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 17580 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17580 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 17989 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17601 0funcg 49191 df-termc 49579 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 49656 prsthinc 49570 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 49684 df-mndtc 49684 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 49680 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17624 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 49672 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 49697 oppgoppchom 49696 oppgoppcid 49698 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17694 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17682 invisoinvl 17703 |
| [Adamek] p. 28 | Example 3.13 | idinv 17702 idiso 17701 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17687 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17661 df-iso 17662 dfiso2 17685 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17668 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17719 cicerALT 49152 |
| [Adamek] p. 29 | Definition 3.15 | cic 17712 df-cic 17709 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17771 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17683 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17684 isoco 17690 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17771 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17794 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 49410 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17787 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 49680 discthing 49567 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 49524 prsthinc 49570 thincciso 49559 thincciso2 49561 thincciso3 49562 thinccisod 49560 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 49684 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17801 cofucla 49202 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 49268 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18024 catcisoi 49506 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18079 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17820 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17819 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18079 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17844 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17850 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17849 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18064 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18064 |
| [Adamek] p. 39 | Remark 3.42 | 2oppf 49238 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 49229 funcoppc 17788 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18012 elcatchom 49503 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17838 fthoppf 49270 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17837 fulloppf 49269 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18021 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 49191 df-catc 18012 |
| [Adamek] p. 45 | Exercise 3G | incat 49707 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 49710 nelsubc3 49177 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 49257 imasubc2 49258 imasubc3 49262 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17751 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17752 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 49177 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17763 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17725 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 49266 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 49265 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 49267 ressffth 17853 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 49708 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 17859 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 17880 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 17884 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 17860 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 17886 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 49191 df-inito 17897 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 49191 df-termc 49579 initc 49197 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21422 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 17898 oppctermo 49342 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 17925 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 17929 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 49343 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 17899 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21423 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 17932 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17660 |
| [Adamek] p. 107 | Example 7.20(7) | thincinv 49575 |
| [Adamek] p. 108 | Example 7.25(4) | thincsect2 49574 |
| [Adamek] p. 110 | Example 7.33(9) | thincmon 49539 |
| [Adamek] p. 110 | Proposition 7.35 | sectmon 17695 |
| [Adamek] p. 112 | Proposition 7.42 | sectepi 17697 |
| [Adamek] p. 185 | Section 10.67 | updjud 9833 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 49751 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 49751 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 49751 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 49752 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 49752 |
| [Adamek] p. 478 | Item Rng | df-ringc 20567 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 48654 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 48676 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14484 df-pfx 14585 df-substr 14555 df-word 14427 lencl 14446 wrd0 14452 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24629 df-nmoo 30732 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32140 hmopidmchi 32138 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32188 pjcmul2i 32189 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 31905 unoplin 31907 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 31906 unopadj2 31925 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 32000 lnopunii 31999 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32073 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 27877 |
| [Alling] p. 184 | Axiom B | bdayfo 27622 |
| [Alling] p. 184 | Axiom O | sltso 27621 |
| [Alling] p. 184 | Axiom SD | nodense 27637 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27724 |
| [Alling] p. 185 | Theorem | conway 27746 |
| [Alling] p. 185 | Axiom FE | noeta 27688 |
| [Alling] p. 186 | Theorem 4 | slerec 27766 slerecd 27767 |
| [Alling], p. 2 | Definition | rp-brsslt 43521 |
| [Alling], p. 3 | Note | nla0001 43524 nla0002 43522 nla0003 43523 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11303 addcan2d 11323 addcan2i 11313 addcand 11322 addcani 11312 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11356 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11415 negsubd 11484 negsubi 11445 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11417 negnegd 11469 negnegi 11437 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11556 subdid 11579 subdii 11572 subdir 11557 subdird 11580 subdiri 11573 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11298 mul01d 11318 mul01i 11309 mul02 11297 mul02d 11317 mul02i 11308 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11760 mulcan2d 11757 mulcand 11756 mulcani 11762 |
| [Apostol] p. 18 | Theorem I.8 | receu 11768 xreceu 32909 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11798 divrecd 11906 divreci 11872 divreczi 11865 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11824 recreci 11859 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11763 mul0ord 11771 mul0ori 11770 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11562 mul2negd 11578 mul2negi 11571 mulneg1 11559 mulneg1d 11576 mulneg1i 11569 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11842 divadddivd 11947 divadddivi 11889 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11827 divmuldivd 11944 divmuldivi 11887 rdivmuldivd 20337 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11828 divdivdivd 11950 divdivdivi 11890 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 12920 rpaddcld 12955 rpmulcl 12921 rpmulcld 12956 |
| [Apostol] p. 20 | Axiom 8 | rpneg 12930 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 12933 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11245 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11716 ltadd1dd 11734 ltadd1i 11677 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 11977 ltmul1a 11976 ltmul1i 12046 ltmul1ii 12056 ltmul2 11978 ltmul2d 12982 ltmul2dd 12996 ltmul2i 12049 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11643 msqgt0d 11690 msqgt0i 11660 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11645 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11629 lt0neg1d 11692 ltneg 11623 ltnegd 11701 ltnegi 11667 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11608 lt2addd 11746 lt2addi 11685 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 12897 |
| [Apostol] p. 21 | Exercise 4 | recgt0 11973 recgt0d 12062 recgt0i 12033 recgt0ii 12034 |
| [Apostol] p. 22 | Definition of integers | df-z 12475 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12145 |
| [Apostol] p. 22 | Definition of rationals | df-q 12853 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9344 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12383 |
| [Apostol] p. 26 | Theorem I.29 | arch 12384 archd 45264 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12582 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12385 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12851 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12850 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13104 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16256 zneo 12562 zneoALTV 47774 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26672 msqsqrtd 15356 resqrtth 15168 sqrtth 15278 sqrtthi 15284 sqsqrtd 15355 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12134 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12817 |
| [Apostol] p. 361 | Remark | crreczi 14141 |
| [Apostol] p. 363 | Remark | absgt0i 15313 |
| [Apostol] p. 363 | Example | abssubd 15369 abssubi 15317 |
| [ApostolNT] p. 7 | Remark | fmtno0 47645 fmtno1 47646 fmtno2 47655 fmtno3 47656 fmtno4 47657 fmtno5fac 47687 fmtnofz04prm 47682 |
| [ApostolNT] p. 7 | Definition | df-fmtno 47633 |
| [ApostolNT] p. 8 | Definition | df-ppi 27043 |
| [ApostolNT] p. 14 | Definition | df-dvds 16170 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16186 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16211 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16206 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16199 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16201 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16187 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16188 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16193 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16228 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16230 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16232 |
| [ApostolNT] p. 15 | Definition | df-gcd 16412 dfgcd2 16463 |
| [ApostolNT] p. 16 | Definition | isprm2 16599 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16570 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16833 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16430 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16464 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16466 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16445 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16437 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16628 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16630 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16846 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16840 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16320 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16504 |
| [ApostolNT] p. 24 | Definition | df-mu 27044 |
| [ApostolNT] p. 25 | Definition | df-phi 16683 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27134 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16708 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16693 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16697 |
| [ApostolNT] p. 32 | Definition | df-vma 27041 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27136 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27160 |
| [ApostolNT] p. 38 | Remark | df-sgm 27045 |
| [ApostolNT] p. 38 | Definition | df-sgm 27045 |
| [ApostolNT] p. 75 | Definition | df-chp 27042 df-cht 27040 |
| [ApostolNT] p. 104 | Definition | congr 16581 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16173 |
| [ApostolNT] p. 106 | Definition | moddvds 16180 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16263 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16264 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13798 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13838 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14151 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16205 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16584 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 16992 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16586 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16700 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16719 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16701 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27015 |
| [ApostolNT] p. 179 | Definition | df-lgs 27239 lgsprme0 27283 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27284 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27260 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27275 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27332 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27351 2lgsoddprm 27360 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27318 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27327 |
| [ApostolNT] p. 188 | Definition | df-lgs 27239 lgs1 27285 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27276 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27278 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27286 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27287 |
| [Baer] p. 40 | Property (b) | mapdord 41743 |
| [Baer] p. 40 | Property (c) | mapd11 41744 |
| [Baer] p. 40 | Property (e) | mapdin 41767 mapdlsm 41769 |
| [Baer] p. 40 | Property (f) | mapd0 41770 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 41730 mapd1o 41753 |
| [Baer] p. 41 | Property (g) | mapdat 41772 |
| [Baer] p. 44 | Part (1) | mapdpg 41811 |
| [Baer] p. 45 | Part (2) | hdmap1eq 41906 mapdheq 41833 mapdheq2 41834 mapdheq2biN 41835 |
| [Baer] p. 45 | Part (3) | baerlem3 41818 |
| [Baer] p. 46 | Part (4) | mapdheq4 41837 mapdheq4lem 41836 |
| [Baer] p. 46 | Part (5) | baerlem5a 41819 baerlem5abmN 41823 baerlem5amN 41821 baerlem5b 41820 baerlem5bmN 41822 |
| [Baer] p. 47 | Part (6) | hdmap1l6 41926 hdmap1l6a 41914 hdmap1l6e 41919 hdmap1l6f 41920 hdmap1l6g 41921 hdmap1l6lem1 41912 hdmap1l6lem2 41913 mapdh6N 41852 mapdh6aN 41840 mapdh6eN 41845 mapdh6fN 41846 mapdh6gN 41847 mapdh6lem1N 41838 mapdh6lem2N 41839 |
| [Baer] p. 48 | Part 9 | hdmapval 41933 |
| [Baer] p. 48 | Part 10 | hdmap10 41945 |
| [Baer] p. 48 | Part 11 | hdmapadd 41948 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 41922 mapdh6hN 41848 |
| [Baer] p. 48 | Part (7) | mapdh75cN 41858 mapdh75d 41859 mapdh75e 41857 mapdh75fN 41860 mapdh7cN 41854 mapdh7dN 41855 mapdh7eN 41853 mapdh7fN 41856 |
| [Baer] p. 48 | Part (8) | mapdh8 41893 mapdh8a 41880 mapdh8aa 41881 mapdh8ab 41882 mapdh8ac 41883 mapdh8ad 41884 mapdh8b 41885 mapdh8c 41886 mapdh8d 41888 mapdh8d0N 41887 mapdh8e 41889 mapdh8g 41890 mapdh8i 41891 mapdh8j 41892 |
| [Baer] p. 48 | Part (9) | mapdh9a 41894 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 41874 |
| [Baer] p. 49 | Part 12 | hdmap11 41953 hdmapeq0 41949 hdmapf1oN 41970 hdmapneg 41951 hdmaprnN 41969 hdmaprnlem1N 41954 hdmaprnlem3N 41955 hdmaprnlem3uN 41956 hdmaprnlem4N 41958 hdmaprnlem6N 41959 hdmaprnlem7N 41960 hdmaprnlem8N 41961 hdmaprnlem9N 41962 hdmapsub 41952 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 41973 hdmap14lem10 41982 hdmap14lem1a 41971 hdmap14lem2N 41974 hdmap14lem2a 41972 hdmap14lem3 41975 hdmap14lem8 41980 hdmap14lem9 41981 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 41983 hdmap14lem12 41984 hdmap14lem13 41985 hdmap14lem14 41986 hdmap14lem15 41987 hgmapval 41992 |
| [Baer] p. 50 | Part 15 | hgmapadd 41999 hgmapmul 42000 hgmaprnlem2N 42002 hgmapvs 41996 |
| [Baer] p. 50 | Part 16 | hgmaprnN 42006 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 42022 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 42023 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 42024 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 42025 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 42027 hgmapvv 42031 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 42026 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 42028 |
| [Baer] p. 111 | Line 15 | hdmapg 42035 hdmapglem7 42034 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26673 2irrexpqALT 26743 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 23 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2564 |
| [BellMachover] p. 460 | Notation | df-mo 2535 |
| [BellMachover] p. 460 | Definition | mo3 2559 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2703 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2707 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5227 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5236 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37115 sepex 5240 |
| [BellMachover] p. 466 | Problem | axpow2 5307 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5308 |
| [BellMachover] p. 466 | Axiom Union | axun2 7676 |
| [BellMachover] p. 468 | Definition | df-ord 6315 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6330 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6337 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6332 |
| [BellMachover] p. 471 | Definition of N | df-om 7803 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7740 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6317 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9538 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7818 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9663 |
| [BellMachover] p. 478 | Definition | rankval2 9717 rankval2b 35117 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9681 r1ord3g 9678 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9488 |
| [BellMachover] p. 488 | Axiom AC | ac5 10374 dfac4 10019 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10007 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 39424 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32340 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32382 chirredi 32381 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32370 |
| [Beran] p. 3 | Definition of join | sshjval3 31341 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 31603 cmcm2i 31580 cmcm2ii 31585 cmt2N 39355 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 31604 lecmi 31589 lecmii 31590 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 31578 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 31607 cm2ji 31612 cm2mi 31613 |
| [Beran] p. 95 | Definition | df-sh 31194 issh2 31196 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31073 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31086 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31077 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 31815 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 31817 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 31816 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 31818 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31069 his1i 31087 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31070 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31071 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31072 |
| [Beran] p. 96 | Definition of norm | df-hnorm 30955 dfhnorm2 31109 normval 31111 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31171 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 30960 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31228 |
| [Beran] p. 96 | Definition of converge | df-hlim 30959 hlimi 31175 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31120 norm-i 31116 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31124 norm-ii 31125 normlem0 31096 normlem1 31097 normlem2 31098 normlem3 31099 normlem4 31100 normlem5 31101 normlem6 31102 normlem7 31103 normlem7tALT 31106 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31126 norm-iii 31127 |
| [Beran] p. 98 | Remark 3.4 | bcs 31168 bcsiALT 31166 bcsiHIL 31167 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31108 normpar 31142 normpari 31141 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31133 normpyth 31132 normpythi 31129 |
| [Beran] p. 99 | Remark | lnfn0 32034 lnfn0i 32029 lnop0 31953 lnop0i 31957 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32013 nmcfnex 32040 nmcfnexi 32038 nmcopex 32016 nmcopexi 32014 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32041 nmcfnlbi 32039 nmcoplb 32017 nmcoplbi 32015 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32043 lnfnconi 32042 lnopcon 32022 lnopconi 32021 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31143 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31140 norm3adifii 31135 norm3dif 31137 norm3difi 31134 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31288 pjhth 31380 pjhtheu 31381 pjpjhth 31412 pjpjhthi 31413 pjth 25372 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31393 ococi 31392 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32048 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32049 riesz4 32051 riesz4i 32050 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32066 cnlnadjeu 32065 cnlnadjeui 32064 cnlnadji 32063 cnlnadjlem1 32054 nmopadjlei 32075 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32078 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32077 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32079 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 31923 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32089 nmopcoadji 32088 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32080 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32090 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32087 pjadj2coi 32191 pjadjcoi 32148 |
