 cdleme00a 40506 cdleme01N 40518 cdleme02N 40519 cdleme0a 40508 cdleme0aa 40507 cdleme0b 40509 cdleme0c 40510 cdleme0cp 40511 cdleme0cq 40512 cdleme0dN 40513 cdleme0e 40514 cdleme0ex1N 40520 cdleme0ex2N 40521 cdleme0fN 40515 cdleme0gN 40516 cdleme0moN 40522 cdleme1 40524 cdleme10 40551 cdleme10tN 40555 cdleme11 40567 cdleme11a 40557 cdleme11c 40558 cdleme11dN 40559 cdleme11e 40560 cdleme11fN 40561 cdleme11g 40562 cdleme11h 40563 cdleme11j 40564 cdleme11k 40565 cdleme11l 40566 cdleme12 40568 cdleme13 40569 cdleme14 40570 cdleme15 40575 cdleme15a 40571 cdleme15b 40572 cdleme15c 40573 cdleme15d 40574 cdleme16 40582 cdleme16aN 40556 cdleme16b 40576 cdleme16c 40577 cdleme16d 40578 cdleme16e 40579 cdleme16f 40580 cdleme16g 40581 cdleme19a 40600 cdleme19b 40601 cdleme19c 40602 cdleme19d 40603 cdleme19e 40604 cdleme19f 40605 cdleme1b 40523 cdleme2 40525 cdleme20aN 40606 cdleme20bN 40607 cdleme20c 40608 cdleme20d 40609 cdleme20e 40610 cdleme20f 40611 cdleme20g 40612 cdleme20h 40613 cdleme20i 40614 cdleme20j 40615 cdleme20k 40616 cdleme20l 40619 cdleme20l1 40617 cdleme20l2 40618 cdleme20m 40620 cdleme20y 40599 cdleme20zN 40598 cdleme21 40634 cdleme21d 40627 cdleme21e 40628 cdleme22a 40637 cdleme22aa 40636 cdleme22b 40638 cdleme22cN 40639 cdleme22d 40640 cdleme22e 40641 cdleme22eALTN 40642 cdleme22f 40643 cdleme22f2 40644 cdleme22g 40645 cdleme23a 40646 cdleme23b 40647 cdleme23c 40648 cdleme26e 40656 cdleme26eALTN 40658 cdleme26ee 40657 cdleme26f 40660 cdleme26f2 40662 cdleme26f2ALTN 40661 cdleme26fALTN 40659 cdleme27N 40666 cdleme27a 40664 cdleme27cl 40663 cdleme28c 40669 cdleme3 40534 cdleme30a 40675 cdleme31fv 40687 cdleme31fv1 40688 cdleme31fv1s 40689 cdleme31fv2 40690 cdleme31id 40691 cdleme31sc 40681 cdleme31sdnN 40684 cdleme31sn 40677 cdleme31sn1 40678 cdleme31sn1c 40685 cdleme31sn2 40686 cdleme31so 40676 cdleme35a 40745 cdleme35b 40747 cdleme35c 40748 cdleme35d 40749 cdleme35e 40750 cdleme35f 40751 cdleme35fnpq 40746 cdleme35g 40752 cdleme35h 40753 cdleme35h2 40754 cdleme35sn2aw 40755 cdleme35sn3a 40756 cdleme36a 40757 cdleme36m 40758 cdleme37m 40759 cdleme38m 40760 cdleme38n 40761 cdleme39a 40762 cdleme39n 40763 cdleme3b 40526 cdleme3c 40527 cdleme3d 40528 cdleme3e 40529 cdleme3fN 40530 cdleme3fa 40533 cdleme3g 40531 cdleme3h 40532 cdleme4 40535 cdleme40m 40764 cdleme40n 40765 cdleme40v 40766 cdleme40w 40767 cdleme41fva11 40774 cdleme41sn3aw 40771 cdleme41sn4aw 40772 cdleme41snaw 40773 cdleme42a 40768 cdleme42b 40775 cdleme42c 40769 cdleme42d 40770 cdleme42e 40776 cdleme42f 40777 cdleme42g 40778 cdleme42h 40779 cdleme42i 40780 cdleme42k 40781 cdleme42ke 40782 cdleme42keg 40783 cdleme42mN 40784 cdleme42mgN 40785 cdleme43aN 40786 cdleme43bN 40787 cdleme43cN 40788 cdleme43dN 40789 cdleme5 40537 cdleme50ex 40856 cdleme50ltrn 40854 cdleme51finvN 40853 cdleme51finvfvN 40852 cdleme51finvtrN 40855 cdleme6 40538 cdleme7 40546 cdleme7a 40540 cdleme7aa 40539 cdleme7b 40541 cdleme7c 40542 cdleme7d 40543 cdleme7e 40544 cdleme7ga 40545 cdleme8 40547 cdleme8tN 40552 cdleme9 40550 cdleme9a 40548 cdleme9b 40549 cdleme9tN 40554 cdleme9taN 40553 cdlemeda 40595 cdlemedb 40594 cdlemednpq 40596 cdlemednuN 40597 cdlemefr27cl 40700 cdlemefr32fva1 40707 cdlemefr32fvaN 40706 cdlemefrs32fva 40697 cdlemefrs32fva1 40698 cdlemefs27cl 40710 cdlemefs32fva1 40720 cdlemefs32fvaN 40719 cdlemesner 40593 cdlemeulpq 40517 |
| [Crawley] p. 114 | Lemma E | 4atex 40373 4atexlem7 40372 cdleme0nex 40587 cdleme17a 40583 cdleme17c 40585 cdleme17d 40795 cdleme17d1 40586 cdleme17d2 40792 cdleme18a 40588 cdleme18b 40589 cdleme18c 40590 cdleme18d 40592 cdleme4a 40536 |
| [Crawley] p. 115 | Lemma E | cdleme21a 40622 cdleme21at 40625 cdleme21b 40623 cdleme21c 40624 cdleme21ct 40626 cdleme21f 40629 cdleme21g 40630 cdleme21h 40631 cdleme21i 40632 cdleme22gb 40591 |
| [Crawley] p. 116 | Lemma F | cdlemf 40860 cdlemf1 40858 cdlemf2 40859 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 40864 cdlemg16 40954 cdlemg28 41001 cdlemg28a 40990 cdlemg28b 41000 cdlemg3a 40894 cdlemg42 41026 cdlemg43 41027 cdlemg44 41030 cdlemg44a 41028 cdlemg46 41032 cdlemg47 41033 cdlemg9 40931 ltrnco 41016 ltrncom 41035 tgrpabl 41048 trlco 41024 |
| [Crawley] p. 116 | Definition of G | df-tgrp 41040 |
| [Crawley] p. 117 | Lemma G | cdlemg17 40974 cdlemg17b 40959 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 41053 df-edring 41054 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 41057 |
| [Crawley] p. 118 | Remark | tendopltp 41077 |
| [Crawley] p. 118 | Lemma H | cdlemh 41114 cdlemh1 41112 cdlemh2 41113 |
| [Crawley] p. 118 | Lemma I | cdlemi 41117 cdlemi1 41115 cdlemi2 41116 |
| [Crawley] p. 118 | Lemma J | cdlemj1 41118 cdlemj2 41119 cdlemj3 41120 tendocan 41121 |
| [Crawley] p. 118 | Lemma K | cdlemk 41271 cdlemk1 41128 cdlemk10 41140 cdlemk11 41146 cdlemk11t 41243 cdlemk11ta 41226 cdlemk11tb 41228 cdlemk11tc 41242 cdlemk11u-2N 41186 cdlemk11u 41168 cdlemk12 41147 cdlemk12u-2N 41187 cdlemk12u 41169 cdlemk13-2N 41173 cdlemk13 41149 cdlemk14-2N 41175 cdlemk14 41151 cdlemk15-2N 41176 cdlemk15 41152 cdlemk16-2N 41177 cdlemk16 41154 cdlemk16a 41153 cdlemk17-2N 41178 cdlemk17 41155 cdlemk18-2N 41183 cdlemk18-3N 41197 cdlemk18 41165 cdlemk19-2N 41184 cdlemk19 41166 cdlemk19u 41267 cdlemk1u 41156 cdlemk2 41129 cdlemk20-2N 41189 cdlemk20 41171 cdlemk21-2N 41188 cdlemk21N 41170 cdlemk22-3 41198 cdlemk22 41190 cdlemk23-3 41199 cdlemk24-3 41200 cdlemk25-3 41201 cdlemk26-3 41203 cdlemk26b-3 41202 cdlemk27-3 41204 cdlemk28-3 41205 cdlemk29-3 41208 cdlemk3 41130 cdlemk30 41191 cdlemk31 41193 cdlemk32 41194 cdlemk33N 41206 cdlemk34 41207 cdlemk35 41209 cdlemk36 41210 cdlemk37 41211 cdlemk38 41212 cdlemk39 41213 cdlemk39u 41265 cdlemk4 41131 cdlemk41 41217 cdlemk42 41238 cdlemk42yN 41241 cdlemk43N 41260 cdlemk45 41244 cdlemk46 41245 cdlemk47 41246 cdlemk48 41247 cdlemk49 41248 cdlemk5 41133 cdlemk50 41249 cdlemk51 41250 cdlemk52 41251 cdlemk53 41254 cdlemk54 41255 cdlemk55 41258 cdlemk55u 41263 cdlemk56 41268 cdlemk5a 41132 cdlemk5auN 41157 cdlemk5u 41158 cdlemk6 41134 cdlemk6u 41159 cdlemk7 41145 cdlemk7u-2N 41185 cdlemk7u 41167 cdlemk8 41135 cdlemk9 41136 cdlemk9bN 41137 cdlemki 41138 cdlemkid 41233 cdlemkj-2N 41179 cdlemkj 41160 cdlemksat 41143 cdlemksel 41142 cdlemksv 41141 cdlemksv2 41144 cdlemkuat 41163 cdlemkuel-2N 41181 cdlemkuel-3 41195 cdlemkuel 41162 cdlemkuv-2N 41180 cdlemkuv2-2 41182 cdlemkuv2-3N 41196 cdlemkuv2 41164 cdlemkuvN 41161 cdlemkvcl 41139 cdlemky 41223 cdlemkyyN 41259 tendoex 41272 |
| [Crawley] p. 120 | Remark | dva1dim 41282 |
| [Crawley] p. 120 | Lemma L | cdleml1N 41273 cdleml2N 41274 cdleml3N 41275 cdleml4N 41276 cdleml5N 41277 cdleml6 41278 cdleml7 41279 cdleml8 41280 cdleml9 41281 dia1dim 41358 |
| [Crawley] p. 120 | Lemma M | dia11N 41345 diaf11N 41346 dialss 41343 diaord 41344 dibf11N 41458 djajN 41434 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 41329 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 41415 dia2dimlem1 41361 dia2dimlem2 41362 dia2dimlem3 41363 dia2dimlem4 41364 dia2dimlem5 41365 diaf1oN 41427 diarnN 41426 dvheveccl 41409 dvhopN 41413 |
| [Crawley] p. 121 | Lemma N | cdlemn 41509 cdlemn10 41503 cdlemn11 41508 cdlemn11a 41504 cdlemn11b 41505 cdlemn11c 41506 cdlemn11pre 41507 cdlemn2 41492 cdlemn2a 41493 cdlemn3 41494 cdlemn4 41495 cdlemn4a 41496 cdlemn5 41498 cdlemn5pre 41497 cdlemn6 41499 cdlemn7 41500 cdlemn8 41501 cdlemn9 41502 diclspsn 41491 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 41470 |
| [Crawley] p. 122 | Lemma N | dih11 41562 dihf11 41564 dihjust 41514 dihjustlem 41513 dihord 41561 dihord1 41515 dihord10 41520 dihord11b 41519 dihord11c 41521 dihord2 41524 dihord2a 41516 dihord2b 41517 dihord2cN 41518 dihord2pre 41522 dihord2pre2 41523 dihordlem6 41510 dihordlem7 41511 dihordlem7b 41512 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 41527 dihfval 41528 dihval 41529 |
| [Diestel] p. 3 | Definition | df-gric 48163 df-grim 48160 isuspgrim 48178 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29468 df-nbgr 29389 |
| [Diestel] p. 3 | Definition by | df-grisom 48159 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 48143 df-subgr 29324 uhgrspan1 29359 uhgrspansubgr 29347 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 29611 vtxdgoddnumeven 29610 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29115 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 34002 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 34014 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 34006 zarcls1 34007 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 34017 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 34020 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 34023 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3905 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9560 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8769 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9568 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9896 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10469 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5251 |
| [Enderton] p. 19 | Definition | df-tp 4586 |
| [Enderton] p. 26 | Exercise 5 | unissb 4897 |
| [Enderton] p. 26 | Exercise 10 | pwel 5327 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5518 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5035 iinin2 5034 iinun2 5029 iunin1 5028 iunin1f 32614 iunin2 5027 uniin1 32608 uniin2 32609 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5033 iundif2 5030 |
| [Enderton] p. 32 | Exercise 20 | unineq 4241 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5054 |
| [Enderton] p. 33 | Exercise 25 | iununi 5055 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5062 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7718 iunpwss 5063 |
| [Enderton] p. 36 | Definition | opthwiener 5463 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5399 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4902 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5419 rnex 7854 rnexg 7846 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5864 rnuni 6107 |
| [Enderton] p. 42 | Definition of a function | dffun7 6520 dffun8 6521 |
| [Enderton] p. 43 | Definition of function value | funfv2 6923 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6562 |
| [Enderton] p. 44 | Definition (d) | dfima2 6022 dfima3 6023 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6932 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10387 ac7g 10388 df-ac 10030 dfac2 10046 dfac2a 10044 dfac2b 10045 dfac3 10035 dfac7 10047 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7194 |
| [Enderton] p. 52 | Definition | df-map 8769 |
| [Enderton] p. 53 | Exercise 21 | coass 6225 |
| [Enderton] p. 53 | Exercise 27 | dmco 6214 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6569 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6062 |
| [Enderton] p. 54 | Remark | ixpf 8862 ixpssmap 8874 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8840 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10397 ac9s 10407 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 38866 erref 8658 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 38869 erthi 8694 |
| [Enderton] p. 57 | Definition | df-ec 8639 |
| [Enderton] p. 58 | Definition | df-qs 8643 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8639 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5860 |
| [Enderton] p. 68 | Definition of successor | df-suc 6324 |
| [Enderton] p. 71 | Definition | df-tr 5207 dftr4 5212 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6399 unisucg 6398 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6399 unisucg 6398 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5221 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5223 trintALT 45157 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8534 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8536 onasuc 8457 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7363 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8535 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8537 onmsuc 8458 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8552 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8539 nnacom 8547 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8553 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8554 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8556 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8540 nnmsucr 8555 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8568 |
| [Enderton] p. 129 | Definition | df-en 8888 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7314 |
| [Enderton] p. 133 | Exercise 1 | xpomen 9929 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16142 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9135 |
| [Enderton] p. 135 | Corollary 6C | php3 9137 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9134 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9166 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9168 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9097 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9101 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9073 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10094 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10095 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10090 dju1en 10086 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9247 unifi 9248 unifi2 9249 |
| [Enderton] p. 144 | Corollary 6K | undif2 4430 unfi 9099 unfi2 9214 |
| [Enderton] p. 145 | Figure 38 | ffoss 7892 |
| [Enderton] p. 145 | Definition | df-dom 8889 |
| [Enderton] p. 146 | Example 1 | domen 8902 domeng 8903 |
| [Enderton] p. 146 | Example 3 | nndomo 9146 nnsdom 9567 nnsdomg 9203 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10098 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9074 xpdom1 9008 xpdom1g 9006 xpdom2g 9005 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9080 |
| [Enderton] p. 151 | Theorem 6M | zorn 10421 zorng 10418 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10406 dfac5 10043 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10490 |
| [Enderton] p. 164 | Example | infdif 10122 |
| [Enderton] p. 168 | Definition | df-po 5533 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6433 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6365 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6432 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6373 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7783 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7728 |
| [Enderton] p. 194 | Remark | onprc 7725 |
| [Enderton] p. 194 | Exercise 16 | suc11 6427 |
| [Enderton] p. 197 | Definition | df-card 9855 |
| [Enderton] p. 197 | Theorem 7P | carden 10465 |
| [Enderton] p. 200 | Exercise 25 | tfis 7799 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9692 |
| [Enderton] p. 202 | Definition | df-r1 9680 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9702 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9783 rankval4b 35237 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9519 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9773 rankprb 9767 rankpw 9759 rankpwi 9739 rankuniss 9782 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9531 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9532 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10024 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 9990 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10004 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8275 |
| [Enderton] p. 222 | Definition of kard | karden 9811 kardex 9810 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8527 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8529 |
| [Enderton] p. 240 | Exercise 25 | oarec 8491 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10164 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17569 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17511 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18480 mrieqv2d 17566 mrieqvd 17565 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17570 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17575 mreexexlem2d 17572 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18486 mreexfidimd 17577 |
| [Frege1879] p. 11 | Statement | df3or2 44045 |
| [Frege1879] p. 12 | Statement | df3an2 44046 dfxor4 44043 dfxor5 44044 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 44067 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 44068 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 44072 |
| [Frege1879] p. 31 | Proposition 4 | frege4 44076 |
| [Frege1879] p. 32 | Proposition 5 | frege5 44077 |
| [Frege1879] p. 33 | Proposition 6 | frege6 44083 |
| [Frege1879] p. 34 | Proposition 7 | frege7 44085 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 44086 axfrege8 44084 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 90 wl-luk-pm2.04 37621 |
| [Frege1879] p. 35 | Proposition 9 | frege9 44089 |
| [Frege1879] p. 36 | Proposition 10 | frege10 44097 |
| [Frege1879] p. 36 | Proposition 11 | frege11 44091 |
| [Frege1879] p. 37 | Proposition 12 | frege12 44090 |
| [Frege1879] p. 37 | Proposition 13 | frege13 44099 |
| [Frege1879] p. 37 | Proposition 14 | frege14 44100 |
| [Frege1879] p. 38 | Proposition 15 | frege15 44103 |
| [Frege1879] p. 38 | Proposition 16 | frege16 44093 |
| [Frege1879] p. 39 | Proposition 17 | frege17 44098 |
| [Frege1879] p. 39 | Proposition 18 | frege18 44095 |
| [Frege1879] p. 39 | Proposition 19 | frege19 44101 |
| [Frege1879] p. 40 | Proposition 20 | frege20 44105 |
| [Frege1879] p. 40 | Proposition 21 | frege21 44104 |
| [Frege1879] p. 41 | Proposition 22 | frege22 44096 |
| [Frege1879] p. 42 | Proposition 23 | frege23 44102 |
| [Frege1879] p. 42 | Proposition 24 | frege24 44092 |
| [Frege1879] p. 42 | Proposition 25 | frege25 44094 rp-frege25 44082 |
| [Frege1879] p. 42 | Proposition 26 | frege26 44087 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 44107 |
| [Frege1879] p. 43 | Proposition 27 | frege27 44088 |
| [Frege1879] p. 43 | Proposition 28 | con3 153 |
| [Frege1879] p. 43 | Proposition 29 | frege29 44108 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 44111 axfrege31 44110 |
| [Frege1879] p. 44 | Proposition 30 | frege30 44109 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 130 |
| [Frege1879] p. 44 | Proposition 32 | frege32 44112 |
| [Frege1879] p. 44 | Proposition 33 | frege33 44113 |
| [Frege1879] p. 45 | Proposition 34 | frege34 44114 |
| [Frege1879] p. 45 | Proposition 35 | frege35 44115 |
| [Frege1879] p. 45 | Proposition 36 | frege36 44116 |
| [Frege1879] p. 46 | Proposition 37 | frege37 44117 |
| [Frege1879] p. 46 | Proposition 38 | frege38 44118 |
| [Frege1879] p. 46 | Proposition 39 | frege39 44119 |
| [Frege1879] p. 46 | Proposition 40 | frege40 44120 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 44122 axfrege41 44121 |
| [Frege1879] p. 47 | Proposition 41 | notnot 142 |
| [Frege1879] p. 47 | Proposition 42 | frege42 44123 |
| [Frege1879] p. 47 | Proposition 43 | frege43 44124 |
| [Frege1879] p. 47 | Proposition 44 | frege44 44125 |
| [Frege1879] p. 47 | Proposition 45 | frege45 44126 |
| [Frege1879] p. 48 | Proposition 46 | frege46 44127 |
| [Frege1879] p. 48 | Proposition 47 | frege47 44128 |
| [Frege1879] p. 49 | Proposition 48 | frege48 44129 |
| [Frege1879] p. 49 | Proposition 49 | frege49 44130 |
| [Frege1879] p. 49 | Proposition 50 | frege50 44131 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 44134 ax-frege52c 44165 frege52aid 44135 frege52b 44166 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 44139 ax-frege54c 44169 frege54b 44170 |
| [Frege1879] p. 50 | Proposition 51 | frege51 44132 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3743 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 44137 frege53aid 44136 frege53b 44167 frege53c 44191 |
| [Frege1879] p. 50 | Proposition 54 | biid 261 eqid 2737 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 44145 frege55aid 44142 frege55b 44174 frege55c 44195 frege55cor1a 44146 frege55lem2a 44144 frege55lem2b 44173 frege55lem2c 44194 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 44148 frege56aid 44147 frege56b 44175 frege56c 44196 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 44152 ax-frege58b 44178 frege58bid 44179 frege58c 44198 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 44150 frege57aid 44149 frege57b 44176 frege57c 44197 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3754 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 44154 frege59b 44181 frege59c 44199 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 44155 frege60b 44182 frege60c 44200 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 44156 frege61b 44183 frege61c 44201 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 44157 frege62b 44184 frege62c 44202 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 44158 frege63b 44185 frege63c 44203 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 44159 frege64b 44186 frege64c 44204 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 44160 frege65b 44187 frege65c 44205 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 44161 frege66b 44188 frege66c 44206 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 44162 frege67b 44189 frege67c 44207 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 44163 frege68b 44190 frege68c 44208 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 44209 |
| [Frege1879] p. 58 | Proposition 70 | frege70 44210 |
| [Frege1879] p. 59 | Proposition 71 | frege71 44211 |
| [Frege1879] p. 59 | Proposition 72 | frege72 44212 |
| [Frege1879] p. 59 | Proposition 73 | frege73 44213 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 44216 |
| [Frege1879] p. 60 | Proposition 74 | frege74 44214 |
| [Frege1879] p. 60 | Proposition 75 | frege75 44215 |
| [Frege1879] p. 62 | Proposition 77 | frege77 44217 frege77d 44023 |
| [Frege1879] p. 63 | Proposition 78 | frege78 44218 |
| [Frege1879] p. 63 | Proposition 79 | frege79 44219 |
| [Frege1879] p. 63 | Proposition 80 | frege80 44220 |
| [Frege1879] p. 63 | Proposition 81 | frege81 44221 frege81d 44024 |
| [Frege1879] p. 64 | Proposition 82 | frege82 44222 |
| [Frege1879] p. 65 | Proposition 83 | frege83 44223 frege83d 44025 |
| [Frege1879] p. 65 | Proposition 84 | frege84 44224 |
| [Frege1879] p. 66 | Proposition 85 | frege85 44225 |
| [Frege1879] p. 66 | Proposition 86 | frege86 44226 |
| [Frege1879] p. 66 | Proposition 87 | frege87 44227 frege87d 44027 |
| [Frege1879] p. 67 | Proposition 88 | frege88 44228 |
| [Frege1879] p. 68 | Proposition 89 | frege89 44229 |
| [Frege1879] p. 68 | Proposition 90 | frege90 44230 |
| [Frege1879] p. 68 | Proposition 91 | frege91 44231 frege91d 44028 |
| [Frege1879] p. 69 | Proposition 92 | frege92 44232 |
| [Frege1879] p. 70 | Proposition 93 | frege93 44233 |
| [Frege1879] p. 70 | Proposition 94 | frege94 44234 |
| [Frege1879] p. 70 | Proposition 95 | frege95 44235 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 44239 |
| [Frege1879] p. 71 | Proposition 96 | frege96 44236 frege96d 44026 |
| [Frege1879] p. 71 | Proposition 97 | frege97 44237 frege97d 44029 |
| [Frege1879] p. 71 | Proposition 98 | frege98 44238 frege98d 44030 |
| [Frege1879] p. 72 | Proposition 100 | frege100 44240 |
| [Frege1879] p. 72 | Proposition 101 | frege101 44241 |
| [Frege1879] p. 72 | Proposition 102 | frege102 44242 frege102d 44031 |
| [Frege1879] p. 73 | Proposition 103 | frege103 44243 |
| [Frege1879] p. 73 | Proposition 104 | frege104 44244 |
| [Frege1879] p. 73 | Proposition 105 | frege105 44245 |
| [Frege1879] p. 73 | Proposition 106 | frege106 44246 frege106d 44032 |
| [Frege1879] p. 74 | Proposition 107 | frege107 44247 |
| [Frege1879] p. 74 | Proposition 108 | frege108 44248 frege108d 44033 |
| [Frege1879] p. 74 | Proposition 109 | frege109 44249 frege109d 44034 |
| [Frege1879] p. 75 | Proposition 110 | frege110 44250 |
| [Frege1879] p. 75 | Proposition 111 | frege111 44251 frege111d 44036 |
| [Frege1879] p. 76 | Proposition 112 | frege112 44252 |
| [Frege1879] p. 76 | Proposition 113 | frege113 44253 |
| [Frege1879] p. 76 | Proposition 114 | frege114 44254 frege114d 44035 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 44255 |
| [Frege1879] p. 77 | Proposition 116 | frege116 44256 |
| [Frege1879] p. 78 | Proposition 117 | frege117 44257 |
| [Frege1879] p. 78 | Proposition 118 | frege118 44258 |
| [Frege1879] p. 78 | Proposition 119 | frege119 44259 |
| [Frege1879] p. 78 | Proposition 120 | frege120 44260 |
| [Frege1879] p. 79 | Proposition 121 | frege121 44261 |
| [Frege1879] p. 79 | Proposition 122 | frege122 44262 frege122d 44037 |
| [Frege1879] p. 79 | Proposition 123 | frege123 44263 |
| [Frege1879] p. 80 | Proposition 124 | frege124 44264 frege124d 44038 |
| [Frege1879] p. 81 | Proposition 125 | frege125 44265 |
| [Frege1879] p. 81 | Proposition 126 | frege126 44266 frege126d 44039 |
| [Frege1879] p. 82 | Proposition 127 | frege127 44267 |
| [Frege1879] p. 83 | Proposition 128 | frege128 44268 |
| [Frege1879] p. 83 | Proposition 129 | frege129 44269 frege129d 44040 |
| [Frege1879] p. 84 | Proposition 130 | frege130 44270 |
| [Frege1879] p. 85 | Proposition 131 | frege131 44271 frege131d 44041 |
| [Frege1879] p. 86 | Proposition 132 | frege132 44272 |
| [Frege1879] p. 86 | Proposition 133 | frege133 44273 frege133d 44042 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 46593 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 46916 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 46616 |
| [Fremlin1] p. 14 | Definition 112A | ismea 46731 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 46751 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 46742 meadjunre 46756 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 46743 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 46744 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 46740 meaiunle 46749 meaiunlelem 46748 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 46761 meaiuninc2 46762 meaiuninc3 46765 meaiuninc3v 46764 meaiunincf 46763 meaiuninclem 46760 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 46767 meaiininc2 46768 meaiininclem 46766 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 46786 caragendifcl 46794 caratheodory 46808 omelesplit 46798 |
| [Fremlin1] p. 19 | Definition 113A | isome 46774 isomennd 46811 isomenndlem 46810 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 46796 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 46815 voncmpl 46901 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 46778 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 46803 carageniuncllem1 46801 carageniuncllem2 46802 caragenuncl 46793 caragenuncllem 46792 caragenunicl 46804 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 46812 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 46806 caratheodorylem2 46807 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 46815 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 46874 hoidmv1lelem1 46871 hoidmv1lelem2 46872 hoidmv1lelem3 46873 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 46918 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 46874 hoidmvle 46880 hoidmvlelem1 46875 hoidmvlelem2 46876 hoidmvlelem3 46877 hoidmvlelem4 46878 hoidmvlelem5 46879 hsphoidmvle2 46865 hsphoif 46856 hsphoival 46859 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 46828 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 46836 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 46863 hoidmvn0val 46864 hoidmvval 46857 hoidmvval0 46867 hoidmvval0b 46870 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 46868 hsphoidmvle 46866 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 46817 df-voln 46819 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 46884 ovn0 46846 ovn0lem 46845 ovnf 46843 ovnome 46853 ovnssle 46841 ovnsslelem 46840 ovnsupge0 46837 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 46883 ovnhoilem1 46881 ovnhoilem2 46882 vonhoi 46947 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 46900 hoidifhspf 46898 hoidifhspval 46888 hoidifhspval2 46895 hoidifhspval3 46899 hspmbl 46909 hspmbllem1 46906 hspmbllem2 46907 hspmbllem3 46908 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 46901 vonmea 46854 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 46852 ovnsubadd2 46926 ovnsubadd2lem 46925 ovnsubaddlem1 46850 ovnsubaddlem2 46851 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 46911 hoimbl2 46945 hoimbllem 46910 hspdifhsp 46896 opnvonmbl 46914 opnvonmbllem2 46913 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 46916 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 46959 iccvonmbllem 46958 ioovonmbl 46957 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 46965 vonicclem2 46964 vonioo 46962 vonioolem2 46961 vonn0icc 46968 vonn0icc2 46972 vonn0ioo 46967 vonn0ioo2 46970 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 46969 snvonmbl 46966 vonct 46973 vonsn 46971 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 46639 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 46638 subsaliuncllem 46637 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 47005 salpreimalegt 46989 salpreimaltle 47006 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 47008 issmff 47014 issmflem 47007 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 47025 issmflelem 47024 smfpreimale 47034 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 47036 issmfgtlem 47035 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 46976 issmf 47008 issmff 47014 issmfge 47050 issmfgelem 47049 issmfgt 47036 issmfgtlem 47035 issmfle 47025 issmflelem 47024 issmflem 47007 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 46987 salpreimagtlt 47010 salpreimalelt 47009 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 47050 issmfgelem 47049 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 47033 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 47031 cnfsmf 47020 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 47047 decsmflem 47046 incsmf 47022 incsmflem 47021 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 46981 pimconstlt1 46982 smfconst 47029 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 47045 smfaddlem1 47043 smfaddlem2 47044 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 47076 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 47075 smfmullem1 47071 smfmullem2 47072 smfmullem3 47073 smfmullem4 47074 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 47077 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 47080 smfpimbor1lem2 47079 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 47082 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 47070 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 47069 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 47078 smfresal 47068 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 47057 smflim2 47086 smflimlem1 47051 smflimlem2 47052 smflimlem3 47053 smflimlem4 47054 smflimlem5 47055 smflimlem6 47056 smflimmpt 47090 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 47094 smfsuplem1 47091 smfsuplem2 47092 smfsuplem3 47093 smfsupmpt 47095 smfsupxr 47096 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 47098 smfinflem 47097 smfinfmpt 47099 |
| [Fremlin1] p. 39 | Remark 121G | smflim 47057 smflim2 47086 smflimmpt 47090 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 47088 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 47118 smfdivdmmbl2 47121 smfinfdmmbl 47129 smfinfdmmbllem 47128 smfsupdmmbl 47125 smfsupdmmbllem 47124 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 47108 smflimsuplem2 47101 smflimsuplem6 47105 smflimsuplem7 47106 smflimsuplem8 47107 smflimsupmpt 47109 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 47111 smfliminflem 47110 smfliminfmpt 47112 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 46976 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 47122 fsupdm2 47123 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 47113 adddmmbl2 47114 finfdm 47126 finfdm2 47127 fsupdm 47122 fsupdm2 47123 muldmmbl 47115 muldmmbl2 47116 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 47126 finfdm2 47127 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25497 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25540 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25550 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 37870 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 37873 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9551 inf1 9535 inf2 9536 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10826 enqer 10836 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10831 df-nq 10827 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10823 df-plq 10829 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7597 df-mpq 10824 df-mq 10830 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10832 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10890 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10891 ltbtwnnq 10893 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10886 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10887 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10894 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10896 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 10908 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 10910 |
| [Gleason] p. 122 | Definition | df-1p 10897 |
| [Gleason] p. 122 | Remark (1) | prub 10909 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 10948 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10900 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 10947 psslinpr 10946 supexpr 10969 suplem1pr 10967 suplem2pr 10968 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 10933 addclprlem1 10931 addclprlem2 10932 df-plp 10898 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 10937 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 10936 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 10949 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 10958 ltexprlem1 10951 ltexprlem2 10952 ltexprlem3 10953 ltexprlem4 10954 ltexprlem5 10955 ltexprlem6 10956 ltexprlem7 10957 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 10960 ltaprlem 10959 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 10961 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 10962 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10899 mulclpr 10935 mulclprlem 10934 reclem2pr 10963 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 10944 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 10939 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 10938 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 10943 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 10966 reclem3pr 10964 reclem4pr 10965 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 10970 enrer 10978 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 10975 df-1r 10976 df-nr 10971 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 10973 df-plr 10972 negexsr 11017 recexsr 11022 recexsrlem 11018 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 10974 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12144 creur 12143 cru 12141 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11103 axcnre 11079 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15042 crimd 15159 crimi 15120 crre 15041 crred 15158 crrei 15119 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15044 remimd 15125 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15211 absval2d 15375 absval2i 15325 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15068 cjaddd 15147 cjaddi 15115 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15069 cjmuld 15148 cjmuli 15116 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15067 cjcjd 15126 cjcji 15098 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15066 cjreb 15050 cjrebd 15129 cjrebi 15101 cjred 15153 rere 15049 rereb 15047 rerebd 15128 rerebi 15100 rered 15151 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15075 addcjd 15139 addcji 15110 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15165 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15206 abscjd 15380 abscji 15329 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15216 abs00d 15376 abs00i 15326 absne0d 15377 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15249 releabsd 15381 releabsi 15330 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15221 absmuld 15384 absmuli 15332 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15209 sqabsaddi 15333 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15258 abstrid 15386 abstrii 15336 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 13989 exp0 13992 expp1 13995 expp1d 14074 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26648 cxpaddd 26686 expadd 14031 expaddd 14075 expaddz 14033 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26657 cxpmuld 26706 expmul 14034 expmuld 14076 expmulz 14035 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26654 mulcxpd 26697 mulexp 14028 mulexpd 14088 mulexpz 14029 |
| [Gleason] p. 140 | Exercise 1 | znnen 16141 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13429 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15559 rlimadd 15570 rlimdiv 15573 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15561 rlimsub 15571 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15560 rlimmul 15572 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15564 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15510 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15531 climcj 15532 climim 15534 climre 15533 rlimabs 15536 rlimcj 15537 rlimim 15539 rlimre 15538 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11175 df-xr 11174 ltxr 13033 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15398 limsupval 15401 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15597 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15606 caucvgb 15607 caucvgbf 45769 caucvgr 15603 climcau 15598 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15743 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15810 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15263 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13752 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21307 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24291 xmet0 24290 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24307 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24298 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24300 mstri 24417 xmettri 24299 xmstri 24416 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24330 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23596 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25270 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24488 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24814 addcn2 15521 mulcn 24816 mulcn2 15523 subcn 24815 subcn2 15522 |
| [Gleason] p. 295 | Remark | bcval3 14233 bcval4 14234 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14248 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14231 df-bc 14230 |
| [Gleason] p. 296 | Remark | bcn0 14237 bcnn 14239 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15757 |
| [Gleason] p. 308 | Equation 2 | ef0 16018 |
| [Gleason] p. 308 | Equation 3 | efcj 16019 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16025 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16030 |
| [Gleason] p. 310 | Equation 14 | sinadd 16093 |
| [Gleason] p. 310 | Equation 15 | cosadd 16094 |