| [Beran] p. 107 | Definition | df-ch 31208 isch2 31210 |
| [Beran] p. 107 | Remark 3.12 | choccl 31293 isch3 31228 occl 31291 ocsh 31270 shoccl 31292 shocsh 31271 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31395 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31319 |
| [Beran] p. 109 | Property (i) | pjadj2 32174 pjadj3 32175 pjadji 31672 pjadjii 31661 |
| [Beran] p. 109 | Property (ii) | pjidmco 32168 pjidmcoi 32164 pjidmi 31660 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32160 |
| [Beran] p. 111 | Remark | ho0val 31737 pjch1 31657 |
| [Beran] p. 111 | Definition | df-hfmul 31721 df-hfsum 31720 df-hodif 31719 df-homul 31718 df-hosum 31717 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 31658 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 31681 pjchi 31419 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31426 pjoc2i 31425 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 31667 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32152 pjssmii 31668 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32151 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32150 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32155 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32153 pjssge0ii 31669 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32154 pjdifnormii 31670 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1777 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1775 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1778 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1773 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34312 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34320 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34318 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34322 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34342 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34373 df-sitm 34351 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34373 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34350 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29033 isuhgrop 29055 isusgrop 29147 isuspgrop 29146 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 47966 df-subgr 29253 uhgrspan1 29288 uhgrspansubgr 29276 |
| [Bollobas] p. 3 | Definition | df-gric 47986 gricuspgr 48023 isuspgrim 48001 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29440 df-clnbgr 47924 df-cusgr 29397 df-nbgr 29318 fusgrmaxsize 29450 |
| [Bollobas] p. 4 | Definition | df-upwlks 48239 df-wlks 29585 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 29536 finsumvtxdgeven 29538 fusgr1th 29537 fusgrvtxdgonume 29540 vtxdgoddnumeven 29539 |
| [Bollobas] p. 5 | Notation | df-pths 29699 |
| [Bollobas] p. 5 | Definition | df-crcts 29771 df-cycls 29772 df-trls 29676 df-wlkson 29586 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29044 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 48305 df-cllaw 48291 df-mgm 18554 df-mgm2 48324 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 48306 df-asslaw 48293 df-sgrp 18633 df-sgrp2 48326 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 48325 df-comlaw 48292 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18649 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33014 mndlactf1o 33018 mndractf1 33016 mndractf1o 33019 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20159 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20077 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 33653 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 33657 assarrginv 33656 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 33698 fldextrspunfld 33696 fldextrspunlem1 33695 fldextrspunlem2 33697 fldextrspunlsp 33694 fldextrspunlsplem 33693 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 33509 dfufd2 33522 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7227 fcofo 7228 |
| [BourbakiTop1] p. | Remark | xnegmnf 13115 xnegpnf 13114 |
| [BourbakiTop1] p. | Remark | rexneg 13116 |
| [BourbakiTop1] p. | Remark 3 | ust0 24141 ustfilxp 24134 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24011 |
| [BourbakiTop1] p. | Criterion | ishmeo 23680 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24204 iducn 24203 snfil 23785 |
| [BourbakiTop1] p. | Example 2 | neifil 23801 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 23988 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24224 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 33977 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23784 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24196 df-ust 24122 filintn0 23782 filn0 23783 istgp 23998 ucnprima 24202 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24207 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24218 df-usp 24178 df-utop 24152 trust 24150 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 33876 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23037 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23190 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24127 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24130 |
| [BourbakiTop1] p. | Property V_ii | innei 23046 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23054 neissex 23048 |
| [BourbakiTop1] p. | Proposition 1 | neips 23034 neiss 23030 ucncn 24205 ustund 24143 ustuqtop 24167 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23188 neiptopreu 23054 utop2nei 24171 utop3cls 24172 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24212 uspreg 24194 utopreg 24173 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23612 imasncls 23613 imasnopn 23611 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 23921 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24129 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24131 |
| [BourbakiTop1] p. | Property V_iii | elnei 23032 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24223 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24128 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24132 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23308 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23767 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 22815 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 33873 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 46165 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 46167 stoweid 46166 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 46104 stoweidlem10 46113 stoweidlem14 46117 stoweidlem15 46118 stoweidlem35 46138 stoweidlem36 46139 stoweidlem37 46140 stoweidlem38 46141 stoweidlem40 46143 stoweidlem41 46144 stoweidlem43 46146 stoweidlem44 46147 stoweidlem46 46149 stoweidlem5 46108 stoweidlem50 46153 stoweidlem52 46155 stoweidlem53 46156 stoweidlem55 46158 stoweidlem56 46159 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 46126 stoweidlem24 46127 stoweidlem27 46130 stoweidlem28 46131 stoweidlem30 46133 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 46137 stoweidlem59 46162 stoweidlem60 46163 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 46148 stoweidlem49 46152 stoweidlem7 46110 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 46134 stoweidlem39 46142 stoweidlem42 46145 stoweidlem48 46151 stoweidlem51 46154 stoweidlem54 46157 stoweidlem57 46160 stoweidlem58 46161 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 46128 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 46120 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 46114 stoweidlem13 46116 stoweidlem26 46129 stoweidlem61 46164 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 46121 |
| [Bruck] p. 1 | Section I.1 | df-clintop 48305 df-mgm 18554 df-mgm2 48324 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18633 df-sgrp2 48326 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 18958 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5175 |
| [Church] p. 129 | Section II.24 | df-ifp 1063 dfifp2 1064 |
| [Clemente] p. 10 | Definition IT | natded 30390 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30390 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30390 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30390 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30390 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30390 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30390 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30390 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30390 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30390 |
| [Clemente] p. 14 | Proof 5.11 | natded 30390 |
| [Clemente] p. 14 | Definition E` `n | natded 30390 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30392 ex-natded5.2 30391 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30395 ex-natded5.3 30394 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30397 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30399 ex-natded5.7 30398 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30401 ex-natded5.8 30400 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30403 ex-natded5.13 30402 |
| [Clemente] p. 32 | Definition I` `n | natded 30390 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30390 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30390 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30390 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30404 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30405 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30407 ex-natded9.26 30406 |
| [Cohen] p. 301 | Remark | relogoprlem 26533 |
| [Cohen] p. 301 | Property 2 | relogmul 26534 relogmuld 26567 |
| [Cohen] p. 301 | Property 3 | relogdiv 26535 relogdivd 26568 |
| [Cohen] p. 301 | Property 4 | relogexp 26538 |
| [Cohen] p. 301 | Property 1a | log1 26527 |
| [Cohen] p. 301 | Property 1b | loge 26528 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26730 |
| [Cohen4] p. 349 | Property | relogbf 26734 |
| [Cohen4] p. 352 | Definition | elogb 26713 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26720 |
| [Cohen4] p. 361 | Property 3 | logbrec 26725 relogbdiv 26722 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26718 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26723 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26711 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26712 |
| [Cohen4] p. 367 | Property | logbchbase 26714 |
| [Cohen4] p. 377 | Property 2 | logblt 26727 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34305 sxbrsigalem4 34307 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18469 acsinfd 18468 acsinfdimd 18470 acsmap2d 18467 acsmapd 18466 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34310 |
| [Connell] p. 57 | Definition | df-scmat 22412 df-scmatalt 48505 |
| [Conway] p. 4 | Definition | slerec 27766 slerecd 27767 |
| [Conway] p. 5 | Definition | addsval 27911 addsval2 27912 df-adds 27909 df-muls 28052 df-negs 27969 |
| [Conway] p. 7 | Theorem | 0slt1s 27779 |
| [Conway] p. 12 | Theorem 12 | pw2cut2 28388 |
| [Conway] p. 16 | Theorem 0(i) | ssltright 27822 |
| [Conway] p. 16 | Theorem 0(ii) | ssltleft 27821 |
| [Conway] p. 16 | Theorem 0(iii) | slerflex 27708 |
| [Conway] p. 17 | Theorem 3 | addsass 27954 addsassd 27955 addscom 27915 addscomd 27916 addsrid 27913 addsridd 27914 |
| [Conway] p. 17 | Definition | df-0s 27774 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 27992 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 27989 negsidd 27990 |
| [Conway] p. 18 | Theorem 5 | sleadd1 27938 sleadd1d 27944 |
| [Conway] p. 18 | Definition | df-1s 27775 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 27984 negscld 27985 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 27929 |
| [Conway] p. 19 | Note | mulsunif2 28115 |
| [Conway] p. 19 | Theorem 7 | addsdi 28100 addsdid 28101 addsdird 28102 mulnegs1d 28105 mulnegs2d 28106 mulsass 28111 mulsassd 28112 mulscom 28084 mulscomd 28085 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28079 mulscld 28080 |
| [Conway] p. 19 | Theorem 8(iii) | slemuld 28083 sltmul 28081 sltmuld 28082 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28089 mulsgt0d 28090 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28162 |
| [Conway] p. 23 | Theorem 11 | eqscut3 27771 |
| [Conway] p. 24 | Definition | df-reno 28402 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28407 remulscl 28410 renegscl 28406 |
| [Conway] p. 27 | Definition | df-ons 28195 elons2 28201 |
| [Conway] p. 27 | Theorem 14 | sltonex 28205 |
| [Conway] p. 28 | Theorem 15 | onscutlt 28207 onswe 28212 |
| [Conway] p. 29 | Remark | madebday 27851 newbday 27853 oldbday 27852 |
| [Conway] p. 29 | Definition | df-made 27794 df-new 27796 df-old 27795 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13771 |
| [Crawley] p. 1 | Definition of poset | df-poset 18225 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 39491 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 40295 dalaw 39991 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 42066 |
| [Crawley] p. 111 | Definition of set W | df-watsN 40095 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 40211 df-ldil 40209 isldil 40215 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 40210 df-trnN 40212 isltrn 40224 ltrnu 40226 |
| [Crawley] p. 112 | Lemma A | cdlema1N 39896 cdlema2N 39897 exatleN 39509 |
| [Crawley] p. 112 | Lemma B | 1cvrat 39581 cdlemb 39899 cdlemb2 40146 cdlemb3 40711 idltrn 40255 l1cvat 39160 lhpat 40148 lhpat2 40150 lshpat 39161 ltrnel 40244 ltrnmw 40256 |
| [Crawley] p. 112 | Lemma C | cdlemc1 40296 cdlemc2 40297 ltrnnidn 40279 trlat 40274 trljat1 40271 trljat2 40272 trljat3 40273 trlne 40290 trlnidat 40278 trlnle 40291 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 40096 |
| [Crawley] p. 113 | Lemma C | cdlemc 40302 cdlemc3 40298 cdlemc4 40299 |
| [Crawley] p. 113 | Lemma D | cdlemd 40312 cdlemd1 40303 cdlemd2 40304 cdlemd3 40305 cdlemd4 40306 cdlemd5 40307 cdlemd6 40308 cdlemd7 40309 cdlemd8 40310 cdlemd9 40311 cdleme31sde 40490 cdleme31se 40487 cdleme31se2 40488 cdleme31snd 40491 cdleme32a 40546 cdleme32b 40547 cdleme32c 40548 cdleme32d 40549 cdleme32e 40550 cdleme32f 40551 cdleme32fva 40542 cdleme32fva1 40543 cdleme32fvcl 40545 cdleme32le 40552 cdleme48fv 40604 cdleme4gfv 40612 cdleme50eq 40646 cdleme50f 40647 cdleme50f1 40648 cdleme50f1o 40651 cdleme50laut 40652 cdleme50ldil 40653 cdleme50lebi 40645 cdleme50rn 40650 cdleme50rnlem 40649 cdlemeg49le 40616 cdlemeg49lebilem 40644 |
| [Crawley] p. 113 | Lemma E | cdleme 40665 cdleme00a 40314 cdleme01N 40326 cdleme02N 40327 cdleme0a 40316 cdleme0aa 40315 cdleme0b 40317 cdleme0c 40318 cdleme0cp 40319 cdleme0cq 40320 cdleme0dN 40321 cdleme0e 40322 cdleme0ex1N 40328 cdleme0ex2N 40329 cdleme0fN 40323 cdleme0gN 40324 cdleme0moN 40330 cdleme1 40332 cdleme10 40359 cdleme10tN 40363 cdleme11 40375 cdleme11a 40365 cdleme11c 40366 cdleme11dN 40367 cdleme11e 40368 cdleme11fN 40369 cdleme11g 40370 cdleme11h 40371 cdleme11j 40372 cdleme11k 40373 cdleme11l 40374 cdleme12 40376 cdleme13 40377 cdleme14 40378 cdleme15 40383 cdleme15a 40379 cdleme15b 40380 cdleme15c 40381 cdleme15d 40382 cdleme16 40390 cdleme16aN 40364 cdleme16b 40384 cdleme16c 40385 cdleme16d 40386 cdleme16e 40387 cdleme16f 40388 cdleme16g 40389 cdleme19a 40408 cdleme19b 40409 cdleme19c 40410 cdleme19d 40411 cdleme19e 40412 cdleme19f 40413 cdleme1b 40331 cdleme2 40333 cdleme20aN 40414 cdleme20bN 40415 cdleme20c 40416 cdleme20d 40417 cdleme20e 40418 cdleme20f 40419 cdleme20g 40420 cdleme20h 40421 cdleme20i 40422 cdleme20j 40423 cdleme20k 40424 cdleme20l 40427 cdleme20l1 40425 cdleme20l2 40426 cdleme20m 40428 cdleme20y 40407 cdleme20zN 40406 cdleme21 40442 cdleme21d 40435 cdleme21e 40436 cdleme22a 40445 cdleme22aa 40444 cdleme22b 40446 cdleme22cN 40447 cdleme22d 40448 cdleme22e 40449 cdleme22eALTN 40450 cdleme22f 40451 cdleme22f2 40452 cdleme22g 40453 cdleme23a 40454 cdleme23b 40455 cdleme23c 40456 cdleme26e 40464 cdleme26eALTN 40466 cdleme26ee 40465 cdleme26f 40468 cdleme26f2 40470 cdleme26f2ALTN 40469 cdleme26fALTN 40467 cdleme27N 40474 cdleme27a 40472 cdleme27cl 40471 cdleme28c 40477 cdleme3 40342 cdleme30a 40483 cdleme31fv 40495 cdleme31fv1 40496 cdleme31fv1s 40497 cdleme31fv2 40498 cdleme31id 40499 cdleme31sc 40489 cdleme31sdnN 40492 cdleme31sn 40485 cdleme31sn1 40486 cdleme31sn1c 40493 cdleme31sn2 40494 cdleme31so 40484 cdleme35a 40553 cdleme35b 40555 cdleme35c 40556 cdleme35d 40557 cdleme35e 40558 cdleme35f 40559 cdleme35fnpq 40554 cdleme35g 40560 cdleme35h 40561 cdleme35h2 40562 cdleme35sn2aw 40563 cdleme35sn3a 40564 cdleme36a 40565 cdleme36m 40566 cdleme37m 40567 cdleme38m 40568 cdleme38n 40569 cdleme39a 40570 cdleme39n 40571 cdleme3b 40334 cdleme3c 40335 cdleme3d 40336 cdleme3e 40337 cdleme3fN 40338 cdleme3fa 40341 cdleme3g 40339 cdleme3h 40340 cdleme4 40343 cdleme40m 40572 cdleme40n 40573 cdleme40v 40574 cdleme40w 40575 cdleme41fva11 40582 cdleme41sn3aw 40579 cdleme41sn4aw 40580 cdleme41snaw 40581 cdleme42a 40576 cdleme42b 40583 cdleme42c 40577 cdleme42d 40578 cdleme42e 40584 cdleme42f 40585 cdleme42g 40586 cdleme42h 40587 cdleme42i 40588 cdleme42k 40589 cdleme42ke 40590 cdleme42keg 40591 cdleme42mN 40592 cdleme42mgN 40593 cdleme43aN 40594 cdleme43bN 40595 cdleme43cN 40596 cdleme43dN 40597 cdleme5 40345 cdleme50ex 40664 cdleme50ltrn 40662 cdleme51finvN 40661 cdleme51finvfvN 40660 cdleme51finvtrN 40663 cdleme6 40346 cdleme7 40354 cdleme7a 40348 cdleme7aa 40347 cdleme7b 40349 cdleme7c 40350 cdleme7d 40351 cdleme7e 40352 cdleme7ga 40353 cdleme8 40355 cdleme8tN 40360 cdleme9 40358 cdleme9a 40356 cdleme9b 40357 cdleme9tN 40362 cdleme9taN 40361 cdlemeda 40403 cdlemedb 40402 cdlemednpq 40404 cdlemednuN 40405 cdlemefr27cl 40508 cdlemefr32fva1 40515 cdlemefr32fvaN 40514 cdlemefrs32fva 40505 cdlemefrs32fva1 40506 cdlemefs27cl 40518 cdlemefs32fva1 40528 cdlemefs32fvaN 40527 cdlemesner 40401 cdlemeulpq 40325 |
| [Crawley] p. 114 | Lemma E | 4atex 40181 4atexlem7 40180 cdleme0nex 40395 cdleme17a 40391 cdleme17c 40393 cdleme17d 40603 cdleme17d1 40394 cdleme17d2 40600 cdleme18a 40396 cdleme18b 40397 cdleme18c 40398 cdleme18d 40400 cdleme4a 40344 |
| [Crawley] p. 115 | Lemma E | cdleme21a 40430 cdleme21at 40433 cdleme21b 40431 cdleme21c 40432 cdleme21ct 40434 cdleme21f 40437 cdleme21g 40438 cdleme21h 40439 cdleme21i 40440 cdleme22gb 40399 |
| [Crawley] p. 116 | Lemma F | cdlemf 40668 cdlemf1 40666 cdlemf2 40667 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 40672 cdlemg16 40762 cdlemg28 40809 cdlemg28a 40798 cdlemg28b 40808 cdlemg3a 40702 cdlemg42 40834 cdlemg43 40835 cdlemg44 40838 cdlemg44a 40836 cdlemg46 40840 cdlemg47 40841 cdlemg9 40739 ltrnco 40824 ltrncom 40843 tgrpabl 40856 trlco 40832 |
| [Crawley] p. 116 | Definition of G | df-tgrp 40848 |
| [Crawley] p. 117 | Lemma G | cdlemg17 40782 cdlemg17b 40767 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 40861 df-edring 40862 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 40865 |
| [Crawley] p. 118 | Remark | tendopltp 40885 |
| [Crawley] p. 118 | Lemma H | cdlemh 40922 cdlemh1 40920 cdlemh2 40921 |
| [Crawley] p. 118 | Lemma I | cdlemi 40925 cdlemi1 40923 cdlemi2 40924 |
| [Crawley] p. 118 | Lemma J | cdlemj1 40926 cdlemj2 40927 cdlemj3 40928 tendocan 40929 |
| [Crawley] p. 118 | Lemma K | cdlemk 41079 cdlemk1 40936 cdlemk10 40948 cdlemk11 40954 cdlemk11t 41051 cdlemk11ta 41034 cdlemk11tb 41036 cdlemk11tc 41050 cdlemk11u-2N 40994 cdlemk11u 40976 cdlemk12 40955 cdlemk12u-2N 40995 cdlemk12u 40977 cdlemk13-2N 40981 cdlemk13 40957 cdlemk14-2N 40983 cdlemk14 40959 cdlemk15-2N 40984 cdlemk15 40960 cdlemk16-2N 40985 cdlemk16 40962 cdlemk16a 40961 cdlemk17-2N 40986 cdlemk17 40963 cdlemk18-2N 40991 cdlemk18-3N 41005 cdlemk18 40973 cdlemk19-2N 40992 cdlemk19 40974 cdlemk19u 41075 cdlemk1u 40964 cdlemk2 40937 cdlemk20-2N 40997 cdlemk20 40979 cdlemk21-2N 40996 cdlemk21N 40978 cdlemk22-3 41006 cdlemk22 40998 cdlemk23-3 41007 cdlemk24-3 41008 cdlemk25-3 41009 cdlemk26-3 41011 cdlemk26b-3 41010 cdlemk27-3 41012 cdlemk28-3 41013 cdlemk29-3 41016 cdlemk3 40938 cdlemk30 40999 cdlemk31 41001 cdlemk32 41002 cdlemk33N 41014 cdlemk34 41015 cdlemk35 41017 cdlemk36 41018 cdlemk37 41019 cdlemk38 41020 cdlemk39 41021 cdlemk39u 41073 cdlemk4 40939 cdlemk41 41025 cdlemk42 41046 cdlemk42yN 41049 cdlemk43N 41068 cdlemk45 41052 cdlemk46 41053 cdlemk47 41054 cdlemk48 41055 cdlemk49 41056 cdlemk5 40941 cdlemk50 41057 cdlemk51 41058 cdlemk52 41059 cdlemk53 41062 cdlemk54 41063 cdlemk55 41066 cdlemk55u 41071 cdlemk56 41076 cdlemk5a 40940 cdlemk5auN 40965 cdlemk5u 40966 cdlemk6 40942 cdlemk6u 40967 cdlemk7 40953 cdlemk7u-2N 40993 cdlemk7u 40975 cdlemk8 40943 cdlemk9 40944 cdlemk9bN 40945 cdlemki 40946 cdlemkid 41041 cdlemkj-2N 40987 cdlemkj 40968 cdlemksat 40951 cdlemksel 40950 cdlemksv 40949 cdlemksv2 40952 cdlemkuat 40971 cdlemkuel-2N 40989 cdlemkuel-3 41003 cdlemkuel 40970 cdlemkuv-2N 40988 cdlemkuv2-2 40990 cdlemkuv2-3N 41004 cdlemkuv2 40972 cdlemkuvN 40969 cdlemkvcl 40947 cdlemky 41031 cdlemkyyN 41067 tendoex 41080 |
| [Crawley] p. 120 | Remark | dva1dim 41090 |
| [Crawley] p. 120 | Lemma L | cdleml1N 41081 cdleml2N 41082 cdleml3N 41083 cdleml4N 41084 cdleml5N 41085 cdleml6 41086 cdleml7 41087 cdleml8 41088 cdleml9 41089 dia1dim 41166 |
| [Crawley] p. 120 | Lemma M | dia11N 41153 diaf11N 41154 dialss 41151 diaord 41152 dibf11N 41266 djajN 41242 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 41137 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 41223 dia2dimlem1 41169 dia2dimlem2 41170 dia2dimlem3 41171 dia2dimlem4 41172 dia2dimlem5 41173 diaf1oN 41235 diarnN 41234 dvheveccl 41217 dvhopN 41221 |
| [Crawley] p. 121 | Lemma N | cdlemn 41317 cdlemn10 41311 cdlemn11 41316 cdlemn11a 41312 cdlemn11b 41313 cdlemn11c 41314 cdlemn11pre 41315 cdlemn2 41300 cdlemn2a 41301 cdlemn3 41302 cdlemn4 41303 cdlemn4a 41304 cdlemn5 41306 cdlemn5pre 41305 cdlemn6 41307 cdlemn7 41308 cdlemn8 41309 cdlemn9 41310 diclspsn 41299 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 41278 |
| [Crawley] p. 122 | Lemma N | dih11 41370 dihf11 41372 dihjust 41322 dihjustlem 41321 dihord 41369 dihord1 41323 dihord10 41328 dihord11b 41327 dihord11c 41329 dihord2 41332 dihord2a 41324 dihord2b 41325 dihord2cN 41326 dihord2pre 41330 dihord2pre2 41331 dihordlem6 41318 dihordlem7 41319 dihordlem7b 41320 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 41335 dihfval 41336 dihval 41337 |
| [Diestel] p. 3 | Definition | df-gric 47986 df-grim 47983 isuspgrim 48001 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29397 df-nbgr 29318 |
| [Diestel] p. 3 | Definition by | df-grisom 47982 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 47966 df-subgr 29253 uhgrspan1 29288 uhgrspansubgr 29276 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 29540 vtxdgoddnumeven 29539 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29044 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 33884 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 33896 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 33888 zarcls1 33889 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 33899 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 33902 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 33905 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3900 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9543 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8758 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9551 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9879 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10452 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5245 |
| [Enderton] p. 19 | Definition | df-tp 4580 |
| [Enderton] p. 26 | Exercise 5 | unissb 4891 |
| [Enderton] p. 26 | Exercise 10 | pwel 5321 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5512 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5029 iinin2 5028 iinun2 5023 iunin1 5022 iunin1f 32544 iunin2 5021 uniin1 32538 uniin2 32539 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5027 iundif2 5024 |
| [Enderton] p. 32 | Exercise 20 | unineq 4237 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5048 |
| [Enderton] p. 33 | Exercise 25 | iununi 5049 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5056 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7710 iunpwss 5057 |
| [Enderton] p. 36 | Definition | opthwiener 5457 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5393 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4896 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5413 rnex 7846 rnexg 7838 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5859 rnuni 6101 |
| [Enderton] p. 42 | Definition of a function | dffun7 6514 dffun8 6515 |
| [Enderton] p. 43 | Definition of function value | funfv2 6916 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6556 |
| [Enderton] p. 44 | Definition (d) | dfima2 6016 dfima3 6017 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6925 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10370 ac7g 10371 df-ac 10013 dfac2 10029 dfac2a 10027 dfac2b 10028 dfac3 10018 dfac7 10030 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7186 |
| [Enderton] p. 52 | Definition | df-map 8758 |
| [Enderton] p. 53 | Exercise 21 | coass 6219 |
| [Enderton] p. 53 | Exercise 27 | dmco 6208 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6563 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6056 |
| [Enderton] p. 54 | Remark | ixpf 8850 ixpssmap 8862 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8828 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10380 ac9s 10390 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 38712 erref 8648 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 38715 erthi 8684 |
| [Enderton] p. 57 | Definition | df-ec 8630 |
| [Enderton] p. 58 | Definition | df-qs 8634 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8630 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5855 |
| [Enderton] p. 68 | Definition of successor | df-suc 6318 |
| [Enderton] p. 71 | Definition | df-tr 5201 dftr4 5206 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6393 unisucg 6392 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6393 unisucg 6392 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5215 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5217 trintALT 44978 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8525 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8527 onasuc 8449 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7355 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8526 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8528 onmsuc 8450 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8543 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8530 nnacom 8538 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8544 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8545 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8547 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8531 nnmsucr 8546 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8559 |
| [Enderton] p. 129 | Definition | df-en 8876 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7306 |
| [Enderton] p. 133 | Exercise 1 | xpomen 9912 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16128 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9122 |
| [Enderton] p. 135 | Corollary 6C | php3 9124 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9121 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9152 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9154 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9084 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9088 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9060 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10077 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10078 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10073 dju1en 10069 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9233 unifi 9234 unifi2 9235 |
| [Enderton] p. 144 | Corollary 6K | undif2 4426 unfi 9086 unfi2 9200 |
| [Enderton] p. 145 | Figure 38 | ffoss 7884 |
| [Enderton] p. 145 | Definition | df-dom 8877 |
| [Enderton] p. 146 | Example 1 | domen 8890 domeng 8891 |
| [Enderton] p. 146 | Example 3 | nndomo 9132 nnsdom 9550 nnsdomg 9189 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10081 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9061 xpdom1 8995 xpdom1g 8993 xpdom2g 8992 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9067 |
| [Enderton] p. 151 | Theorem 6M | zorn 10404 zorng 10401 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10389 dfac5 10026 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10472 |
| [Enderton] p. 164 | Example | infdif 10105 |
| [Enderton] p. 168 | Definition | df-po 5527 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6427 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6359 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6426 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6367 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7775 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7720 |
| [Enderton] p. 194 | Remark | onprc 7717 |
| [Enderton] p. 194 | Exercise 16 | suc11 6421 |
| [Enderton] p. 197 | Definition | df-card 9838 |
| [Enderton] p. 197 | Theorem 7P | carden 10448 |
| [Enderton] p. 200 | Exercise 25 | tfis 7791 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9675 |
| [Enderton] p. 202 | Definition | df-r1 9663 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9685 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9766 rankval4b 35118 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9502 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9756 rankprb 9750 rankpw 9742 rankpwi 9722 rankuniss 9765 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9514 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9515 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10007 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 9973 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 9987 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8267 |
| [Enderton] p. 222 | Definition of kard | karden 9794 kardex 9793 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8518 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8520 |
| [Enderton] p. 240 | Exercise 25 | oarec 8483 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10147 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17554 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17496 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18465 mrieqv2d 17551 mrieqvd 17550 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17555 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17560 mreexexlem2d 17557 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18471 mreexfidimd 17562 |
| [Frege1879] p. 11 | Statement | df3or2 43866 |
| [Frege1879] p. 12 | Statement | df3an2 43867 dfxor4 43864 dfxor5 43865 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 43888 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 43889 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 43893 |
| [Frege1879] p. 31 | Proposition 4 | frege4 43897 |
| [Frege1879] p. 32 | Proposition 5 | frege5 43898 |
| [Frege1879] p. 33 | Proposition 6 | frege6 43904 |
| [Frege1879] p. 34 | Proposition 7 | frege7 43906 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 43907 axfrege8 43905 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 90 wl-luk-pm2.04 37496 |
| [Frege1879] p. 35 | Proposition 9 | frege9 43910 |
| [Frege1879] p. 36 | Proposition 10 | frege10 43918 |
| [Frege1879] p. 36 | Proposition 11 | frege11 43912 |
| [Frege1879] p. 37 | Proposition 12 | frege12 43911 |
| [Frege1879] p. 37 | Proposition 13 | frege13 43920 |
| [Frege1879] p. 37 | Proposition 14 | frege14 43921 |
| [Frege1879] p. 38 | Proposition 15 | frege15 43924 |
| [Frege1879] p. 38 | Proposition 16 | frege16 43914 |
| [Frege1879] p. 39 | Proposition 17 | frege17 43919 |
| [Frege1879] p. 39 | Proposition 18 | frege18 43916 |
| [Frege1879] p. 39 | Proposition 19 | frege19 43922 |
| [Frege1879] p. 40 | Proposition 20 | frege20 43926 |
| [Frege1879] p. 40 | Proposition 21 | frege21 43925 |
| [Frege1879] p. 41 | Proposition 22 | frege22 43917 |
| [Frege1879] p. 42 | Proposition 23 | frege23 43923 |
| [Frege1879] p. 42 | Proposition 24 | frege24 43913 |
| [Frege1879] p. 42 | Proposition 25 | frege25 43915 rp-frege25 43903 |
| [Frege1879] p. 42 | Proposition 26 | frege26 43908 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 43928 |
| [Frege1879] p. 43 | Proposition 27 | frege27 43909 |
| [Frege1879] p. 43 | Proposition 28 | con3 153 |
| [Frege1879] p. 43 | Proposition 29 | frege29 43929 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 43932 axfrege31 43931 |
| [Frege1879] p. 44 | Proposition 30 | frege30 43930 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 130 |
| [Frege1879] p. 44 | Proposition 32 | frege32 43933 |
| [Frege1879] p. 44 | Proposition 33 | frege33 43934 |
| [Frege1879] p. 45 | Proposition 34 | frege34 43935 |
| [Frege1879] p. 45 | Proposition 35 | frege35 43936 |
| [Frege1879] p. 45 | Proposition 36 | frege36 43937 |
| [Frege1879] p. 46 | Proposition 37 | frege37 43938 |
| [Frege1879] p. 46 | Proposition 38 | frege38 43939 |
| [Frege1879] p. 46 | Proposition 39 | frege39 43940 |
| [Frege1879] p. 46 | Proposition 40 | frege40 43941 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 43943 axfrege41 43942 |
| [Frege1879] p. 47 | Proposition 41 | notnot 142 |
| [Frege1879] p. 47 | Proposition 42 | frege42 43944 |
| [Frege1879] p. 47 | Proposition 43 | frege43 43945 |
| [Frege1879] p. 47 | Proposition 44 | frege44 43946 |
| [Frege1879] p. 47 | Proposition 45 | frege45 43947 |
| [Frege1879] p. 48 | Proposition 46 | frege46 43948 |
| [Frege1879] p. 48 | Proposition 47 | frege47 43949 |
| [Frege1879] p. 49 | Proposition 48 | frege48 43950 |
| [Frege1879] p. 49 | Proposition 49 | frege49 43951 |
| [Frege1879] p. 49 | Proposition 50 | frege50 43952 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 43955 ax-frege52c 43986 frege52aid 43956 frege52b 43987 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 43960 ax-frege54c 43990 frege54b 43991 |
| [Frege1879] p. 50 | Proposition 51 | frege51 43953 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3738 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 43958 frege53aid 43957 frege53b 43988 frege53c 44012 |
| [Frege1879] p. 50 | Proposition 54 | biid 261 eqid 2731 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 43966 frege55aid 43963 frege55b 43995 frege55c 44016 frege55cor1a 43967 frege55lem2a 43965 frege55lem2b 43994 frege55lem2c 44015 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 43969 frege56aid 43968 frege56b 43996 frege56c 44017 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 43973 ax-frege58b 43999 frege58bid 44000 frege58c 44019 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 43971 frege57aid 43970 frege57b 43997 frege57c 44018 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3749 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 43975 frege59b 44002 frege59c 44020 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 43976 frege60b 44003 frege60c 44021 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 43977 frege61b 44004 frege61c 44022 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 43978 frege62b 44005 frege62c 44023 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 43979 frege63b 44006 frege63c 44024 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 43980 frege64b 44007 frege64c 44025 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 43981 frege65b 44008 frege65c 44026 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 43982 frege66b 44009 frege66c 44027 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 43983 frege67b 44010 frege67c 44028 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 43984 frege68b 44011 frege68c 44029 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 44030 |
| [Frege1879] p. 58 | Proposition 70 | frege70 44031 |
| [Frege1879] p. 59 | Proposition 71 | frege71 44032 |
| [Frege1879] p. 59 | Proposition 72 | frege72 44033 |
| [Frege1879] p. 59 | Proposition 73 | frege73 44034 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 44037 |
| [Frege1879] p. 60 | Proposition 74 | frege74 44035 |
| [Frege1879] p. 60 | Proposition 75 | frege75 44036 |
| [Frege1879] p. 62 | Proposition 77 | frege77 44038 frege77d 43844 |
| [Frege1879] p. 63 | Proposition 78 | frege78 44039 |
| [Frege1879] p. 63 | Proposition 79 | frege79 44040 |
| [Frege1879] p. 63 | Proposition 80 | frege80 44041 |
| [Frege1879] p. 63 | Proposition 81 | frege81 44042 frege81d 43845 |
| [Frege1879] p. 64 | Proposition 82 | frege82 44043 |
| [Frege1879] p. 65 | Proposition 83 | frege83 44044 frege83d 43846 |
| [Frege1879] p. 65 | Proposition 84 | frege84 44045 |
| [Frege1879] p. 66 | Proposition 85 | frege85 44046 |
| [Frege1879] p. 66 | Proposition 86 | frege86 44047 |
| [Frege1879] p. 66 | Proposition 87 | frege87 44048 frege87d 43848 |
| [Frege1879] p. 67 | Proposition 88 | frege88 44049 |
| [Frege1879] p. 68 | Proposition 89 | frege89 44050 |
| [Frege1879] p. 68 | Proposition 90 | frege90 44051 |
| [Frege1879] p. 68 | Proposition 91 | frege91 44052 frege91d 43849 |
| [Frege1879] p. 69 | Proposition 92 | frege92 44053 |
| [Frege1879] p. 70 | Proposition 93 | frege93 44054 |
| [Frege1879] p. 70 | Proposition 94 | frege94 44055 |
| [Frege1879] p. 70 | Proposition 95 | frege95 44056 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 44060 |
| [Frege1879] p. 71 | Proposition 96 | frege96 44057 frege96d 43847 |
| [Frege1879] p. 71 | Proposition 97 | frege97 44058 frege97d 43850 |
| [Frege1879] p. 71 | Proposition 98 | frege98 44059 frege98d 43851 |
| [Frege1879] p. 72 | Proposition 100 | frege100 44061 |
| [Frege1879] p. 72 | Proposition 101 | frege101 44062 |
| [Frege1879] p. 72 | Proposition 102 | frege102 44063 frege102d 43852 |
| [Frege1879] p. 73 | Proposition 103 | frege103 44064 |
| [Frege1879] p. 73 | Proposition 104 | frege104 44065 |
| [Frege1879] p. 73 | Proposition 105 | frege105 44066 |
| [Frege1879] p. 73 | Proposition 106 | frege106 44067 frege106d 43853 |
| [Frege1879] p. 74 | Proposition 107 | frege107 44068 |
| [Frege1879] p. 74 | Proposition 108 | frege108 44069 frege108d 43854 |
| [Frege1879] p. 74 | Proposition 109 | frege109 44070 frege109d 43855 |
| [Frege1879] p. 75 | Proposition 110 | frege110 44071 |
| [Frege1879] p. 75 | Proposition 111 | frege111 44072 frege111d 43857 |
| [Frege1879] p. 76 | Proposition 112 | frege112 44073 |
| [Frege1879] p. 76 | Proposition 113 | frege113 44074 |
| [Frege1879] p. 76 | Proposition 114 | frege114 44075 frege114d 43856 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 44076 |
| [Frege1879] p. 77 | Proposition 116 | frege116 44077 |
| [Frege1879] p. 78 | Proposition 117 | frege117 44078 |
| [Frege1879] p. 78 | Proposition 118 | frege118 44079 |
| [Frege1879] p. 78 | Proposition 119 | frege119 44080 |
| [Frege1879] p. 78 | Proposition 120 | frege120 44081 |
| [Frege1879] p. 79 | Proposition 121 | frege121 44082 |
| [Frege1879] p. 79 | Proposition 122 | frege122 44083 frege122d 43858 |
| [Frege1879] p. 79 | Proposition 123 | frege123 44084 |
| [Frege1879] p. 80 | Proposition 124 | frege124 44085 frege124d 43859 |
| [Frege1879] p. 81 | Proposition 125 | frege125 44086 |
| [Frege1879] p. 81 | Proposition 126 | frege126 44087 frege126d 43860 |
| [Frege1879] p. 82 | Proposition 127 | frege127 44088 |
| [Frege1879] p. 83 | Proposition 128 | frege128 44089 |
| [Frege1879] p. 83 | Proposition 129 | frege129 44090 frege129d 43861 |
| [Frege1879] p. 84 | Proposition 130 | frege130 44091 |
| [Frege1879] p. 85 | Proposition 131 | frege131 44092 frege131d 43862 |
| [Frege1879] p. 86 | Proposition 132 | frege132 44093 |
| [Frege1879] p. 86 | Proposition 133 | frege133 44094 frege133d 43863 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 46416 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 46739 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 46439 |
| [Fremlin1] p. 14 | Definition 112A | ismea 46554 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 46574 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 46565 meadjunre 46579 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 46566 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 46567 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 46563 meaiunle 46572 meaiunlelem 46571 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 46584 meaiuninc2 46585 meaiuninc3 46588 meaiuninc3v 46587 meaiunincf 46586 meaiuninclem 46583 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 46590 meaiininc2 46591 meaiininclem 46589 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 46609 caragendifcl 46617 caratheodory 46631 omelesplit 46621 |
| [Fremlin1] p. 19 | Definition 113A | isome 46597 isomennd 46634 isomenndlem 46633 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 46619 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 46638 voncmpl 46724 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 46601 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 46626 carageniuncllem1 46624 carageniuncllem2 46625 caragenuncl 46616 caragenuncllem 46615 caragenunicl 46627 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 46635 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 46629 caratheodorylem2 46630 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 46638 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 46697 hoidmv1lelem1 46694 hoidmv1lelem2 46695 hoidmv1lelem3 46696 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 46741 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 46697 hoidmvle 46703 hoidmvlelem1 46698 hoidmvlelem2 46699 hoidmvlelem3 46700 hoidmvlelem4 46701 hoidmvlelem5 46702 hsphoidmvle2 46688 hsphoif 46679 hsphoival 46682 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 46651 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 46659 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 46686 hoidmvn0val 46687 hoidmvval 46680 hoidmvval0 46690 hoidmvval0b 46693 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 46691 hsphoidmvle 46689 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 46640 df-voln 46642 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 46707 ovn0 46669 ovn0lem 46668 ovnf 46666 ovnome 46676 ovnssle 46664 ovnsslelem 46663 ovnsupge0 46660 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 46706 ovnhoilem1 46704 ovnhoilem2 46705 vonhoi 46770 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 46723 hoidifhspf 46721 hoidifhspval 46711 hoidifhspval2 46718 hoidifhspval3 46722 hspmbl 46732 hspmbllem1 46729 hspmbllem2 46730 hspmbllem3 46731 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 46724 vonmea 46677 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 46675 ovnsubadd2 46749 ovnsubadd2lem 46748 ovnsubaddlem1 46673 ovnsubaddlem2 46674 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 46734 hoimbl2 46768 hoimbllem 46733 hspdifhsp 46719 opnvonmbl 46737 opnvonmbllem2 46736 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 46739 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 46782 iccvonmbllem 46781 ioovonmbl 46780 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 46788 vonicclem2 46787 vonioo 46785 vonioolem2 46784 vonn0icc 46791 vonn0icc2 46795 vonn0ioo 46790 vonn0ioo2 46793 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 46792 snvonmbl 46789 vonct 46796 vonsn 46794 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 46462 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 46461 subsaliuncllem 46460 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 46828 salpreimalegt 46812 salpreimaltle 46829 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 46831 issmff 46837 issmflem 46830 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 46848 issmflelem 46847 smfpreimale 46857 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 46859 issmfgtlem 46858 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 46799 issmf 46831 issmff 46837 issmfge 46873 issmfgelem 46872 issmfgt 46859 issmfgtlem 46858 issmfle 46848 issmflelem 46847 issmflem 46830 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 46810 salpreimagtlt 46833 salpreimalelt 46832 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 46873 issmfgelem 46872 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 46856 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 46854 cnfsmf 46843 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 46870 decsmflem 46869 incsmf 46845 incsmflem 46844 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 46804 pimconstlt1 46805 smfconst 46852 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 46868 smfaddlem1 46866 smfaddlem2 46867 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 46899 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 46898 smfmullem1 46894 smfmullem2 46895 smfmullem3 46896 smfmullem4 46897 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 46900 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 46903 smfpimbor1lem2 46902 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 46905 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 46893 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 46892 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 46901 smfresal 46891 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 46880 smflim2 46909 smflimlem1 46874 smflimlem2 46875 smflimlem3 46876 smflimlem4 46877 smflimlem5 46878 smflimlem6 46879 smflimmpt 46913 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 46917 smfsuplem1 46914 smfsuplem2 46915 smfsuplem3 46916 smfsupmpt 46918 smfsupxr 46919 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 46921 smfinflem 46920 smfinfmpt 46922 |