| [Gleason] p. 311 | Equation 17 | sincossq 16105 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16110 sinbnd 16109 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14143 sqeqori 14141 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 15999 |
| [Godowski] p. 730 | Equation SF | goeqi 32331 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 31726 |
| [Golan] p. 1 | Remark | srgisid 20148 |
| [Golan] p. 1 | Definition | df-srg 20126 |
| [Golan] p. 149 | Definition | df-slmd 33264 |
| [Gonshor] p. 7 | Definition | df-scut 27760 |
| [Gonshor] p. 9 | Theorem 2.5 | slerec 27797 slerecd 27798 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 27902 cofcut1d 27903 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 27904 cofcut2d 27905 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 27906 cofcutr1d 27907 cofcutr2d 27908 |
| [Gonshor] p. 13 | Definition | df-adds 27942 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 27958 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 27984 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28112 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28132 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28437 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28439 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28438 |
| [Gonshor] p. 39 | Theorem 4.4(b) | elreno2 28474 |
| [Gonshor] p. 95 | Theorem 6.1 | addsbday 28000 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36334 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17509 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17511 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 48470 df-cllaw 48468 df-comlaw 48469 |
| [Hall] p. 2 | Section 1.2 | df-clintop 48482 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 48503 |
| [Halmos] p. 28 | Partition ` ` | df-parts 39040 dfmembpart2 39045 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32123 riesz2 32124 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 31999 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32231 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32243 elpjidm 32242 pjnmopi 32206 |
| [Halmos] p. 44 | Remark | pjinormi 31745 pjinormii 31734 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32247 pjrn 31765 pjrni 31760 pjvec 31754 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 31785 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32212 hmopidmpji 32210 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32249 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32238 pjocvec 31755 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32227 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32230 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32233 pjssdif2i 32232 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 31913 |
| [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 1797 |
| [Hatcher] p. 25 | Definition | df-phtpc 24951 df-phtpy 24930 |
| [Hatcher] p. 26 | Definition | df-pco 24965 df-pi1 24968 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 24954 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 25010 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22438 df-dmatalt 48680 |
| [Helfgott] p. 2 | Theorem | tgoldbach 48099 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 48084 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 48096 bgoldbtbnd 48091 bgoldbtbnd 48091 tgblthelfgott 48097 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 34780 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 34781 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 34795 hgt750lemb 34794 hgt750leme 34796 hgt750lemf 34791 hgt750lemg 34792 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 48093 tgoldbachgt 34801 tgoldbachgtALTV 48094 tgoldbachgtd 34800 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 34782 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30551 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 18878 grpoideu 30567 mndideu 18674 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 18908 grpoinveu 30577 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 18939 grpo2inv 30589 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 18952 grpoinvop 30591 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 18974 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1770 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1771 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1773 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32478 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32491 cdj3i 32499 cdj3lem1 32492 cdjreui 32490 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32489 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 42258 |
| [Holland95] p. 14 | Line 15 | hgmapvs 42188 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 42210 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 42211 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 42208 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 42214 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 42133 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 42228 |
| [Holland95] p. 204 | Definition of involution | df-srng 20777 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 39800 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 41825 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 41778 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 40230 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 41674 poml4N 40250 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 41765 pexmidALTN 40275 pexmidN 40266 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 41830 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 39421 ldualset 39422 |
| [Holland95] p. 222 | Item 1 | df-lines 39798 df-pointsN 39799 |
| [Holland95] p. 222 | Item 2 | df-polarityN 40200 |
| [Holland95] p. 223 | Remark | ispsubcl2N 40244 omllaw4 39543 pol1N 40207 polcon3N 40214 |
| [Holland95] p. 223 | Definition | df-psubclN 40232 |
| [Holland95] p. 223 | Equation for polarity | polval2N 40203 |
| [Holmes] p. 40 | Definition | df-xrn 38552 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31142 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32240 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 32021 eigre 31893 eigrei 31892 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 32022 eigorth 31896 eigorthi 31895 |
| [Hughes] p. 137 | Remark (ii) | eigposi 31894 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30367 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30363 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30364 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30365 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30383 frgrregorufr0 30382 frgrregorufrg 30384 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30390 frrusgrord 30399 frrusgrord0 30398 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30146 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30373 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30376 frgrwopreg2 30377 frgrwopregasn 30374 frgrwopregbsn 30375 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30379 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30393 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30396 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30144 numclwlk1 30429 numclwlk1lem1 30427 numclwlk1lem2 30428 numclwwlk1 30419 numclwwlk8 30450 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30370 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 29827 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30405 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30431 numclwwlkovh0 30430 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30439 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 30036 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30443 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30446 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30449 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30461 natded 30461 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30461 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30461 natded 30461 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30461 |
| [Jech] p. 4 | Definition of class | cv 1541 cvjust 2731 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10494 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10492 alephmul 10493 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10491 infmap2 10131 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9730 |
| [Jech] p. 72 | Equation 9.3 | scott0 9802 scottex 9801 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9783 rankval4b 35237 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9807 |
| [Jech] p. 78 | Note | opthprc 5689 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 43193 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 43281 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 43282 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 43205 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 43209 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 43210 rmyp1 43211 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 43212 rmym1 43213 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 43203 rmx1 43204 rmxluc 43214 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 43207 rmy1 43208 rmyluc 43215 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 43217 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 43218 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 43238 jm2.17b 43239 jm2.17c 43240 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 43271 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 43275 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 43266 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 43241 jm2.24nn 43237 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 43280 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 43286 rmygeid 43242 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 43298 |
| [Juillerat] p. 11 | Section *5 | etransc 46563 etransclem47 46561 etransclem48 46562 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 46558 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 46560 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 46546 |
| [Juillerat] p. 13 | Proof | etransclem35 46549 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 46552 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 46538 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 46555 |
| [Juillerat] p. 14 | Proof | etransclem23 46537 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1969 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2014 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2019 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2009 cbvaliw 2008 wl-cbvmotv 37689 wl-motae 37691 wl-moteq 37690 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 1988 spimw 1972 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2035 spw 2036 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31574 chabs1i 31576 chabs2 31575 chabs2i 31577 chjass 31591 chjassi 31544 latabs1 18402 latabs2 18403 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32396 ela 32397 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32341 cvrval2 39571 |
| [Kalmbach] p. 16 | Definition | df-ol 39475 df-oml 39476 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 31642 cmbri 31648 cmtvalN 39508 df-cm 31641 df-cmtN 39474 |
| [Kalmbach] p. 22 | Remark | omllaw5N 39544 pjoml5 31671 pjoml5i 31646 |
| [Kalmbach] p. 22 | Definition | pjoml2 31669 pjoml2i 31643 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 31672 cmcmi 31650 cmcmii 31655 cmtcomN 39546 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 39542 omlsi 31462 pjoml 31494 pjomli 31493 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 39541 |
| [Kalmbach] p. 23 | Remark | cmbr2i 31654 cmcm3 31673 cmcm3i 31652 cmcm3ii 31657 cmcm4i 31653 cmt3N 39548 cmt4N 39549 cmtbr2N 39550 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 31666 cmbr3i 31658 cmtbr3N 39551 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 31676 fh1i 31679 fh2 31677 fh2i 31680 omlfh1N 39555 |
| [Kalmbach] p. 65 | Remark | chjatom 32415 chslej 31556 chsleji 31516 shslej 31438 shsleji 31428 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31553 chocini 31512 chsupcl 31398 chsupval2 31468 h0elch 31313 helch 31301 hsupval2 31467 ocin 31354 ococss 31351 shococss 31352 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31370 |
| [Kalmbach] p. 66 | Remark | df-pjh 31453 pjssmi 32223 pjssmii 31739 |
| [Kalmbach] p. 67 | Lemma 3 | osum 31703 osumi 31700 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32258 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32458 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32368 |
| [Kalmbach] p. 140 | Remark | hatomic 32418 hatomici 32417 hatomistici 32420 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 39616 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32439 lsatexch 39340 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32413 cvlcvr1 39636 cvr1 39707 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32432 cvexchi 32427 cvrexch 39717 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32422 hlrelat 39699 hlrelat5N 39698 lrelat 39311 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21100 lsmsatcv 39307 spansncv 31711 spansncvi 31710 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 39326 spansncv2 32351 |
| [Kalmbach] p. 266 | Definition | df-st 32269 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 31907 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10561 fpwwe2 10558 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10562 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10569 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10564 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10566 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10579 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10583 gchxpidm 10584 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10595 gchhar 10594 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10129 unxpwdom 9498 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10585 |
| [Kreyszig] p. 3 | Property M1 | metcl 24280 xmetcl 24279 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24287 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24520 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11862 muleqadd 11785 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24386 |
| [Kreyszig] p. 19 | Remark | mopntopon 24387 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24446 mopnm 24392 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24444 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24449 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24490 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23206 lmmbr 25218 lmmbr2 25219 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23328 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25273 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25236 iscmet2 25254 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25276 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23409 metelcls 25265 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25266 metcld2 25267 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25059 lmodvneg1 20860 nvinv 30697 vcm 30634 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25055 lmod0vs 20850 slmd0vs 33287 vc0 30632 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20851 slmdvs0 33288 vcz 30633 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 30749 ngpmet 24551 nrmmetd 24522 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 30744 imsdval2 30745 ncvspds 25121 ngpds 24552 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24537 nvnd 30746 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24566 nmge0 24565 nvge0 30731 nvz 30727 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24572 nvabs 30730 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 30859 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 30803 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 30865 blocni 30863 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 30864 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25164 ipeq0 21597 ipz 30777 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25176 pythi 30908 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 30912 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25198 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15783 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25396 minveco 30942 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 30808 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25289 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 30931 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32181 leopg 32180 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32199 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 30976 |
| [Kulpa] p. 547 | Theorem | poimir 37825 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 37824 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 37823 |
| [Kulpa] p. 548 | Theorem | broucube 37826 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 37818 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 37819 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2388 axnul 5251 |
| [Kunen] p. 11 | Axiom 3 | axnul 5251 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 7901 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8779 mapvalg 8777 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10436 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7885 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9680 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9722 r1elssi 9721 |
| [Kunen] p. 107 | Exercise 4 | rankop 9774 rankopb 9768 rankuni 9779 rankxplim 9795 rankxpsuc 9798 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 45231 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 45239 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 45238 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 45240 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 45245 rexabso 45246 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 45252 n0abso 45253 ssabso 45251 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 45254 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 45264 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 45259 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 45262 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 45263 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 45258 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 45270 wfaxpr 45275 wfaxreg 45277 wfaxrep 45271 wfaxsep 45272 wfaxun 45276 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 45261 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 45274 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 45270 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 45269 omelaxinf2 45266 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 45279 wfaxinf2 45278 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 45292 permaxext 45282 permaxinf2 45290 permaxnul 45285 permaxpow 45286 permaxpr 45287 permaxrep 45283 permaxsep 45284 permaxun 45288 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 45280 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 45291 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4960 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 33803 |
| [Lang] p. | Definition | df-rn 5636 |
| [Lang] p. 3 | Statement | lidrideqd 18598 mndbn0 18679 |
| [Lang] p. 3 | Definition | df-mnd 18664 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18616 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18770 |