| [Fremlin1] p. 39 | Remark 121G | smflim 46880 smflim2 46909 smflimmpt 46913 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 46911 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 46941 smfdivdmmbl2 46944 smfinfdmmbl 46952 smfinfdmmbllem 46951 smfsupdmmbl 46948 smfsupdmmbllem 46947 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 46931 smflimsuplem2 46924 smflimsuplem6 46928 smflimsuplem7 46929 smflimsuplem8 46930 smflimsupmpt 46932 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 46934 smfliminflem 46933 smfliminfmpt 46935 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 46799 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 46945 fsupdm2 46946 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 46936 adddmmbl2 46937 finfdm 46949 finfdm2 46950 fsupdm 46945 fsupdm2 46946 muldmmbl 46938 muldmmbl2 46939 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 46949 finfdm2 46950 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25470 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25513 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25523 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 37744 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 37747 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9534 inf1 9518 inf2 9519 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10808 enqer 10818 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10813 df-nq 10809 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10805 df-plq 10811 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7589 df-mpq 10806 df-mq 10812 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10814 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10872 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10873 ltbtwnnq 10875 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10868 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10869 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10876 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10878 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 10890 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 10892 |
| [Gleason] p. 122 | Definition | df-1p 10879 |
| [Gleason] p. 122 | Remark (1) | prub 10891 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 10930 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10882 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 10929 psslinpr 10928 supexpr 10951 suplem1pr 10949 suplem2pr 10950 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 10915 addclprlem1 10913 addclprlem2 10914 df-plp 10880 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 10919 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 10918 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 10931 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 10940 ltexprlem1 10933 ltexprlem2 10934 ltexprlem3 10935 ltexprlem4 10936 ltexprlem5 10937 ltexprlem6 10938 ltexprlem7 10939 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 10942 ltaprlem 10941 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 10943 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 10944 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10881 mulclpr 10917 mulclprlem 10916 reclem2pr 10945 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 10926 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 10921 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 10920 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 10925 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 10948 reclem3pr 10946 reclem4pr 10947 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 10952 enrer 10960 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 10957 df-1r 10958 df-nr 10953 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 10955 df-plr 10954 negexsr 10999 recexsr 11004 recexsrlem 11000 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 10956 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12126 creur 12125 cru 12123 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11085 axcnre 11061 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15028 crimd 15145 crimi 15106 crre 15027 crred 15144 crrei 15105 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15030 remimd 15111 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15197 absval2d 15361 absval2i 15311 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15054 cjaddd 15133 cjaddi 15101 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15055 cjmuld 15134 cjmuli 15102 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15053 cjcjd 15112 cjcji 15084 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15052 cjreb 15036 cjrebd 15115 cjrebi 15087 cjred 15139 rere 15035 rereb 15033 rerebd 15114 rerebi 15086 rered 15137 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15061 addcjd 15125 addcji 15096 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15151 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15192 abscjd 15366 abscji 15315 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15202 abs00d 15362 abs00i 15312 absne0d 15363 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15235 releabsd 15367 releabsi 15316 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15207 absmuld 15370 absmuli 15318 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15195 sqabsaddi 15319 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15244 abstrid 15372 abstrii 15322 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 13975 exp0 13978 expp1 13981 expp1d 14060 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26621 cxpaddd 26659 expadd 14017 expaddd 14061 expaddz 14019 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26630 cxpmuld 26679 expmul 14020 expmuld 14062 expmulz 14021 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26627 mulcxpd 26670 mulexp 14014 mulexpd 14074 mulexpz 14015 |
| [Gleason] p. 140 | Exercise 1 | znnen 16127 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13415 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15545 rlimadd 15556 rlimdiv 15559 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15547 rlimsub 15557 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15546 rlimmul 15558 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15550 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15496 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15517 climcj 15518 climim 15520 climre 15519 rlimabs 15522 rlimcj 15523 rlimim 15525 rlimre 15524 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11157 df-xr 11156 ltxr 13020 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15384 limsupval 15387 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15583 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15592 caucvgb 15593 caucvgbf 45592 caucvgr 15589 climcau 15584 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15729 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15796 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15249 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13738 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21291 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24264 xmet0 24263 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24280 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24271 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24273 mstri 24390 xmettri 24272 xmstri 24389 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24303 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23569 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25243 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24461 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24787 addcn2 15507 mulcn 24789 mulcn2 15509 subcn 24788 subcn2 15508 |
| [Gleason] p. 295 | Remark | bcval3 14219 bcval4 14220 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14234 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14217 df-bc 14216 |
| [Gleason] p. 296 | Remark | bcn0 14223 bcnn 14225 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15743 |
| [Gleason] p. 308 | Equation 2 | ef0 16004 |
| [Gleason] p. 308 | Equation 3 | efcj 16005 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16011 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16016 |
| [Gleason] p. 310 | Equation 14 | sinadd 16079 |
| [Gleason] p. 310 | Equation 15 | cosadd 16080 |
| [Gleason] p. 311 | Equation 17 | sincossq 16091 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16096 sinbnd 16095 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14129 sqeqori 14127 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 15985 |
| [Godowski] p. 730 | Equation SF | goeqi 32260 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 31655 |
| [Golan] p. 1 | Remark | srgisid 20133 |
| [Golan] p. 1 | Definition | df-srg 20111 |
| [Golan] p. 149 | Definition | df-slmd 33177 |
| [Gonshor] p. 7 | Definition | df-scut 27729 |
| [Gonshor] p. 9 | Theorem 2.5 | slerec 27766 slerecd 27767 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 27870 cofcut1d 27871 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 27872 cofcut2d 27873 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 27874 cofcutr1d 27875 cofcutr2d 27876 |
| [Gonshor] p. 13 | Definition | df-adds 27909 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 27925 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 27951 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28075 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28095 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28384 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28386 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28385 |
| [Gonshor] p. 95 | Theorem 6.1 | addsbday 27966 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36210 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17494 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17496 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 48293 df-cllaw 48291 df-comlaw 48292 |
| [Hall] p. 2 | Section 1.2 | df-clintop 48305 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 48326 |
| [Halmos] p. 28 | Partition ` ` | df-parts 38869 dfmembpart2 38874 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32052 riesz2 32053 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 31928 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32160 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32172 elpjidm 32171 pjnmopi 32135 |
| [Halmos] p. 44 | Remark | pjinormi 31674 pjinormii 31663 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32176 pjrn 31694 pjrni 31689 pjvec 31683 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 31714 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32141 hmopidmpji 32139 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32178 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32167 pjocvec 31684 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32156 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32159 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32162 pjssdif2i 32161 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 31842 |
| [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 1796 |
| [Hatcher] p. 25 | Definition | df-phtpc 24924 df-phtpy 24903 |
| [Hatcher] p. 26 | Definition | df-pco 24938 df-pi1 24941 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 24927 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 24983 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22411 df-dmatalt 48504 |
| [Helfgott] p. 2 | Theorem | tgoldbach 47922 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 47907 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 47919 bgoldbtbnd 47914 bgoldbtbnd 47914 tgblthelfgott 47920 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 34662 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 34663 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 34677 hgt750lemb 34676 hgt750leme 34678 hgt750lemf 34673 hgt750lemg 34674 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 47916 tgoldbachgt 34683 tgoldbachgtALTV 47917 tgoldbachgtd 34682 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 34664 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30480 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 18863 grpoideu 30496 mndideu 18659 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 18893 grpoinveu 30506 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 18924 grpo2inv 30518 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 18937 grpoinvop 30520 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 18959 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1769 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1770 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1772 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32407 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32420 cdj3i 32428 cdj3lem1 32421 cdjreui 32419 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32418 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 42066 |
| [Holland95] p. 14 | Line 15 | hgmapvs 41996 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 42018 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 42019 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 42016 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 42022 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 41941 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 42036 |
| [Holland95] p. 204 | Definition of involution | df-srng 20761 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 39608 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 41633 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 41586 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 40038 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 41482 poml4N 40058 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 41573 pexmidALTN 40083 pexmidN 40074 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 41638 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 39229 ldualset 39230 |
| [Holland95] p. 222 | Item 1 | df-lines 39606 df-pointsN 39607 |
| [Holland95] p. 222 | Item 2 | df-polarityN 40008 |
| [Holland95] p. 223 | Remark | ispsubcl2N 40052 omllaw4 39351 pol1N 40015 polcon3N 40022 |
| [Holland95] p. 223 | Definition | df-psubclN 40040 |
| [Holland95] p. 223 | Equation for polarity | polval2N 40011 |
| [Holmes] p. 40 | Definition | df-xrn 38410 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31071 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32169 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 31950 eigre 31822 eigrei 31821 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 31951 eigorth 31825 eigorthi 31824 |
| [Hughes] p. 137 | Remark (ii) | eigposi 31823 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30296 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30292 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30293 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30294 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30312 frgrregorufr0 30311 frgrregorufrg 30313 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30319 frrusgrord 30328 frrusgrord0 30327 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30075 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30302 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30305 frgrwopreg2 30306 frgrwopregasn 30303 frgrwopregbsn 30304 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30308 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30322 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30325 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30073 numclwlk1 30358 numclwlk1lem1 30356 numclwlk1lem2 30357 numclwwlk1 30348 numclwwlk8 30379 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30299 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 29756 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30334 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30360 numclwwlkovh0 30359 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30368 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 29965 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30372 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30375 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30378 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30390 natded 30390 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30390 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30390 natded 30390 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30390 |
| [Jech] p. 4 | Definition of class | cv 1540 cvjust 2725 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10476 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10474 alephmul 10475 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10473 infmap2 10114 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9713 |
| [Jech] p. 72 | Equation 9.3 | scott0 9785 scottex 9784 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9766 rankval4b 35118 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9790 |
| [Jech] p. 78 | Note | opthprc 5683 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 43013 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 43101 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 43102 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 43025 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 43029 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 43030 rmyp1 43031 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 43032 rmym1 43033 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 43023 rmx1 43024 rmxluc 43034 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 43027 rmy1 43028 rmyluc 43035 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 43037 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 43038 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 43058 jm2.17b 43059 jm2.17c 43060 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 43091 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 43095 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 43086 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 43061 jm2.24nn 43057 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 43100 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 43106 rmygeid 43062 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 43118 |
| [Juillerat] p. 11 | Section *5 | etransc 46386 etransclem47 46384 etransclem48 46385 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 46381 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 46383 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 46369 |
| [Juillerat] p. 13 | Proof | etransclem35 46372 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 46375 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 46361 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 46378 |
| [Juillerat] p. 14 | Proof | etransclem23 46360 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1968 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2013 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2018 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2008 cbvaliw 2007 wl-cbvmotv 37564 wl-motae 37566 wl-moteq 37565 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 1987 spimw 1971 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2034 spw 2035 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31503 chabs1i 31505 chabs2 31504 chabs2i 31506 chjass 31520 chjassi 31473 latabs1 18387 latabs2 18388 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32325 ela 32326 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32270 cvrval2 39379 |
| [Kalmbach] p. 16 | Definition | df-ol 39283 df-oml 39284 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 31571 cmbri 31577 cmtvalN 39316 df-cm 31570 df-cmtN 39282 |
| [Kalmbach] p. 22 | Remark | omllaw5N 39352 pjoml5 31600 pjoml5i 31575 |
| [Kalmbach] p. 22 | Definition | pjoml2 31598 pjoml2i 31572 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 31601 cmcmi 31579 cmcmii 31584 cmtcomN 39354 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 39350 omlsi 31391 pjoml 31423 pjomli 31422 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 39349 |
| [Kalmbach] p. 23 | Remark | cmbr2i 31583 cmcm3 31602 cmcm3i 31581 cmcm3ii 31586 cmcm4i 31582 cmt3N 39356 cmt4N 39357 cmtbr2N 39358 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 31595 cmbr3i 31587 cmtbr3N 39359 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 31605 fh1i 31608 fh2 31606 fh2i 31609 omlfh1N 39363 |
| [Kalmbach] p. 65 | Remark | chjatom 32344 chslej 31485 chsleji 31445 shslej 31367 shsleji 31357 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31482 chocini 31441 chsupcl 31327 chsupval2 31397 h0elch 31242 helch 31230 hsupval2 31396 ocin 31283 ococss 31280 shococss 31281 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31299 |
| [Kalmbach] p. 66 | Remark | df-pjh 31382 pjssmi 32152 pjssmii 31668 |
| [Kalmbach] p. 67 | Lemma 3 | osum 31632 osumi 31629 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32187 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32387 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32297 |
| [Kalmbach] p. 140 | Remark | hatomic 32347 hatomici 32346 hatomistici 32349 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 39424 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32368 lsatexch 39148 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32342 cvlcvr1 39444 cvr1 39515 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32361 cvexchi 32356 cvrexch 39525 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32351 hlrelat 39507 hlrelat5N 39506 lrelat 39119 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21084 lsmsatcv 39115 spansncv 31640 spansncvi 31639 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 39134 spansncv2 32280 |
| [Kalmbach] p. 266 | Definition | df-st 32198 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 31836 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10543 fpwwe2 10540 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10544 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10551 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10546 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10548 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10561 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10565 gchxpidm 10566 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10577 gchhar 10576 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10112 unxpwdom 9481 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10567 |
| [Kreyszig] p. 3 | Property M1 | metcl 24253 xmetcl 24252 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24260 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24493 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11844 muleqadd 11767 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24359 |
| [Kreyszig] p. 19 | Remark | mopntopon 24360 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24419 mopnm 24365 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24417 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24422 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24463 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23179 lmmbr 25191 lmmbr2 25192 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23301 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25246 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25209 iscmet2 25227 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25249 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23382 metelcls 25238 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25239 metcld2 25240 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25032 lmodvneg1 20844 nvinv 30626 vcm 30563 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25028 lmod0vs 20834 slmd0vs 33200 vc0 30561 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20835 slmdvs0 33201 vcz 30562 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 30678 ngpmet 24524 nrmmetd 24495 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 30673 imsdval2 30674 ncvspds 25094 ngpds 24525 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24510 nvnd 30675 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24539 nmge0 24538 nvge0 30660 nvz 30656 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24545 nvabs 30659 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 30788 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 30732 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 30794 blocni 30792 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 30793 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25137 ipeq0 21581 ipz 30706 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25149 pythi 30837 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 30841 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25171 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15769 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25369 minveco 30871 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 30737 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25262 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 30860 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32110 leopg 32109 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32128 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 30905 |
| [Kulpa] p. 547 | Theorem | poimir 37699 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 37698 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 37697 |
| [Kulpa] p. 548 | Theorem | broucube 37700 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 37692 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 37693 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2383 axnul 5245 |
| [Kunen] p. 11 | Axiom 3 | axnul 5245 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 7893 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8768 mapvalg 8766 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10419 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7877 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9663 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9705 r1elssi 9704 |
| [Kunen] p. 107 | Exercise 4 | rankop 9757 rankopb 9751 rankuni 9762 rankxplim 9778 rankxpsuc 9781 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 45052 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 45060 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 45059 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 45061 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 45066 rexabso 45067 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 45073 n0abso 45074 ssabso 45072 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 45075 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 45085 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 45080 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 45083 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 45084 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 45079 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 45091 wfaxpr 45096 wfaxreg 45098 wfaxrep 45092 wfaxsep 45093 wfaxun 45097 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 45082 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 45095 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 45091 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 45090 omelaxinf2 45087 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 45100 wfaxinf2 45099 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 45113 permaxext 45103 permaxinf2 45111 permaxnul 45106 permaxpow 45107 permaxpr 45108 permaxrep 45104 permaxsep 45105 permaxun 45109 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 45101 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 45112 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4954 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 33685 |
| [Lang] p. | Definition | df-rn 5630 |
| [Lang] p. 3 | Statement | lidrideqd 18583 mndbn0 18664 |
| [Lang] p. 3 | Definition | df-mnd 18649 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18601 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18755 |
| [Lang] p. 5 | Equation | gsumreidx 19835 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 48287 |
| [Lang] p. 6 | Example | nn0mnd 48284 |
| [Lang] p. 6 | Equation | gsumxp2 19898 |
| [Lang] p. 6 | Statement | cycsubm 19120 |
| [Lang] p. 6 | Definition | mulgnn0gsum 18999 |
| [Lang] p. 6 | Observation | mndlsmidm 19588 |
| [Lang] p. 7 | Definition | dfgrp2e 18882 |
| [Lang] p. 30 | Definition | df-tocyc 33083 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33128 |
| [Lang] p. 32 | Property (b) | cyc3conja 33133 cycpmconjv 33118 |
| [Lang] p. 53 | Definition | df-cat 17580 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18010 cat1lem 18009 |
| [Lang] p. 54 | Definition | df-iso 17662 |
| [Lang] p. 57 | Definition | df-inito 17897 df-termo 17898 |
| [Lang] p. 58 | Example | irinitoringc 21422 |
| [Lang] p. 58 | Statement | initoeu1 17924 termoeu1 17931 |
| [Lang] p. 62 | Definition | df-func 17771 |
| [Lang] p. 65 | Definition | df-nat 17859 |
| [Lang] p. 91 | Note | df-ringc 20567 |
| [Lang] p. 92 | Statement | mxidlprm 33442 |
| [Lang] p. 92 | Definition | isprmidlc 33419 |
| [Lang] p. 128 | Remark | dsmmlmod 21688 |
| [Lang] p. 129 | Proof | lincscm 48536 lincscmcl 48538 lincsum 48535 lincsumcl 48537 |
| [Lang] p. 129 | Statement | lincolss 48540 |
| [Lang] p. 129 | Observation | dsmmfi 21681 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 33647 qusdimsum 33648 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 33627 |
| [Lang] p. 147 | Definition | snlindsntor 48577 |
| [Lang] p. 504 | Statement | mat1 22368 matring 22364 |
| [Lang] p. 504 | Definition | df-mamu 22312 |
| [Lang] p. 505 | Statement | mamuass 22323 mamutpos 22379 matassa 22365 mattposvs 22376 tposmap 22378 |
| [Lang] p. 513 | Definition | mdet1 22522 mdetf 22516 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22612 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22508 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22532 |
| [Lang] p. 515 | Definition | df-minmar1 22556 smadiadetr 22596 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22531 mdetralt 22529 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22544 |
| [Lang] p. 518 | Definition | df-madu 22555 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22566 madurid 22565 matinv 22598 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 22811 |
| [Lang], p. 224 | Proposition 1.1 | extdgfialg 33714 finextalg 33718 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 33683 fedgmul 33651 |
| [Lang], p. 225 | Proposition 1.4 | algextdeg 33745 |
| [Lang], p. 561 | Remark | chpmatply1 22753 |
| [Lang], p. 561 | Definition | df-chpmat 22748 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 44432 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 44427 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 44433 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5245 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2710 |
| [Levy] p. 59 | Definition | df-ttrcl 9604 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9650 |
| [Levy] p. 338 | Axiom | df-clel 2806 df-cleq 2723 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2806 df-cleq 2723 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2710 |
| [Levy] p. 358 | Axiom | df-clab 2710 |
| [Levy58] p. 2 | Definition I | isfin1-3 10283 |
| [Levy58] p. 2 | Definition II | df-fin2 10183 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10182 |
| [Levy58] p. 2 | Definition III | df-fin3 10185 |
| [Levy58] p. 3 | Definition V | df-fin5 10186 |
| [Levy58] p. 3 | Definition IV | df-fin4 10184 |
| [Levy58] p. 4 | Definition VI | df-fin6 10187 |
| [Levy58] p. 4 | Definition VII | df-fin7 10188 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10312 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27631 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27642 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27674 nosupbnd1 27659 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27676 nosupbnd2 27661 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27680 noetasuplem4 27681 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27677 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1769 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1770 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1772 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32395 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32399 mdsymi 32398 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32393 mdsymlem6 32395 mdsymlem7 32396 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32397 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32300 ssdmd2 32301 ssmd1 32298 ssmd2 32299 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32296 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32268 df-md 32267 mdbr 32281 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32318 mdslj1i 32306 mdslj2i 32307 mdslle1i 32304 mdslle2i 32305 mdslmd1i 32316 mdslmd2i 32317 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32308 mdsl2bi 32310 mdsl2i 32309 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32322 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32319 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32320 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32297 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32302 mdsl3 32303 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32321 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32416 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 39426 hlrelat1 39505 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 39144 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32323 cvmdi 32311 cvnbtwn4 32276 cvrnbtwn4 39384 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32324 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 39445 cvp 32362 cvrp 39521 lcvp 39145 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32386 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32385 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 39438 hlexch4N 39497 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32388 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 39548 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 39854 atpsubN 39858 df-pointsN 39607 pointpsubN 39856 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 39609 pmap11 39867 pmaple 39866 pmapsub 39873 pmapval 39862 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 39870 pmap1N 39872 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 39875 pmapglb2N 39876 pmapglb2xN 39877 pmapglbx 39874 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 39957 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 39582 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 39901 paddclN 39947 paddidm 39946 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 39583 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 39943 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 39582 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 39583 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19593 lsmmod2 19594 lssats 39117 shatomici 32345 shatomistici 32348 shmodi 31377 shmodsi 31376 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32287 mdsymlem7 32396 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 31576 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31480 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32402 |
| [Margaris] p. 40 | Rule C | exlimiv 1931 |
| [Margaris] p. 49 | Axiom A1 | ax-1 6 |
| [Margaris] p. 49 | Axiom A2 | ax-2 7 |
| [Margaris] p. 49 | Axiom A3 | ax-3 8 |
| [Margaris] p. 49 | Definition | df-an 396 df-ex 1781 df-or 848 dfbi2 474 |
| [Margaris] p. 51 | Theorem 1 | idALT 23 |
| [Margaris] p. 56 | Theorem 3 | conventions 30387 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 45012 |
| [Margaris] p. 60 | Theorem 8 | jcn 162 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 45013 |
| [Margaris] p. 79 | Rule C | exinst01 44723 exinst11 44724 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1977 19.2g 2191 r19.2z 4444 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2205 rr19.3v 3617 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2162 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1827 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1782 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2184 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2208 19.9h 2288 exlimd 2221 exlimdh 2292 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2165 excomim 2166 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2328 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30388 conventions-labels 30388 conventions-labels 30388 conventions-labels 30388 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1828 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 44476 albi 1819 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2228 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2229 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 44478 exbi 1848 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2232 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 44475 2alimdv 1919 alimd 2215 alimdh 1818 alimdv 1917 ax-4 1810 ralimdaa 3233 ralimdv 3146 ralimdva 3144 ralimdvva 3179 sbcimdv 3805 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2210 19.21h 2289 19.21t 2209 19.21vv 44474 alrimd 2218 alrimdd 2217 alrimdh 1864 alrimdv 1930 alrimi 2216 alrimih 1825 alrimiv 1928 alrimivv 1929 hbralrimi 3122 r19.21be 3225 r19.21bi 3224 ralrimd 3237 ralrimdv 3130 ralrimdva 3132 ralrimdvv 3176 ralrimdvva 3187 ralrimi 3230 ralrimia 3231 ralrimiv 3123 ralrimiva 3124 ralrimivv 3173 ralrimivva 3175 ralrimivvva 3178 ralrimivw 3128 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 44477 2eximdv 1920 exim 1835 eximd 2219 eximdh 1865 eximdv 1918 rexim 3073 reximd2a 3242 reximdai 3234 reximdd 45250 reximddv 3148 reximddv2 3191 reximddv3 3149 reximdv 3147 reximdv2 3142 reximdva 3145 reximdvai 3143 reximdvva 3180 reximi2 3065 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2214 19.23bi 2194 19.23h 2290 19.23t 2213 exlimdv 1934 exlimdvv 1935 exlimexi 44622 exlimiv 1931 exlimivv 1933 rexlimd3 45246 rexlimdv 3131 rexlimdv3a 3137 rexlimdva 3133 rexlimdva2 3135 rexlimdvaa 3134 rexlimdvv 3188 rexlimdvva 3189 rexlimdvvva 3190 rexlimdvw 3138 rexlimiv 3126 rexlimiva 3125 rexlimivv 3174 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 1992 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1881 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1871 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2230 r19.27z 4454 r19.27zv 4455 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2231 19.28vv 44484 r19.28z 4447 r19.28zf 45261 r19.28zv 4450 rr19.28v 3618 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1874 r19.29d2r 3119 r19.29imd 3097 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1882 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2237 19.31vv 44482 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2236 r19.32 47203 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 44480 19.33 1885 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 1993 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1878 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2233 19.36vv 44481 r19.36zv 4456 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2235 19.37vv 44483 r19.37zv 4451 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1840 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 1991 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1888 19.40 1887 r19.40 3098 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2238 19.41rg 44648 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2239 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1883 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2240 r19.44zv 4453 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2241 r19.45zv 4452 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2605 |
| [Mayet] p. 370 | Remark | jpi 32257 largei 32254 stri 32244 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32199 ishst 32201 |
| [Mayet3] p. 10 | Theorem | hstrbi 32253 hstri 32252 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 31715 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 31716 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32265 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31319 chsupcl 31327 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32347 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32341 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32368 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 40088 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18399 latj32 18397 latjass 18395 |
| [Megill] p. 444 | Axiom C5 | ax-5 1911 ax5ALT 39012 |
| [Megill] p. 444 | Section 7 | conventions 30387 |
| [Megill] p. 445 | Lemma L12 | aecom-o 39006 ax-c11n 38993 axc11n 2426 |
| [Megill] p. 446 | Lemma L17 | equtrr 2023 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 39001 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 39033 hbnae 2432 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2481 sbid 2258 sbidd-misc 49825 sbidd 49824 |
| [Megill] p. 448 | Remark 9.6 | axc14 2463 |
| [Megill] p. 448 | Scheme C4' | ax-c4 38989 |
| [Megill] p. 448 | Scheme C5' | ax-c5 38988 sp 2186 |
| [Megill] p. 448 | Scheme C6' | ax-11 2160 |
| [Megill] p. 448 | Scheme C7' | ax-c7 38990 |
| [Megill] p. 448 | Scheme C8' | ax-7 2009 |
| [Megill] p. 448 | Scheme C9' | ax-c9 38995 |
| [Megill] p. 448 | Scheme C10' | ax-6 1968 ax-c10 38991 |
| [Megill] p. 448 | Scheme C11' | ax-c11 38992 |
| [Megill] p. 448 | Scheme C12' | ax-8 2113 |
| [Megill] p. 448 | Scheme C13' | ax-9 2121 |
| [Megill] p. 448 | Scheme C14' | ax-c14 38996 |
| [Megill] p. 448 | Scheme C15' | ax-c15 38994 |
| [Megill] p. 448 | Scheme C16' | ax-c16 38997 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 39009 dral1 2439 dral2-o 39035 dral2 2438 drex1 2441 drex2 2442 drsb1 2495 drsb2 2269 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2176 sbequ 2086 sbid2v 2509 |
| [Megill] p. 450 | Example in Appendix | hba1-o 39002 hba1 2295 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 46997 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 23 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3825 rspsbca 3826 stdpc4 2071 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 38989 ra4 3832 stdpc5 2211 |
| [Mendelson] p. 81 | Rule C | exlimiv 1931 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2029 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2253 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3734 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5457 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4347 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4348 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4226 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4283 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4227 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4090 |
| [Mendelson] p. 231 | Definition of union | dfun3 4225 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5394 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4855 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5510 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4567 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5511 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4882 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5771 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6222 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7714 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6318 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8516 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9059 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 8980 xpsneng 8981 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 8987 xpcomeng 8988 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 8990 |
| [Mendelson] p. 255 | Definition | brsdom 8903 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 8983 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8760 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 8965 mapsnend 8964 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9065 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9064 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8812 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 8968 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 8984 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10076 djucomen 10075 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10080 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10074 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8452 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8479 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10456 |