| [Lang] p. 5 | Equation | gsumreidx 19850 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 48464 |
| [Lang] p. 6 | Example | nn0mnd 48461 |
| [Lang] p. 6 | Equation | gsumxp2 19913 |
| [Lang] p. 6 | Statement | cycsubm 19135 |
| [Lang] p. 6 | Definition | mulgnn0gsum 19014 |
| [Lang] p. 6 | Observation | mndlsmidm 19603 |
| [Lang] p. 7 | Definition | dfgrp2e 18897 |
| [Lang] p. 30 | Definition | df-tocyc 33170 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33215 |
| [Lang] p. 32 | Property (b) | cyc3conja 33220 cycpmconjv 33205 |
| [Lang] p. 53 | Definition | df-cat 17595 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18025 cat1lem 18024 |
| [Lang] p. 54 | Definition | df-iso 17677 |
| [Lang] p. 57 | Definition | df-inito 17912 df-termo 17913 |
| [Lang] p. 58 | Example | irinitoringc 21438 |
| [Lang] p. 58 | Statement | initoeu1 17939 termoeu1 17946 |
| [Lang] p. 62 | Definition | df-func 17786 |
| [Lang] p. 65 | Definition | df-nat 17874 |
| [Lang] p. 91 | Note | df-ringc 20583 |
| [Lang] p. 92 | Statement | mxidlprm 33532 |
| [Lang] p. 92 | Definition | isprmidlc 33509 |
| [Lang] p. 128 | Remark | dsmmlmod 21704 |
| [Lang] p. 129 | Proof | lincscm 48712 lincscmcl 48714 lincsum 48711 lincsumcl 48713 |
| [Lang] p. 129 | Statement | lincolss 48716 |
| [Lang] p. 129 | Observation | dsmmfi 21697 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 33765 qusdimsum 33766 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 33745 |
| [Lang] p. 147 | Definition | snlindsntor 48753 |
| [Lang] p. 504 | Statement | mat1 22395 matring 22391 |
| [Lang] p. 504 | Definition | df-mamu 22339 |
| [Lang] p. 505 | Statement | mamuass 22350 mamutpos 22406 matassa 22392 mattposvs 22403 tposmap 22405 |
| [Lang] p. 513 | Definition | mdet1 22549 mdetf 22543 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22639 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22535 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22559 |
| [Lang] p. 515 | Definition | df-minmar1 22583 smadiadetr 22623 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22558 mdetralt 22556 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22571 |
| [Lang] p. 518 | Definition | df-madu 22582 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22593 madurid 22592 matinv 22625 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 22838 |
| [Lang], p. 190 | Chapter 6 | vieta 33717 |
| [Lang], p. 224 | Proposition 1.1 | extdgfialg 33832 finextalg 33836 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 33801 fedgmul 33769 |
| [Lang], p. 225 | Proposition 1.4 | algextdeg 33863 |
| [Lang], p. 561 | Remark | chpmatply1 22780 |
| [Lang], p. 561 | Definition | df-chpmat 22775 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 44611 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 44606 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 44612 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5251 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2716 |
| [Levy] p. 59 | Definition | df-ttrcl 9621 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9667 |
| [Levy] p. 338 | Axiom | df-clel 2812 df-cleq 2729 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2812 df-cleq 2729 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2716 |
| [Levy] p. 358 | Axiom | df-clab 2716 |
| [Levy58] p. 2 | Definition I | isfin1-3 10300 |
| [Levy58] p. 2 | Definition II | df-fin2 10200 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10199 |
| [Levy58] p. 2 | Definition III | df-fin3 10202 |
| [Levy58] p. 3 | Definition V | df-fin5 10203 |
| [Levy58] p. 3 | Definition IV | df-fin4 10201 |
| [Levy58] p. 4 | Definition VI | df-fin6 10204 |
| [Levy58] p. 4 | Definition VII | df-fin7 10205 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10329 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27658 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27669 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27701 nosupbnd1 27686 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27703 nosupbnd2 27688 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27707 noetasuplem4 27708 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27704 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1770 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1771 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1773 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32466 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32470 mdsymi 32469 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32464 mdsymlem6 32466 mdsymlem7 32467 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32468 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32371 ssdmd2 32372 ssmd1 32369 ssmd2 32370 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32367 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32339 df-md 32338 mdbr 32352 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32389 mdslj1i 32377 mdslj2i 32378 mdslle1i 32375 mdslle2i 32376 mdslmd1i 32387 mdslmd2i 32388 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32379 mdsl2bi 32381 mdsl2i 32380 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32393 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32390 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32391 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32368 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32373 mdsl3 32374 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32392 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32487 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 39618 hlrelat1 39697 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 39336 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32394 cvmdi 32382 cvnbtwn4 32347 cvrnbtwn4 39576 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32395 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 39637 cvp 32433 cvrp 39713 lcvp 39337 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32457 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32456 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 39630 hlexch4N 39689 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32459 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 39740 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 40046 atpsubN 40050 df-pointsN 39799 pointpsubN 40048 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 39801 pmap11 40059 pmaple 40058 pmapsub 40065 pmapval 40054 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 40062 pmap1N 40064 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 40067 pmapglb2N 40068 pmapglb2xN 40069 pmapglbx 40066 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 40149 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 39774 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 40093 paddclN 40139 paddidm 40138 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 39775 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 40135 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 39774 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 39775 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19608 lsmmod2 19609 lssats 39309 shatomici 32416 shatomistici 32419 shmodi 31448 shmodsi 31447 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32358 mdsymlem7 32467 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 31647 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31551 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32473 |
| [Margaris] p. 40 | Rule C | exlimiv 1932 |
| [Margaris] p. 49 | Axiom A1 | ax-1 6 |
| [Margaris] p. 49 | Axiom A2 | ax-2 7 |
| [Margaris] p. 49 | Axiom A3 | ax-3 8 |
| [Margaris] p. 49 | Definition | df-an 396 df-ex 1782 df-or 849 dfbi2 474 |
| [Margaris] p. 51 | Theorem 1 | idALT 23 |
| [Margaris] p. 56 | Theorem 3 | conventions 30458 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 45191 |
| [Margaris] p. 60 | Theorem 8 | jcn 162 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 45192 |
| [Margaris] p. 79 | Rule C | exinst01 44902 exinst11 44903 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1978 19.2g 2196 r19.2z 4453 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2210 rr19.3v 3622 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2165 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1828 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1783 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2189 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2213 19.9h 2293 exlimd 2226 exlimdh 2297 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2168 excomim 2169 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2333 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30459 conventions-labels 30459 conventions-labels 30459 conventions-labels 30459 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1829 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 44655 albi 1820 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2233 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2234 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 44657 exbi 1849 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2237 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 44654 2alimdv 1920 alimd 2220 alimdh 1819 alimdv 1918 ax-4 1811 ralimdaa 3238 ralimdv 3151 ralimdva 3149 ralimdvva 3184 sbcimdv 3810 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2215 19.21h 2294 19.21t 2214 19.21vv 44653 alrimd 2223 alrimdd 2222 alrimdh 1865 alrimdv 1931 alrimi 2221 alrimih 1826 alrimiv 1929 alrimivv 1930 hbralrimi 3127 r19.21be 3230 r19.21bi 3229 ralrimd 3242 ralrimdv 3135 ralrimdva 3137 ralrimdvv 3181 ralrimdvva 3192 ralrimi 3235 ralrimia 3236 ralrimiv 3128 ralrimiva 3129 ralrimivv 3178 ralrimivva 3180 ralrimivvva 3183 ralrimivw 3133 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 44656 2eximdv 1921 exim 1836 eximd 2224 eximdh 1866 eximdv 1919 rexim 3078 reximd2a 3247 reximdai 3239 reximdd 45428 reximddv 3153 reximddv2 3196 reximddv3 3154 reximdv 3152 reximdv2 3147 reximdva 3150 reximdvai 3148 reximdvva 3185 reximi2 3070 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2219 19.23bi 2199 19.23h 2295 19.23t 2218 exlimdv 1935 exlimdvv 1936 exlimexi 44801 exlimiv 1932 exlimivv 1934 rexlimd3 45424 rexlimdv 3136 rexlimdv3a 3142 rexlimdva 3138 rexlimdva2 3140 rexlimdvaa 3139 rexlimdvv 3193 rexlimdvva 3194 rexlimdvvva 3195 rexlimdvw 3143 rexlimiv 3131 rexlimiva 3130 rexlimivv 3179 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 1993 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1882 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1872 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2235 r19.27z 4464 r19.27zv 4465 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2236 19.28vv 44663 r19.28z 4456 r19.28zf 45439 r19.28zv 4460 rr19.28v 3623 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1875 r19.29d2r 3124 r19.29imd 3102 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1883 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2242 19.31vv 44661 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2241 r19.32 47380 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 44659 19.33 1886 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 1994 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1879 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2238 19.36vv 44660 r19.36zv 4466 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2240 19.37vv 44662 r19.37zv 4461 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1841 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 1992 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1889 19.40 1888 r19.40 3103 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2243 19.41rg 44827 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2244 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1884 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2245 r19.44zv 4463 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2246 r19.45zv 4462 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2611 |
| [Mayet] p. 370 | Remark | jpi 32328 largei 32325 stri 32315 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32270 ishst 32272 |
| [Mayet3] p. 10 | Theorem | hstrbi 32324 hstri 32323 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 31786 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 31787 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32336 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31390 chsupcl 31398 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32418 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32412 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32439 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 40280 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18414 latj32 18412 latjass 18410 |
| [Megill] p. 444 | Axiom C5 | ax-5 1912 ax5ALT 39204 |
| [Megill] p. 444 | Section 7 | conventions 30458 |
| [Megill] p. 445 | Lemma L12 | aecom-o 39198 ax-c11n 39185 axc11n 2431 |
| [Megill] p. 446 | Lemma L17 | equtrr 2024 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 39193 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 39225 hbnae 2437 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2486 sbid 2263 sbidd-misc 50000 sbidd 49999 |
| [Megill] p. 448 | Remark 9.6 | axc14 2468 |
| [Megill] p. 448 | Scheme C4' | ax-c4 39181 |
| [Megill] p. 448 | Scheme C5' | ax-c5 39180 sp 2191 |
| [Megill] p. 448 | Scheme C6' | ax-11 2163 |
| [Megill] p. 448 | Scheme C7' | ax-c7 39182 |
| [Megill] p. 448 | Scheme C8' | ax-7 2010 |
| [Megill] p. 448 | Scheme C9' | ax-c9 39187 |
| [Megill] p. 448 | Scheme C10' | ax-6 1969 ax-c10 39183 |
| [Megill] p. 448 | Scheme C11' | ax-c11 39184 |
| [Megill] p. 448 | Scheme C12' | ax-8 2116 |
| [Megill] p. 448 | Scheme C13' | ax-9 2124 |
| [Megill] p. 448 | Scheme C14' | ax-c14 39188 |
| [Megill] p. 448 | Scheme C15' | ax-c15 39186 |
| [Megill] p. 448 | Scheme C16' | ax-c16 39189 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 39201 dral1 2444 dral2-o 39227 dral2 2443 drex1 2446 drex2 2447 drsb1 2500 drsb2 2274 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2179 sbequ 2089 sbid2v 2514 |
| [Megill] p. 450 | Example in Appendix | hba1-o 39194 hba1 2300 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 47174 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 23 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3830 rspsbca 3831 stdpc4 2074 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 39181 ra4 3837 stdpc5 2216 |
| [Mendelson] p. 81 | Rule C | exlimiv 1932 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2030 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2258 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3739 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5463 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4351 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4352 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4230 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4287 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4231 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4094 |
| [Mendelson] p. 231 | Definition of union | dfun3 4229 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5400 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4861 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5516 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4573 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5517 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4888 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5776 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6228 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7722 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6324 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8525 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9072 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 8993 xpsneng 8994 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9000 xpcomeng 9001 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9003 |
| [Mendelson] p. 255 | Definition | brsdom 8915 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 8996 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8771 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 8978 mapsnend 8977 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9078 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9077 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8824 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 8981 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 8997 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10093 djucomen 10092 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10097 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10091 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8460 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8487 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10473 |
| [Mendelson] p. 281 | Definition | df-r1 9680 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9729 |
| [Mendelson] p. 287 | Axiom system MK | ru 3739 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30317 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30352 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30354 vdgn1frgrv3 30355 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30356 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30349 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30342 2pthfrgrrn 30340 2pthfrgrrn2 30341 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31310 |
| [Monk1] p. 22 | Remark | conventions 30458 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30458 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4192 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5733 ssrelf 32675 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5734 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5162 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6222 coi2 6223 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5870 rn0 5876 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 6100 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5643 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5879 rnxp 6129 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5724 xp0 5725 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6037 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6034 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7858 imaexg 7857 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6031 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7022 funfvop 6997 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6889 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6900 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6539 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7202 dff13f 7203 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7167 funrnex 7900 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7195 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6186 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4920 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 7952 df-1st 7935 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 7953 df-2nd 7936 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9770 ranksnb 9743 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9771 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9772 rankunb 9766 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9754 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9680 r1val2 9753 |