| [Mendelson] p. 281 | Definition | df-r1 9663 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9712 |
| [Mendelson] p. 287 | Axiom system MK | ru 3734 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30246 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30281 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30283 vdgn1frgrv3 30284 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30285 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30278 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30271 2pthfrgrrn 30269 2pthfrgrrn2 30270 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31239 |
| [Monk1] p. 22 | Remark | conventions 30387 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30387 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4188 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5727 ssrelf 32605 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5728 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5156 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6216 coi2 6217 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5865 rn0 5871 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 6094 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5637 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5874 rnxp 6123 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5718 xp0 5719 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6031 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6028 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7850 imaexg 7849 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6025 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7014 funfvop 6989 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6882 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6893 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6533 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7194 dff13f 7195 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7159 funrnex 7892 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7187 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6180 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4914 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 7944 df-1st 7927 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 7945 df-2nd 7928 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9753 ranksnb 9726 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9754 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9755 rankunb 9749 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9737 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9663 r1val2 9736 |
| [Monk1] p. 117 | Lemma | zorn2 10403 zorn2g 10400 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9885 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10458 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9880 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1810 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2009 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2180 ax-c15 38994 ax12v2 2182 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 38989 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2160 |
| [Monk2] p. 109 | Lemma 15 | equvini 2455 equvinv 2030 eqvinop 5430 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1911 ax5ALT 39012 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2144 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2160 |
| [Monk2] p. 114 | Lemma 21 | sp 2186 |
| [Monk2] p. 114 | Lemma 22 | axc4 2322 hba1-o 39002 hba1 2295 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2156 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2179 nfra2 3342 nfra2w 3268 |
| [Moore] p. 53 | Part I | df-mre 17494 |
| [Munkres] p. 77 | Example 2 | distop 22916 indistop 22923 indistopon 22922 |
| [Munkres] p. 77 | Example 3 | fctop 22925 fctop2 22926 |
| [Munkres] p. 77 | Example 4 | cctop 22927 |
| [Munkres] p. 78 | Definition of basis | df-bases 22867 isbasis3g 22870 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17353 tgval2 22877 |
| [Munkres] p. 79 | Remark | tgcl 22890 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 22884 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 22908 tgss3 22907 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 22909 basgen2 22910 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 37400 topdifinfeq 37401 topdifinffin 37399 topdifinfindis 37397 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23081 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 22959 topcld 22956 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 22960 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 22962 |
| [Munkres] p. 94 | Definition of closure | clsval 22958 |
| [Munkres] p. 94 | Definition of interior | ntrval 22957 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 22996 elcls 22994 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 23004 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23069 neindisj 23038 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23071 |
| [Munkres] p. 97 | Definition of limit point | islp2 23066 lpval 23060 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23236 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23148 iscn 23156 iscn2 23159 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23201 cncnp2 23202 cncnpi 23199 df-cnp 23149 iscnp 23158 iscnp2 23160 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24464 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25244 |
| [Nathanson] p. 123 | Remark | reprgt 34641 reprinfz1 34642 reprlt 34639 |
| [Nathanson] p. 123 | Definition | df-repr 34629 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 34661 |
| [Nathanson] p. 123 | Proposition | breprexp 34653 breprexpnat 34654 itgexpif 34626 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32091 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 47915 |
| [Pfenning] p. 17 | Definition XM | natded 30390 |
| [Pfenning] p. 17 | Definition NNC | natded 30390 notnotrd 133 |
| [Pfenning] p. 17 | Definition ` `C | natded 30390 |
| [Pfenning] p. 18 | Rule" | natded 30390 |
| [Pfenning] p. 18 | Definition /\I | natded 30390 |
| [Pfenning] p. 18 | Definition ` `E | natded 30390 natded 30390 natded 30390 natded 30390 natded 30390 |
| [Pfenning] p. 18 | Definition ` `I | natded 30390 natded 30390 natded 30390 natded 30390 natded 30390 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30390 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30390 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30390 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30390 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30390 |
| [Pfenning] p. 127 | Definition =E | natded 30390 |
| [Pfenning] p. 127 | Definition =I | natded 30390 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25135 df-dip 30688 dip0l 30705 ip0l 21579 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25176 ipval 30690 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 30701 ipcj 21577 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25138 dipdir 30829 ipdir 21582 ipdiri 30817 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 30697 nmsq 25127 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 30812 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 30814 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 30815 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25144 dipass 30832 ipass 21588 ipassi 30828 |
| [Prugovecki] p. 186 | Definition of bra | braval 31931 df-bra 31837 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 31838 kbval 31941 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32369 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 39993 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32383 atcvat4i 32384 cvrat3 39547 cvrat4 39548 lsatcvat3 39157 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32269 cvrval 39374 df-cv 32266 df-lcv 39124 lspsncv0 21089 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 40005 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 40006 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2710 rabid 3416 rabidd 45257 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2281 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2723 |
| [Quine] p. 19 | Definition 2.9 | conventions 30387 df-v 3438 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2870 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2867 abid2f 2925 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2278 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2088 sbalex 2245 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2806 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2731 eqid1 30454 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2738 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3737 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3738 dfsbcq2 3739 |
| [Quine] p. 43 | Theorem 6.8 | vex 3440 |
| [Quine] p. 43 | Theorem 6.9 | isset 3450 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3541 spcgv 3546 spcimgf 3503 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3749 spsbcd 3750 |
| [Quine] p. 44 | Theorem 6.12 | elex 3457 |
| [Quine] p. 44 | Theorem 6.13 | elab 3630 elabg 3627 elabgf 3625 |
| [Quine] p. 44 | Theorem 6.14 | noel 4287 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4669 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4578 df-sn 4576 |
| [Quine] p. 49 | Theorem 7.4 | snss 4736 snssg 4735 |
| [Quine] p. 49 | Theorem 7.5 | prss 4771 prssg 4770 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4714 prid1g 4712 prid2 4715 prid2g 4713 snid 4614 snidg 4612 |
| [Quine] p. 51 | Theorem 7.12 | snex 5376 |
| [Quine] p. 51 | Theorem 7.13 | prex 5377 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4877 unisnALT 45023 unisng 4876 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4881 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4889 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4886 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6457 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 47191 dfiota2 6444 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 47200 iotaval 6461 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6467 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6463 |
| [Quine] p. 58 | Definition 9.1 | df-op 4582 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5468 opabidw 5467 opelopab 5485 opelopaba 5479 opelopabaf 5487 opelopabf 5488 opelopabg 5481 opelopabga 5476 opelopabgf 5483 oprabid 7384 oprabidw 7383 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5625 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5627 |
| [Quine] p. 64 | Definition 9.15 | df-id 5514 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6552 |
| [Quine] p. 65 | Theorem 10.4 | funi 6519 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6540 funsng 6538 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6489 |
| [Quine] p. 65 | Definition 10.2 | args 6046 dffv4 6825 |
| [Quine] p. 68 | Definition 10.11 | conventions 30387 df-fv 6495 fv2 6823 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14185 nn0opth2i 14184 nn0opthi 14183 omopthi 8582 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8335 |
| [Quine] p. 232 | Equation i | carddom 10451 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6575 funimaexg 6574 |
| [Quine] p. 331 | Axiom system NF | ru 3734 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31071 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 30688 polid 31146 polid2i 31144 polidi 31145 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 30800 |
| [ReedSimon] p. 195 | Remark | lnophm 32006 lnophmi 32005 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32119 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32121 leopmuli 32120 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32124 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 31839 leoppos 32113 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32123 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32112 |
| [Roman] p. 4 | Definition | df-dmat 22411 df-dmatalt 48504 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20077 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20159 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 48591 |
| [Roman] p. 112 | Note | isldepslvec2 48591 ldepsnlinc 48614 zlmodzxznm 48603 |
| [Roman] p. 112 | Example | zlmodzxzequa 48602 zlmodzxzequap 48605 zlmodzxzldep 48610 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 22811 |
| [Rosenlicht] p. 80 | Theorem | heicant 37701 |
| [Rosser] p. 281 | Definition | df-op 4582 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 34665 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 34666 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 48471 pmtr3ncom 19393 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19389 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19332 cayleyth 19333 |
| [Rudin] p. 164 | Equation 27 | efcan 16009 |
| [Rudin] p. 164 | Equation 30 | efzval 16017 |
| [Rudin] p. 167 | Equation 48 | absefi 16111 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 197 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1772 |
| [Sanford] p. 39 | Rule 4 | mptxor 1770 |
| [Sanford] p. 40 | Rule 1 | mptnan 1769 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6067 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6070 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6066 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6064 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17494 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17495 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17495 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17497 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10034 |
| [Schechter] p. 141 | Definition (MC) | dfac11 43160 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10343 axdc3 10351 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20161 isrngo 37943 |
| [Schechter] p. 276 | Remark 11.6.e | span0 31529 |
| [Schechter] p. 276 | Definition of span | df-span 31296 spanval 31320 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 22914 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6337 onelord 43349 ordelon 6336 ordelord 6334 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 43350 sucidg 6395 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6367 onsuc 7749 ord0 6366 ordsuci 7747 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 43351 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5204 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 43126 elon2 6323 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6318 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5522 epelg 5520 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9491 epirron 43352 ordirr 6330 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 43354 oneptr 43353 ontr1 6359 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6355 oneptri 43355 ordtri3or 6344 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8422 ord0eln0 6368 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6381 onsucss 43364 trsucss 6402 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7754 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6408 ordnbtwn 6407 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 43366 ordnexbtwnsuc 43365 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10298 onsucf1lem 43367 onsucf1o 43370 onsucf1olem 43368 onsucrn 43369 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 43371 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7781 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 43360 ordne0gt0 43359 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 43362 limnsuc 43363 onsucelab 43361 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9539 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7796 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9542 ordom 7812 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9543 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8561 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7719 ssorduni 7718 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8452 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9546 limom 7818 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8391 df1o2 8398 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8437 oa0suclim 43373 oalim 8453 oasuc 8445 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8438 om0suclim 43374 omlim 8454 omsuc 8447 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8443 oe0m1 8442 oe0suclim 43375 oelim 8455 oesuc 8448 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 43327 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 43377 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 43378 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 43379 limexissupab 43381 limiun 43380 limuni 6374 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8459 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8463 om1om1r 43382 om1r 8464 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8456 oaomoecl 43376 oecl 8458 omcl 8457 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 43329 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8465 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8466 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 43383 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 43384 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8532 nnamecl 43385 nnecl 8534 nnmcl 8533 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 43386 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8473 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8474 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8481 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 43388 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 43389 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 43391 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8480 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 43395 omword1 8494 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 43394 oaordnrex 43393 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 43390 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 43396 omword2 8495 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 43397 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 43398 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 43399 omordi 8487 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8489 omord2com 43400 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 43401 df-2o 8392 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 43404 oewordi 8512 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 43405 oeworde 8514 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 43406 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 43407 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 43403 omnord1ex 43402 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 43408 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 43410 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 43414 oenord1ex 43413 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 43415 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8482 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 43409 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8500 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8501 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 43417 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8518 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 43418 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 43419 cantnfub2 43420 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 43423 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 28899 axtgcgrrflx 28446 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 28900 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 28901 axtgcgrid 28447 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28432 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 28912 axtgsegcon 28448 df-trkgcb 28434 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 28923 axtg5seg 28449 df-trkgcb 28434 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 28924 axtgbtwnid 28450 df-trkgb 28433 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 28926 axtgpasch 28451 df-trkgb 28433 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 28945 df-trkg2d 34685 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28454 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28455 df-trkg2d 34685 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 28948 axtgeucl 28456 df-trkge 28435 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 28961 axtgcont 28453 axtgcont1 28452 df-trkgb 28433 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 36038 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 36040 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 36043 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 36047 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 36048 tgcgrcomimp 28461 tgcgrcoml 28463 tgcgrcomr 28462 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 36053 tgcgrtriv 28468 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 36057 tg5segofs 34693 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 34690 df-ofs 36034 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 36059 tgcgrextend 28469 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 36061 tgsegconeq 28470 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36073 btwntriv2 36063 tgbtwntriv2 28471 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 36064 tgbtwncom 28472 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36067 tgbtwntriv1 28475 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36068 tgbtwnswapid 28476 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36074 btwnintr 36070 tgbtwnexch2 28480 tgbtwnintr 28477 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36076 btwnexch3 36071 tgbtwnexch 28482 tgbtwnexch3 28478 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36075 tgbtwnouttr 28481 tgbtwnouttr2 28479 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 28944 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36078 tgbtwndiff 28490 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28483 trisegint 36079 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36095 tgifscgr 28492 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28542 colrot1 28543 colrot2 28544 lncom 28606 lnrot1 28607 lnrot2 28608 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36091 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36096 tgcgrsub 28493 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36106 tgcgrxfr 28502 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28501 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36092 df-cgrg 28495 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28495 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36107 tgbtwnxfr 28514 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36113 colinearperm2 36115 colinearperm3 36114 colinearperm4 36116 colinearperm5 36117 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28517 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36090 tgellng 28537 tglng 28530 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36118 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36126 lnxfr 28550 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36127 lnext 28551 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36131 tgfscgr 28552 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36132 lncgr 28553 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36093 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36134 lnid 28554 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36135 tgidinside 28555 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36152 tgbtwnconn1 28559 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36153 tgbtwnconn2 28560 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36154 tgbtwnconn3 28561 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36160 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36158 legov 28569 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28570 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28583 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36161 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36163 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36165 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36166 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36167 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36164 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36169 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28571 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28573 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28574 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28575 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28576 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36176 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36177 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36172 df-outsideof 36171 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36173 ishlg 28586 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28591 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28593 outsideofrflx 36178 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28587 hlcomd 28588 outsideofcom 36179 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28594 outsideoftr 36180 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 28602 outsideofeu 36182 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36189 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36190 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36183 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36198 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36199 tglineelsb2 28616 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36201 linerflx1 36200 linerflx2 36202 tglinecom 28619 tglinerflx1 28617 tglinerflx2 28618 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36204 tglinethru 28620 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36188 tglng 28530 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28578 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36207 tglinethrueu 28623 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36208 tglineineq 28627 tglineinteq 28629 tglineintmo 28626 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28633 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28634 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 28635 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 28650 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 28646 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 28638 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 28637 ismir 28643 mirbtwn 28642 mircgr 28641 mirfv 28640 mirval 28639 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 28648 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 28649 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 28650 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 28653 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 28654 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 28659 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 28656 mirbtwni 28655 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 28657 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 28669 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 28673 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 28670 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 28671 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 28672 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 28675 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 28676 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 28682 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 28678 israg 28681 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 28683 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 28684 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 28686 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 28687 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 28688 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 28689 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 28690 ragncol 28693 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 28691 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 28697 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 28701 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 28698 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 28680 isperp 28696 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 28699 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 28706 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 28714 colperpexlem2 28715 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 28717 colperpexlem3 28716 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 28722 midex 28721 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 28719 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 28728 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 28723 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 28732 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 28735 opphllem6 28736 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 28738 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28451 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 28739 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 28747 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 28742 hpgbr 28744 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 28749 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 28748 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 28750 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 28751 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 28752 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 28753 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 28754 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 28768 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 28758 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 28772 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 28773 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 28774 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 28775 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 28776 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 28779 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 28781 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 28759 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 28782 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 28785 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 28786 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 28787 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 28788 trgcopyeu 28790 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 28814 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 28793 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 28802 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 28800 cgrahl2 28801 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 28803 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 28804 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 28806 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 28807 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 28810 cgrahl 28811 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 28815 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 28816 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 28817 acopyeu 28818 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 28825 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 28829 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 28822 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 28837 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 28830 isleag 28831 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 28839 tgsas1 28838 tgsas2 28840 tgsas3 28841 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 28843 tgasa1 28842 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 28844 tgsss2 28845 tgsss3 28846 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27215 dchrsum 27213 dchrsum2 27212 sumdchr 27216 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27217 sum2dchr 27218 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 19986 ablfacrp2 19987 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27160 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27161 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27168 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27426 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27429 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27483 vmalogdivsum2 27482 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27473 dirith2 27472 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27471 rpvmasum 27470 rpvmasum2 27456 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27431 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27469 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27436 dchrisumlem1 27433 dchrisumlem2 27434 dchrisumlem3 27435 dchrisumlema 27432 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27439 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27468 dchrmusumlem 27466 dchrvmasumlem 27467 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27438 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27440 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27464 dchrisum0re 27457 dchrisumn0 27465 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27450 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27454 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27455 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27510 pntrsumbnd2 27511 pntrsumo1 27509 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27474 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27476 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27478 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27481 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27486 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27487 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27492 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27494 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27495 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27503 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27504 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27501 selberg3lem2 27502 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27505 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27499 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27512 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27513 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27514 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27528 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27540 pntlemb 27541 pntlemc 27539 pntlemd 27538 pntlemg 27542 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27540 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27532 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27537 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27540 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27553 pntleml 27555 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 33763 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 33750 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 33782 constrinvcl 33793 constrmulcl 33791 constrnegcl 33783 constrsqrtcl 33799 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 33769 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 33779 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 33801 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 33811 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4255 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4354 dif0 4327 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4441 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4424 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4246 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4247 |
| [Stoll] p. 20 | Remark | invdif 4228 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4584 |
| [Stoll] p. 43 | Definition | uniiun 5009 |
| [Stoll] p. 44 | Definition | intiin 5010 |
| [Stoll] p. 45 | Definition | df-iin 4944 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4943 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 401 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4255 |
| [Strang] p. 242 | Section 6.3 | expgrowth 44433 |
| [Suppes] p. 22 | Theorem 2 | eq0 4299 eq0f 4296 |
| [Suppes] p. 22 | Theorem 4 | eqss 3945 eqssd 3947 eqssi 3946 |
| [Suppes] p. 23 | Theorem 5 | ss0 4351 ss0b 4350 |
| [Suppes] p. 23 | Theorem 6 | sstr 3938 sstrALT2 44932 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4052 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4053 |
| [Suppes] p. 23 | Theorem 9 | psstr 4056 |
| [Suppes] p. 23 | Theorem 10 | pssss 4047 |
| [Suppes] p. 25 | Theorem 12 | elin 3913 elun 4102 |
| [Suppes] p. 26 | Theorem 15 | inidm 4176 |
| [Suppes] p. 26 | Theorem 16 | in0 4344 |
| [Suppes] p. 27 | Theorem 23 | unidm 4106 |
| [Suppes] p. 27 | Theorem 24 | un0 4343 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4127 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4135 |
| [Suppes] p. 27 | Theorem 27 | unss 4139 |
| [Suppes] p. 27 | Theorem 28 | indir 4235 |
| [Suppes] p. 27 | Theorem 29 | undir 4236 |
| [Suppes] p. 28 | Theorem 32 | difid 4325 |
| [Suppes] p. 29 | Theorem 33 | difin 4221 |
| [Suppes] p. 29 | Theorem 34 | indif 4229 |
| [Suppes] p. 29 | Theorem 35 | undif1 4425 |
| [Suppes] p. 29 | Theorem 36 | difun2 4430 |
| [Suppes] p. 29 | Theorem 37 | difin0 4423 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4421 |
| [Suppes] p. 29 | Theorem 39 | difundi 4239 |
| [Suppes] p. 29 | Theorem 40 | difindi 4241 |
| [Suppes] p. 30 | Theorem 41 | nalset 5253 |
| [Suppes] p. 39 | Theorem 61 | uniss 4866 |
| [Suppes] p. 39 | Theorem 65 | uniop 5458 |
| [Suppes] p. 41 | Theorem 70 | intsn 4934 |
| [Suppes] p. 42 | Theorem 71 | intpr 4932 intprg 4931 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5414 |
| [Suppes] p. 42 | Theorem 78 | intun 4930 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4982 dfiun2g 4980 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4983 |
| [Suppes] p. 47 | Theorem 86 | elpw 4553 elpw2 5274 elpw2g 5273 elpwg 4552 elpwgdedVD 45014 |
| [Suppes] p. 47 | Theorem 87 | pwid 4571 |
| [Suppes] p. 47 | Theorem 89 | pw0 4763 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4764 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5634 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5778 xpindir 5779 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5688 xpundir 5689 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9489 |
| [Suppes] p. 58 | Theorem 2 | relss 5726 |
| [Suppes] p. 59 | Theorem 4 | eldm 5845 eldm2 5846 eldm2g 5844 eldmg 5843 |
| [Suppes] p. 59 | Definition 3 | df-dm 5629 |
| [Suppes] p. 60 | Theorem 6 | dmin 5856 |
| [Suppes] p. 60 | Theorem 8 | rnun 6098 |
| [Suppes] p. 60 | Theorem 9 | rnin 6099 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5833 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5827 brcnvg 5824 |
| [Suppes] p. 62 | Equation 5 | elcnv 5821 elcnv2 5822 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6058 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6097 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6095 |
| [Suppes] p. 63 | Definition | dftrrels2 38677 |
| [Suppes] p. 63 | Theorem 20 | co02 6214 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5919 |
| [Suppes] p. 63 | Definition 7 | df-co 5628 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5830 |
| [Suppes] p. 64 | Theorem 27 | coass 6219 |
| [Suppes] p. 65 | Theorem 31 | resundi 5947 |
| [Suppes] p. 65 | Theorem 34 | elima 6019 elima2 6020 elima3 6021 elimag 6018 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6102 |
| [Suppes] p. 66 | Theorem 40 | dminss 6106 |
| [Suppes] p. 66 | Theorem 41 | imainss 6107 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6110 |
| [Suppes] p. 81 | Definition 34 | dfec2 8631 |
| [Suppes] p. 82 | Theorem 72 | elec 8674 elecALTV 38309 elecg 8672 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 38713 erth 8682 erth2 8683 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 38716 erdisj 8685 |
| [Suppes] p. 83 | Definition 35, | df-parts 38869 dfmembpart2 38874 |
| [Suppes] p. 89 | Theorem 96 | map0b 8813 |
| [Suppes] p. 89 | Theorem 97 | map0 8817 map0g 8814 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8818 mapsnd 8816 |
| [Suppes] p. 89 | Theorem 99 | mapss 8819 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 9965 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 9964 |
| [Suppes] p. 92 | Theorem 1 | enref 8913 enrefg 8912 |
| [Suppes] p. 92 | Theorem 2 | ensym 8931 ensymb 8930 ensymi 8932 |
| [Suppes] p. 92 | Theorem 3 | entr 8934 |
| [Suppes] p. 92 | Theorem 4 | unen 8973 |
| [Suppes] p. 94 | Theorem 15 | endom 8907 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 8928 |
| [Suppes] p. 94 | Theorem 17 | domtr 8935 |
| [Suppes] p. 95 | Theorem 18 | sbth 9016 |
| [Suppes] p. 97 | Theorem 23 | canth2 9049 canth2g 9050 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9020 df-sdom 8878 dfsdom2 9019 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9033 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9022 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9021 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9031 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8910 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9034 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9029 |
| [Suppes] p. 98 | Exercise 4 | fundmen 8959 fundmeng 8960 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 8994 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9030 |
| [Suppes] p. 104 | Theorem 37 | fofi 9203 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9209 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9209 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10448 |
| [Suppes] p. 130 | Definition 3 | df-tr 5201 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7719 |
| [Suppes] p. 134 | Definition 6 | df-suc 6318 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7836 finds 7832 finds1 7835 finds2 7834 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9548 isfinite2 9188 isfiniteg 9190 unbnn 9186 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10815 df-ltpq 10807 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7799 tfinds 7796 tfinds2 7800 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8472 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8474 |
| [Suppes] p. 211 | Theorem 25 | oaass 8482 |
| [Suppes] p. 225 | Definition 8 | iscard2 9875 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10460 |
| [Suppes] p. 228 | Theorem 59 | harcard 9877 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 9963 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6364 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7732 onminsb 7733 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10469 |
| [Suppes] p. 229 | Theorem 65 | alephcard 9967 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 9974 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 9968 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9839 |
| [Suppes] p. 242 | Theorem 6 | weth 10392 |
| [Suppes] p. 242 | Theorem 8 | entric 10454 |