| [Monk1] p. 117 | Lemma | zorn2 10420 zorn2g 10417 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9902 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10475 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9897 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1811 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2010 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2185 ax-c15 39186 ax12v2 2187 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 39181 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2163 |
| [Monk2] p. 109 | Lemma 15 | equvini 2460 equvinv 2031 eqvinop 5436 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1912 ax5ALT 39204 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2147 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2163 |
| [Monk2] p. 114 | Lemma 21 | sp 2191 |
| [Monk2] p. 114 | Lemma 22 | axc4 2327 hba1-o 39194 hba1 2300 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2159 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2182 nfra2 3347 nfra2w 3273 |
| [Moore] p. 53 | Part I | df-mre 17509 |
| [Munkres] p. 77 | Example 2 | distop 22943 indistop 22950 indistopon 22949 |
| [Munkres] p. 77 | Example 3 | fctop 22952 fctop2 22953 |
| [Munkres] p. 77 | Example 4 | cctop 22954 |
| [Munkres] p. 78 | Definition of basis | df-bases 22894 isbasis3g 22897 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17367 tgval2 22904 |
| [Munkres] p. 79 | Remark | tgcl 22917 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 22911 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 22935 tgss3 22934 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 22936 basgen2 22937 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 37525 topdifinfeq 37526 topdifinffin 37524 topdifinfindis 37522 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23108 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 22986 topcld 22983 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 22987 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 22989 |
| [Munkres] p. 94 | Definition of closure | clsval 22985 |
| [Munkres] p. 94 | Definition of interior | ntrval 22984 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 23023 elcls 23021 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 23031 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23096 neindisj 23065 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23098 |
| [Munkres] p. 97 | Definition of limit point | islp2 23093 lpval 23087 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23263 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23175 iscn 23183 iscn2 23186 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23228 cncnp2 23229 cncnpi 23226 df-cnp 23176 iscnp 23185 iscnp2 23187 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24491 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25271 |
| [Nathanson] p. 123 | Remark | reprgt 34759 reprinfz1 34760 reprlt 34757 |
| [Nathanson] p. 123 | Definition | df-repr 34747 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 34779 |
| [Nathanson] p. 123 | Proposition | breprexp 34771 breprexpnat 34772 itgexpif 34744 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32162 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 48092 |
| [Pfenning] p. 17 | Definition XM | natded 30461 |
| [Pfenning] p. 17 | Definition NNC | natded 30461 notnotrd 133 |
| [Pfenning] p. 17 | Definition ` `C | natded 30461 |
| [Pfenning] p. 18 | Rule" | natded 30461 |
| [Pfenning] p. 18 | Definition /\I | natded 30461 |
| [Pfenning] p. 18 | Definition ` `E | natded 30461 natded 30461 natded 30461 natded 30461 natded 30461 |
| [Pfenning] p. 18 | Definition ` `I | natded 30461 natded 30461 natded 30461 natded 30461 natded 30461 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30461 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30461 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30461 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30461 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30461 |
| [Pfenning] p. 127 | Definition =E | natded 30461 |
| [Pfenning] p. 127 | Definition =I | natded 30461 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25162 df-dip 30759 dip0l 30776 ip0l 21595 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25203 ipval 30761 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 30772 ipcj 21593 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25165 dipdir 30900 ipdir 21598 ipdiri 30888 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 30768 nmsq 25154 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 30883 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 30885 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 30886 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25171 dipass 30903 ipass 21604 ipassi 30899 |
| [Prugovecki] p. 186 | Definition of bra | braval 32002 df-bra 31908 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 31909 kbval 32012 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32440 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 40185 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32454 atcvat4i 32455 cvrat3 39739 cvrat4 39740 lsatcvat3 39349 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32340 cvrval 39566 df-cv 32337 df-lcv 39316 lspsncv0 21105 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 40197 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 40198 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2716 rabid 3421 rabidd 45435 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2286 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2729 |
| [Quine] p. 19 | Definition 2.9 | conventions 30458 df-v 3443 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2876 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2873 abid2f 2930 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2283 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2091 sbalex 2250 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2812 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2737 eqid1 30525 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2744 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3742 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3743 dfsbcq2 3744 |
| [Quine] p. 43 | Theorem 6.8 | vex 3445 |
| [Quine] p. 43 | Theorem 6.9 | isset 3455 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3546 spcgv 3551 spcimgf 3508 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3754 spsbcd 3755 |
| [Quine] p. 44 | Theorem 6.12 | elex 3462 |
| [Quine] p. 44 | Theorem 6.13 | elab 3635 elabg 3632 elabgf 3630 |
| [Quine] p. 44 | Theorem 6.14 | noel 4291 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4675 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4584 df-sn 4582 |
| [Quine] p. 49 | Theorem 7.4 | snss 4742 snssg 4741 |
| [Quine] p. 49 | Theorem 7.5 | prss 4777 prssg 4776 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4720 prid1g 4718 prid2 4721 prid2g 4719 snid 4620 snidg 4618 |
| [Quine] p. 51 | Theorem 7.12 | snex 5382 |
| [Quine] p. 51 | Theorem 7.13 | prex 5383 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4883 unisnALT 45202 unisng 4882 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4887 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4895 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4892 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6463 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 47368 dfiota2 6450 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 47377 iotaval 6467 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6473 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6469 |
| [Quine] p. 58 | Definition 9.1 | df-op 4588 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5474 opabidw 5473 opelopab 5491 opelopaba 5485 opelopabaf 5493 opelopabf 5494 opelopabg 5487 opelopabga 5482 opelopabgf 5489 oprabid 7392 oprabidw 7391 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5631 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5633 |
| [Quine] p. 64 | Definition 9.15 | df-id 5520 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6558 |
| [Quine] p. 65 | Theorem 10.4 | funi 6525 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6546 funsng 6544 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6495 |
| [Quine] p. 65 | Definition 10.2 | args 6052 dffv4 6832 |
| [Quine] p. 68 | Definition 10.11 | conventions 30458 df-fv 6501 fv2 6830 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14199 nn0opth2i 14198 nn0opthi 14197 omopthi 8591 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8343 |
| [Quine] p. 232 | Equation i | carddom 10468 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6581 funimaexg 6580 |
| [Quine] p. 331 | Axiom system NF | ru 3739 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31142 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 30759 polid 31217 polid2i 31215 polidi 31216 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 30871 |
| [ReedSimon] p. 195 | Remark | lnophm 32077 lnophmi 32076 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32190 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32192 leopmuli 32191 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32195 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 31910 leoppos 32184 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32194 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32183 |
| [Roman] p. 4 | Definition | df-dmat 22438 df-dmatalt 48680 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20092 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20174 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 48767 |
| [Roman] p. 112 | Note | isldepslvec2 48767 ldepsnlinc 48790 zlmodzxznm 48779 |
| [Roman] p. 112 | Example | zlmodzxzequa 48778 zlmodzxzequap 48781 zlmodzxzldep 48786 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 22838 |
| [Rosenlicht] p. 80 | Theorem | heicant 37827 |
| [Rosser] p. 281 | Definition | df-op 4588 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 34783 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 34784 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 48648 pmtr3ncom 19408 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19404 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19347 cayleyth 19348 |
| [Rudin] p. 164 | Equation 27 | efcan 16023 |
| [Rudin] p. 164 | Equation 30 | efzval 16031 |
| [Rudin] p. 167 | Equation 48 | absefi 16125 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 197 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1773 |
| [Sanford] p. 39 | Rule 4 | mptxor 1771 |
| [Sanford] p. 40 | Rule 1 | mptnan 1770 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6073 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6076 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6072 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6070 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17509 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17510 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17510 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17512 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10051 |
| [Schechter] p. 141 | Definition (MC) | dfac11 43340 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10360 axdc3 10368 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20176 isrngo 38069 |
| [Schechter] p. 276 | Remark 11.6.e | span0 31600 |
| [Schechter] p. 276 | Definition of span | df-span 31367 spanval 31391 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 22941 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6343 onelord 43529 ordelon 6342 ordelord 6340 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 43530 sucidg 6401 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6373 onsuc 7757 ord0 6372 ordsuci 7755 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 43531 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5210 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 43306 elon2 6329 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6324 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5528 epelg 5526 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9508 epirron 43532 ordirr 6336 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 43534 oneptr 43533 ontr1 6365 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6361 oneptri 43535 ordtri3or 6350 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8430 ord0eln0 6374 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6387 onsucss 43544 trsucss 6408 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7762 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6414 ordnbtwn 6413 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 43546 ordnexbtwnsuc 43545 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10315 onsucf1lem 43547 onsucf1o 43550 onsucf1olem 43548 onsucrn 43549 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 43551 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7789 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 43540 ordne0gt0 43539 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 43542 limnsuc 43543 onsucelab 43541 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9556 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7804 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9559 ordom 7820 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9560 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8570 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7727 ssorduni 7726 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8460 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9563 limom 7826 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8399 df1o2 8406 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8445 oa0suclim 43553 oalim 8461 oasuc 8453 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8446 om0suclim 43554 omlim 8462 omsuc 8455 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8451 oe0m1 8450 oe0suclim 43555 oelim 8463 oesuc 8456 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 43507 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 43557 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 43558 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 43559 limexissupab 43561 limiun 43560 limuni 6380 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8467 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8471 om1om1r 43562 om1r 8472 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8464 oaomoecl 43556 oecl 8466 omcl 8465 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 43509 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8473 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8474 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 43563 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 43564 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8541 nnamecl 43565 nnecl 8543 nnmcl 8542 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 43566 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8481 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8482 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8489 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 43568 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 43569 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 43571 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8488 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 43575 omword1 8502 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 43574 oaordnrex 43573 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 43570 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 43576 omword2 8503 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 43577 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 43578 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 43579 omordi 8495 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8497 omord2com 43580 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 43581 df-2o 8400 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 43584 oewordi 8521 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 43585 oeworde 8523 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 43586 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 43587 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 43583 omnord1ex 43582 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 43588 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 43590 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 43594 oenord1ex 43593 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 43595 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8490 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 43589 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8508 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8509 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 43597 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8527 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 43598 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 43599 cantnfub2 43600 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 43603 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 28970 axtgcgrrflx 28517 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 28971 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 28972 axtgcgrid 28518 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28503 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 28983 axtgsegcon 28519 df-trkgcb 28505 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 28994 axtg5seg 28520 df-trkgcb 28505 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 28995 axtgbtwnid 28521 df-trkgb 28504 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 28997 axtgpasch 28522 df-trkgb 28504 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 29016 df-trkg2d 34803 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28525 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28526 df-trkg2d 34803 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 29019 axtgeucl 28527 df-trkge 28506 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 29032 axtgcont 28524 axtgcont1 28523 df-trkgb 28504 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 36162 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 36164 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 36167 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 36171 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 36172 tgcgrcomimp 28532 tgcgrcoml 28534 tgcgrcomr 28533 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 36177 tgcgrtriv 28539 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 36181 tg5segofs 34811 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 34808 df-ofs 36158 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 36183 tgcgrextend 28540 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 36185 tgsegconeq 28541 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36197 btwntriv2 36187 tgbtwntriv2 28542 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 36188 tgbtwncom 28543 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36191 tgbtwntriv1 28546 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36192 tgbtwnswapid 28547 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36198 btwnintr 36194 tgbtwnexch2 28551 tgbtwnintr 28548 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36200 btwnexch3 36195 tgbtwnexch 28553 tgbtwnexch3 28549 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36199 tgbtwnouttr 28552 tgbtwnouttr2 28550 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 29015 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36202 tgbtwndiff 28561 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28554 trisegint 36203 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36219 tgifscgr 28563 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28613 colrot1 28614 colrot2 28615 lncom 28677 lnrot1 28678 lnrot2 28679 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36215 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36220 tgcgrsub 28564 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36230 tgcgrxfr 28573 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28572 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36216 df-cgrg 28566 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28566 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36231 tgbtwnxfr 28585 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36237 colinearperm2 36239 colinearperm3 36238 colinearperm4 36240 colinearperm5 36241 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28588 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36214 tgellng 28608 tglng 28601 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36242 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36250 lnxfr 28621 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36251 lnext 28622 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36255 tgfscgr 28623 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36256 lncgr 28624 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36217 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36258 lnid 28625 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36259 tgidinside 28626 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36276 tgbtwnconn1 28630 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36277 tgbtwnconn2 28631 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36278 tgbtwnconn3 28632 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36284 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36282 legov 28640 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28641 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28654 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36285 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36287 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36289 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36290 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36291 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36288 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36293 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28642 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28644 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28645 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28646 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28647 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36300 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36301 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36296 df-outsideof 36295 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36297 ishlg 28657 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28662 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28664 outsideofrflx 36302 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28658 hlcomd 28659 outsideofcom 36303 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28665 outsideoftr 36304 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 28673 outsideofeu 36306 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36313 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36314 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36307 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36322 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36323 tglineelsb2 28687 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36325 linerflx1 36324 linerflx2 36326 tglinecom 28690 tglinerflx1 28688 tglinerflx2 28689 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36328 tglinethru 28691 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36312 tglng 28601 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28649 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36331 tglinethrueu 28694 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36332 tglineineq 28698 tglineinteq 28700 tglineintmo 28697 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28704 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28705 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 28706 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 28721 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 28717 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 28709 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 28708 ismir 28714 mirbtwn 28713 mircgr 28712 mirfv 28711 mirval 28710 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 28719 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 28720 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 28721 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 28724 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 28725 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 28730 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 28727 mirbtwni 28726 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 28728 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 28740 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 28744 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 28741 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 28742 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 28743 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 28746 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 28747 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 28753 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 28749 israg 28752 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 28754 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 28755 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 28757 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 28758 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 28759 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 28760 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 28761 ragncol 28764 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 28762 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 28768 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 28772 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 28769 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 28751 isperp 28767 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 28770 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 28777 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 28785 colperpexlem2 28786 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 28788 colperpexlem3 28787 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 28793 midex 28792 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 28790 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 28799 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 28794 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 28803 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 28806 opphllem6 28807 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 28809 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28522 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 28810 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 28818 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 28813 hpgbr 28815 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 28820 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 28819 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 28821 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 28822 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 28823 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 28824 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 28825 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 28839 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 28829 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 28843 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 28844 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 28845 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 28846 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 28847 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 28850 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 28852 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 28830 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 28853 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 28856 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 28857 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 28858 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 28859 trgcopyeu 28861 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 28885 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 28864 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 28873 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 28871 cgrahl2 28872 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 28874 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 28875 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 28877 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 28878 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 28881 cgrahl 28882 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 28886 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 28887 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 28888 acopyeu 28889 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 28896 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 28900 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 28893 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 28908 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 28901 isleag 28902 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 28910 tgsas1 28909 tgsas2 28911 tgsas3 28912 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 28914 tgasa1 28913 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 28915 tgsss2 28916 tgsss3 28917 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27242 dchrsum 27240 dchrsum2 27239 sumdchr 27243 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27244 sum2dchr 27245 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 20001 ablfacrp2 20002 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27187 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27188 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27195 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27453 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27456 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27510 vmalogdivsum2 27509 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27500 dirith2 27499 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27498 rpvmasum 27497 rpvmasum2 27483 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27458 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27496 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27463 dchrisumlem1 27460 dchrisumlem2 27461 dchrisumlem3 27462 dchrisumlema 27459 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27466 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27495 dchrmusumlem 27493 dchrvmasumlem 27494 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27465 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27467 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27491 dchrisum0re 27484 dchrisumn0 27492 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27477 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27481 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27482 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27537 pntrsumbnd2 27538 pntrsumo1 27536 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27501 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27503 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27505 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27508 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27513 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27514 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27519 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27521 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27522 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27530 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27531 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27528 selberg3lem2 27529 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27532 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27526 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27539 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27540 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27541 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27555 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27567 pntlemb 27568 pntlemc 27566 pntlemd 27565 pntlemg 27569 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27567 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27559 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27564 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27567 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27580 pntleml 27582 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 33881 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 33868 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 33900 constrinvcl 33911 constrmulcl 33909 constrnegcl 33901 constrsqrtcl 33917 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 33887 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 33897 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 33919 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 33929 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4259 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4358 dif0 4331 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4445 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4428 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4250 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4251 |
| [Stoll] p. 20 | Remark | invdif 4232 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4590 |
| [Stoll] p. 43 | Definition | uniiun 5015 |
| [Stoll] p. 44 | Definition | intiin 5016 |
| [Stoll] p. 45 | Definition | df-iin 4950 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4949 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 401 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4259 |
| [Strang] p. 242 | Section 6.3 | expgrowth 44612 |
| [Suppes] p. 22 | Theorem 2 | eq0 4303 eq0f 4300 |
| [Suppes] p. 22 | Theorem 4 | eqss 3950 eqssd 3952 eqssi 3951 |
| [Suppes] p. 23 | Theorem 5 | ss0 4355 ss0b 4354 |
| [Suppes] p. 23 | Theorem 6 | sstr 3943 sstrALT2 45111 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4056 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4057 |
| [Suppes] p. 23 | Theorem 9 | psstr 4060 |
| [Suppes] p. 23 | Theorem 10 | pssss 4051 |
| [Suppes] p. 25 | Theorem 12 | elin 3918 elun 4106 |
| [Suppes] p. 26 | Theorem 15 | inidm 4180 |
| [Suppes] p. 26 | Theorem 16 | in0 4348 |
| [Suppes] p. 27 | Theorem 23 | unidm 4110 |
| [Suppes] p. 27 | Theorem 24 | un0 4347 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4131 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4139 |
| [Suppes] p. 27 | Theorem 27 | unss 4143 |
| [Suppes] p. 27 | Theorem 28 | indir 4239 |
| [Suppes] p. 27 | Theorem 29 | undir 4240 |
| [Suppes] p. 28 | Theorem 32 | difid 4329 |
| [Suppes] p. 29 | Theorem 33 | difin 4225 |
| [Suppes] p. 29 | Theorem 34 | indif 4233 |
| [Suppes] p. 29 | Theorem 35 | undif1 4429 |
| [Suppes] p. 29 | Theorem 36 | difun2 4434 |
| [Suppes] p. 29 | Theorem 37 | difin0 4427 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4425 |
| [Suppes] p. 29 | Theorem 39 | difundi 4243 |
| [Suppes] p. 29 | Theorem 40 | difindi 4245 |
| [Suppes] p. 30 | Theorem 41 | nalset 5259 |
| [Suppes] p. 39 | Theorem 61 | uniss 4872 |
| [Suppes] p. 39 | Theorem 65 | uniop 5464 |
| [Suppes] p. 41 | Theorem 70 | intsn 4940 |
| [Suppes] p. 42 | Theorem 71 | intpr 4938 intprg 4937 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5420 |
| [Suppes] p. 42 | Theorem 78 | intun 4936 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4988 dfiun2g 4986 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4989 |
| [Suppes] p. 47 | Theorem 86 | elpw 4559 elpw2 5280 elpw2g 5279 elpwg 4558 elpwgdedVD 45193 |
| [Suppes] p. 47 | Theorem 87 | pwid 4577 |
| [Suppes] p. 47 | Theorem 89 | pw0 4769 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4770 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5640 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5783 xpindir 5784 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5694 xpundir 5695 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9506 |
| [Suppes] p. 58 | Theorem 2 | relss 5732 |
| [Suppes] p. 59 | Theorem 4 | eldm 5850 eldm2 5851 eldm2g 5849 eldmg 5848 |
| [Suppes] p. 59 | Definition 3 | df-dm 5635 |
| [Suppes] p. 60 | Theorem 6 | dmin 5861 |
| [Suppes] p. 60 | Theorem 8 | rnun 6104 |
| [Suppes] p. 60 | Theorem 9 | rnin 6105 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5838 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5832 brcnvg 5829 |
| [Suppes] p. 62 | Equation 5 | elcnv 5826 elcnv2 5827 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6064 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6103 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6101 |
| [Suppes] p. 63 | Definition | dftrrels2 38831 |
| [Suppes] p. 63 | Theorem 20 | co02 6220 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5925 |
| [Suppes] p. 63 | Definition 7 | df-co 5634 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5835 |
| [Suppes] p. 64 | Theorem 27 | coass 6225 |
| [Suppes] p. 65 | Theorem 31 | resundi 5953 |
| [Suppes] p. 65 | Theorem 34 | elima 6025 elima2 6026 elima3 6027 elimag 6024 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6108 |
| [Suppes] p. 66 | Theorem 40 | dminss 6112 |
| [Suppes] p. 66 | Theorem 41 | imainss 6113 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6116 |
| [Suppes] p. 81 | Definition 34 | dfec2 8640 |
| [Suppes] p. 82 | Theorem 72 | elec 8684 elecALTV 38443 elecg 8682 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 38867 erth 8692 erth2 8693 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 38870 erdisj 8695 |
| [Suppes] p. 83 | Definition 35, | df-parts 39040 dfmembpart2 39045 |
| [Suppes] p. 89 | Theorem 96 | map0b 8825 |
| [Suppes] p. 89 | Theorem 97 | map0 8829 map0g 8826 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8830 mapsnd 8828 |
| [Suppes] p. 89 | Theorem 99 | mapss 8831 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 9982 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 9981 |
| [Suppes] p. 92 | Theorem 1 | enref 8926 enrefg 8925 |
| [Suppes] p. 92 | Theorem 2 | ensym 8944 ensymb 8943 ensymi 8945 |
| [Suppes] p. 92 | Theorem 3 | entr 8947 |
| [Suppes] p. 92 | Theorem 4 | unen 8986 |
| [Suppes] p. 94 | Theorem 15 | endom 8920 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 8941 |
| [Suppes] p. 94 | Theorem 17 | domtr 8948 |
| [Suppes] p. 95 | Theorem 18 | sbth 9029 |
| [Suppes] p. 97 | Theorem 23 | canth2 9062 canth2g 9063 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9033 df-sdom 8890 dfsdom2 9032 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9046 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9035 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9034 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9044 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8923 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9047 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9042 |
| [Suppes] p. 98 | Exercise 4 | fundmen 8972 fundmeng 8973 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9007 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9043 |
| [Suppes] p. 104 | Theorem 37 | fofi 9217 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9223 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9223 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10465 |
| [Suppes] p. 130 | Definition 3 | df-tr 5207 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7727 |
| [Suppes] p. 134 | Definition 6 | df-suc 6324 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7844 finds 7840 finds1 7843 finds2 7842 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9565 isfinite2 9202 isfiniteg 9204 unbnn 9200 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10833 df-ltpq 10825 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7807 tfinds 7804 tfinds2 7808 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8480 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8482 |
| [Suppes] p. 211 | Theorem 25 | oaass 8490 |
| [Suppes] p. 225 | Definition 8 | iscard2 9892 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10477 |
| [Suppes] p. 228 | Theorem 59 | harcard 9894 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 9980 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6370 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7740 onminsb 7741 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10487 |
| [Suppes] p. 229 | Theorem 65 | alephcard 9984 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 9991 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 9985 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9856 |
| [Suppes] p. 242 | Theorem 6 | weth 10409 |
| [Suppes] p. 242 | Theorem 8 | entric 10471 |
| [Suppes] p. 242 | Theorem 9 | carden 10465 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 35871 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 35875 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2709 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2729 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2812 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2731 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2757 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7364 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3739 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5367 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4606 elpr2 4608 elpr2g 4607 elprg 4604 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4596 elsn2 4623 elsn2g 4622 elsng 4595 velsn 4597 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5416 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4591 sneqr 4797 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4602 dfsn2 4594 dfsn2ALT 4603 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7688 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5425 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5413 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5397 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7691 unexg 7690 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4649 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4865 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3909 df-un 3907 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4881 uniprg 4880 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5323 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4647 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6390 elsucg 6388 sstr2 3941 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4111 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4162 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4125 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4181 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4237 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4238 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3922 df-ss 3919 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4557 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4140 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3920 sseqin2 4176 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3957 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4190 inss2 4191 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 3999 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4875 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5398 sspwimp 45194 sspwimpALT 45201 sspwimpALT2 45204 sspwimpcf 45196 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5405 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5225 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3401 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5253 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3905 |
| [TakeutiZaring] p. 20 | Definition 5.14 | dfnul2 4289 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4329 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4306 n0f 4302 neq0 4305 neq0f 4301 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9505 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9645 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9660 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3443 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5261 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4353 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5267 ssexg 5269 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5263 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9514 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9508 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4319 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4088 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4253 undif3VD 45158 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4089 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4096 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3053 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3062 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7700 xpexg 7697 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5632 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6564 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6740 fun11 6567 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6506 svrelfun 6565 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5837 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5839 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5637 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5638 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5634 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6153 dfrel2 6148 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5641 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5761 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5768 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5781 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 5965 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5945 opelresi 5947 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 5972 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5961 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 5966 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6535 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6068 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6533 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6742 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2610 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30458 df-fv 6501 fv3 6853 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7869 cnvexg 7868 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7853 dmexg 7845 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7854 rnexg 7846 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 44730 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7864 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6848 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 47456 tz6.12-1-afv2 47523 tz6.12-1 6858 tz6.12-afv 47455 tz6.12-afv2 47522 tz6.12 6859 tz6.12c-afv2 47524 tz6.12c 6857 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 47519 tz6.12-2 6822 tz6.12i-afv2 47525 tz6.12i 6861 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6496 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6497 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6499 wfo 6491 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6498 wf1 6490 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6500 wf1o 6492 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 6978 eqfnfv2 6979 eqfnfv2f 6982 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6933 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7165 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7163 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6581 funimaexg 6580 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5100 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5534 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5586 dffr3 6059 eliniseg 6054 iniseg 6057 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5525 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5602 fr3nr 7719 frirr 5601 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5578 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7721 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5589 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5611 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6306 tz6.26i 6307 wefrc 5619 wereu2 5622 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6308 wfii 6309 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6502 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7277 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7278 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7284 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7285 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7286 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7290 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7297 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7299 |
| [TakeutiZaring] p. 35 | Notation | wtr 5206 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 44731 tz7.2 5608 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5211 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6331 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6339 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6340 ordelordALT 44814 ordelordALTVD 45143 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6346 ordelssne 6345 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6344 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6348 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7729 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7730 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6322 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6350 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 44826 ordon 7724 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7725 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7797 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6366 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5208 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7739 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7775 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6424 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6423 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7726 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4895 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6324 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6400 sucidg 6401 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7757 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6414 ordnbtwn 6413 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7772 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6323 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7825 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7830 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7785 ordelsuc 7764 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7766 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7795 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7812 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7833 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7834 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7835 |
| [TakeutiZaring] p. 43 | Remark | omon 7822 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9548 omex 9556 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7820 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7839 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7836 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7837 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7815 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4918 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5224 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4919 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5290 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7742 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6369 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4904 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9573 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7737 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8309 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8330 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8331 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8332 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8339 tz7.44-2 8340 tz7.44-3 8341 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8301 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8296 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8280 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8378 tz7.49c 8379 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8376 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8375 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8377 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2657 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 9925 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 9926 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8461 oasuc 8453 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7805 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8464 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8445 oa0r 8467 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8465 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8477 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8549 nnaordi 8548 oaord 8476 oaordi 8475 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5006 uniss2 4898 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8479 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8484 oawordex 8486 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8541 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8578 |
| [TakeutiZaring] p. 60 | Remark | oancom 9564 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8489 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8546 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8481 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8448 omlim 8462 omsuc 8455 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8446 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8543 nnmcl 8542 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8562 nnmordi 8561 omord 8497 omordi 8495 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8498 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8566 omwordri 8501 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8468 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8471 om1r 8472 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8504 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8506 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8507 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8508 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8509 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8538 oe0 8451 oelim 8463 oesuc 8456 onesuc 8459 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8449 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8516 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8517 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8450 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8474 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8518 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8524 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8522 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8523 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8527 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8529 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9641 tz9.1 9642 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9680 r10 9684 r1lim 9688 r1limg 9687 r1suc 9686 r1sucg 9685 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9696 r1ord2 9697 r1ordg 9694 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9706 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9731 tz9.13 9707 tz9.13g 9708 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9681 rankval 9732 rankvalb 9713 rankvalg 9733 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9755 rankelb 9740 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9769 rankval3 9756 rankval3b 9742 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9745 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9711 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9750 rankr1c 9737 rankr1g 9748 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9751 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9765 rankssb 9764 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9758 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9757 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10389 dfac3 10035 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 9944 numth 10386 numth2 10385 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10460 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10461 cardid2 9869 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9876 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10465 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9875 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9860 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9881 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9873 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9082 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 8959 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9087 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9011 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9879 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10012 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9134 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9142 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10013 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9139 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10002 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 9980 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9888 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10130 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9227 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8891 isfi 8916 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9143 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10448 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9004 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10440 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10100 unxpdom 9163 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9890 cardsdomelir 9889 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9165 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 9928 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8769 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10476 infxpidm2 9931 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10121 infxp 10128 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9016 pw2f1o 9014 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9075 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10401 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10396 ac6s5 10405 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10457 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10458 uniimadomf 10459 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10188 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10183 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10168 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10165 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10171 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10178 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10187 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10497 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10166 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10190 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10011 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10010 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10022 alephfp2 10023 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10614 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10026 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10484 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10498 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10499 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 39180 |
| [Tarski] p. 67 | Scheme B5 | sp 2191 |
| [Tarski] p. 68 | Lemma 6 | avril1 30521 equid 2014 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2019 |
| [Tarski] p. 70 | Lemma 14 | spim 2392 spime 2394 spimew 1973 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2185 ax-c15 39186 ax12i 1968 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2091 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1970 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1912 ax5ALT 39204 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2010 ax-8 2116 ax-9 2124 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28519 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28520 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28522 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28522 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28523 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16172 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 37831 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 37833 |
| [Weierstrass] p. 272 | Definition | df-mdet 22533 mdetuni 22570 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 904 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 869 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 870 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 920 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 970 |
| [WhiteheadRussell] p. 100 | Theorem *2.01 | pm2.01 188 |
| [WhiteheadRussell] p. 100 | Theorem *2.02 | ax-1 6 |
| [WhiteheadRussell] p. 100 | Theorem *2.03 | con2 135 |
| [WhiteheadRussell] p. 100 | Theorem *2.04 | pm2.04 90 wl-luk-pm2.04 37621 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 44077 imim2 58 wl-luk-imim2 37616 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 47301 imim1 83 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 897 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2664 syl 17 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 903 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 22 wl-luk-id 37619 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 895 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 142 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 898 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 130 notnotrALT2 45203 wl-luk-notnotr 37620 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 146 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 44107 axfrege28 44106 con3 153 |
| [WhiteheadRussell] p. 103 | Theorem *2.17 | ax-3 8 |
| [WhiteheadRussell] p. 103 | Theorem *2.18 | pm2.18 128 |
| [WhiteheadRussell] p. 104 | Theorem *2.2 | orc 868 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 925 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 123 wl-luk-pm2.21 37613 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 124 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 890 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 942 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 30459 pm2.27 42 wl-luk-pm2.27 37611 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 923 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 38543 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 924 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 972 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 973 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 971 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1088 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 907 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 908 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 945 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 56 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 882 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 883 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5 169 pm2.5g 168 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6 191 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 884 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 885 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 886 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 172 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 852 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 853 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 889 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 891 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 192 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 900 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 943 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 944 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 193 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 892 pm2.67 893 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 176 pm2.521g 174 pm2.521g2 175 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 899 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 975 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 901 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 203 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 976 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 977 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 934 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 932 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 974 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 978 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 84 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 933 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 109 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 994 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 469 pm3.2im 160 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 995 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 996 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 997 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 998 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 471 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 459 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 402 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 803 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 448 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 449 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 482 simplim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 484 simprim 166 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 765 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 766 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 808 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 623 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 810 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 492 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 493 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 963 pm3.44 962 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 809 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 473 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 966 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34b 316 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 261 |
| [WhiteheadRussell] p. 117 | Theorem *4.11 | notbi 319 |
| [WhiteheadRussell] p. 117 | Theorem *4.12 | con2bi 353 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotb 315 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14 807 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 833 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 222 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 806 bitr 805 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 563 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 905 pm4.25 906 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 460 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1010 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 871 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 468 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 922 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 634 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 918 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 638 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 979 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1089 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1008 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1054 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1025 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 999 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 1001 pm4.45 1000 pm4.45im 828 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 985 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 854 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 545 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 984 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 987 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 988 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 989 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 990 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 986 pm4.56 991 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 992 pm4.57 993 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 404 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 857 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 397 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 850 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 405 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 851 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67 398 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 557 pm4.71d 561 pm4.71i 559 pm4.71r 558 pm4.71rd 562 pm4.71ri 560 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 952 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 527 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 937 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 517 pm4.76 518 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 964 pm4.77 965 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 935 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1006 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 392 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81 393 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 1026 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1027 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 347 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 348 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 351 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 387 impexp 450 pm4.87 844 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 824 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 947 pm5.11g 946 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 948 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 950 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 949 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1015 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1016 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1014 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbn 383 pm5.18 381 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 386 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 825 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1017 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1050 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1051 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 902 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 572 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 388 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 361 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6 1004 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 956 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 831 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 573 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 836 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 826 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 834 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 389 pm5.41 390 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 543 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 542 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 1007 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1020 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 951 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1003 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1021 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1022 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1030 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 366 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 270 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 1031 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 44635 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 44636 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1872 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 44637 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 44638 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 44639 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1895 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 44640 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 44641 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 44642 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 44643 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 44644 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 44646 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 44647 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 44648 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 44645 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2096 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 44651 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 44652 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2076 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2166 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1831 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1832 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 44653 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 44654 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 44655 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 44656 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 44658 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 44657 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1889 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 44660 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 44661 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 44659 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1830 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 44662 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 44663 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1848 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 44664 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2351 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1862 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 44669 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 44665 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 44666 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 44667 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 44668 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 44673 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 44670 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 44671 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 44672 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 44674 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2570 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 44684 pm13.13b 44685 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 44686 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3014 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3015 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3621 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 44692 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 44693 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 44687 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 44829 pm13.193 44688 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 44689 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 44690 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 44691 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 44698 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 44697 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 44696 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3804 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 44699 pm14.122b 44700 pm14.122c 44701 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 44702 pm14.123b 44703 pm14.123c 44704 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 44706 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 44705 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 44707 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6474 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 44708 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6475 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 44709 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 44711 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2634 eupickbi 2637 sbaniota 44712 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 44710 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2585 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 44713 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30458 df-fv 6501 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 9917 pm54.43lem 9916 |
| [Young] p. 141 | Definition of operator ordering | leop2 32182 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32188 idleop 32189 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 43106 |
| [vandenDries] p. 43 | Theorem 62 | pellex 43113 pellexlem1 43107 |