| [Suppes] p. 242 | Theorem 9 | carden 10448 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 35747 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 35751 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2703 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2723 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2806 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2725 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2751 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7356 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3734 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5361 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4600 elpr2 4602 elpr2g 4601 elprg 4598 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4590 elsn2 4617 elsn2g 4616 elsng 4589 velsn 4591 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5410 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4585 sneqr 4791 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4596 dfsn2 4588 dfsn2ALT 4597 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7680 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5419 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5407 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5391 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7683 unexg 7682 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4643 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4859 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3904 df-un 3902 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4875 uniprg 4874 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5317 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4641 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6384 elsucg 6382 sstr2 3936 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4107 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4158 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4121 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4177 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4233 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4234 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3917 df-ss 3914 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4551 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4136 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3915 sseqin2 4172 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3952 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4186 inss2 4187 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 3994 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4869 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5392 sspwimp 45015 sspwimpALT 45022 sspwimpALT2 45025 sspwimpcf 45017 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5399 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5219 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3396 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5247 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3900 |
| [TakeutiZaring] p. 20 | Definition 5.14 | dfnul2 4285 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4325 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4302 n0f 4298 neq0 4301 neq0f 4297 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9488 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9628 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9643 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3438 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5255 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4349 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5261 ssexg 5263 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5257 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9497 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9491 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4315 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4084 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4249 undif3VD 44979 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4085 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4092 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3048 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3057 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7692 xpexg 7689 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5626 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6558 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6734 fun11 6561 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6500 svrelfun 6559 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5832 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5834 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5631 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5632 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5628 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6147 dfrel2 6142 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5635 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5755 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5763 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5776 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 5959 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5939 opelresi 5941 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 5966 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5955 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 5960 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6529 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6062 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6527 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6736 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2604 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30387 df-fv 6495 fv3 6846 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7861 cnvexg 7860 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7845 dmexg 7837 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7846 rnexg 7838 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 44551 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7856 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6841 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 47279 tz6.12-1-afv2 47346 tz6.12-1 6851 tz6.12-afv 47278 tz6.12-afv2 47345 tz6.12 6852 tz6.12c-afv2 47347 tz6.12c 6850 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 47342 tz6.12-2 6815 tz6.12i-afv2 47348 tz6.12i 6854 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6490 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6491 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6493 wfo 6485 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6492 wf1 6484 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6494 wf1o 6486 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 6970 eqfnfv2 6971 eqfnfv2f 6974 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6926 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7157 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7155 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6575 funimaexg 6574 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5094 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5528 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5580 dffr3 6053 eliniseg 6048 iniseg 6051 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5519 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5596 fr3nr 7711 frirr 5595 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5572 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7713 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5583 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5605 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6300 tz6.26i 6301 wefrc 5613 wereu2 5616 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6302 wfii 6303 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6496 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7269 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7270 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7276 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7277 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7278 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7282 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7289 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7291 |
| [TakeutiZaring] p. 35 | Notation | wtr 5200 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 44552 tz7.2 5602 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5205 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6325 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6333 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6334 ordelordALT 44635 ordelordALTVD 44964 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6340 ordelssne 6339 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6338 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6342 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7721 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7722 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6316 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6344 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 44647 ordon 7716 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7717 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7789 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6360 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5202 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7731 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7767 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6418 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6417 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7718 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4889 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6318 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6394 sucidg 6395 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7749 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6408 ordnbtwn 6407 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7764 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6317 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7817 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7822 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7777 ordelsuc 7756 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7758 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7787 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7804 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7825 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7826 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7827 |
| [TakeutiZaring] p. 43 | Remark | omon 7814 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9531 omex 9539 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7812 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7831 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7828 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7829 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7807 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4912 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5218 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4913 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5284 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7734 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6363 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4898 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9556 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7729 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8301 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8322 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8323 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8324 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8331 tz7.44-2 8332 tz7.44-3 8333 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8293 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8288 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8272 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8370 tz7.49c 8371 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8368 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8367 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8369 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2651 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 9908 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 9909 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8453 oasuc 8445 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7797 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8456 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8437 oa0r 8459 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8457 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8469 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8540 nnaordi 8539 oaord 8468 oaordi 8467 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5000 uniss2 4892 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8471 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8476 oawordex 8478 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8532 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8569 |
| [TakeutiZaring] p. 60 | Remark | oancom 9547 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8481 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8537 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8473 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8440 omlim 8454 omsuc 8447 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8438 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8534 nnmcl 8533 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8553 nnmordi 8552 omord 8489 omordi 8487 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8490 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8557 omwordri 8493 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8460 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8463 om1r 8464 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8496 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8498 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8499 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8500 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8501 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8529 oe0 8443 oelim 8455 oesuc 8448 onesuc 8451 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8441 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8507 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8508 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8442 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8466 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8509 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8515 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8513 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8514 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8518 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8520 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9624 tz9.1 9625 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9663 r10 9667 r1lim 9671 r1limg 9670 r1suc 9669 r1sucg 9668 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9679 r1ord2 9680 r1ordg 9677 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9689 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9714 tz9.13 9690 tz9.13g 9691 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9664 rankval 9715 rankvalb 9696 rankvalg 9716 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9738 rankelb 9723 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9752 rankval3 9739 rankval3b 9725 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9728 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9694 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9733 rankr1c 9720 rankr1g 9731 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9734 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9748 rankssb 9747 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9741 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9740 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10372 dfac3 10018 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 9927 numth 10369 numth2 10368 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10443 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10444 cardid2 9852 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9859 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10448 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9858 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9843 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9864 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9856 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9069 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 8946 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9074 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 8998 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9862 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 9995 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9121 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9129 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 9996 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9126 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 9985 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 9963 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9871 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10113 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9213 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8879 isfi 8904 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9130 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10431 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 8991 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10423 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10083 unxpdom 9149 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9873 cardsdomelir 9872 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9151 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 9911 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8758 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10459 infxpidm2 9914 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10104 infxp 10111 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9003 pw2f1o 9001 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9062 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10384 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10379 ac6s5 10388 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10440 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10441 uniimadomf 10442 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10171 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10166 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10151 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10148 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10154 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10161 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10170 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10479 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10149 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10173 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 9994 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 9993 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10005 alephfp2 10006 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10596 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10009 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10466 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10480 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10481 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 38988 |
| [Tarski] p. 67 | Scheme B5 | sp 2186 |
| [Tarski] p. 68 | Lemma 6 | avril1 30450 equid 2013 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2018 |
| [Tarski] p. 70 | Lemma 14 | spim 2387 spime 2389 spimew 1972 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2180 ax-c15 38994 ax12i 1967 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2088 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1969 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1911 ax5ALT 39012 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2009 ax-8 2113 ax-9 2121 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28448 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28449 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28451 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28451 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28452 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16158 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 37705 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 37707 |
| [Weierstrass] p. 272 | Definition | df-mdet 22506 mdetuni 22543 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 903 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 868 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 869 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 919 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 969 |
| [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 37496 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 43898 imim2 58 wl-luk-imim2 37491 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 47124 imim1 83 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 896 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2658 syl 17 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 902 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 22 wl-luk-id 37494 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 894 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 142 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 897 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 130 notnotrALT2 45024 wl-luk-notnotr 37495 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 146 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 43928 axfrege28 43927 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 867 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 924 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 123 wl-luk-pm2.21 37488 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 124 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 889 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 941 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 30388 pm2.27 42 wl-luk-pm2.27 37486 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 922 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 38401 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 923 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 971 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 972 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 970 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1087 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 906 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 907 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 944 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 56 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 881 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 882 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5 169 pm2.5g 168 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6 191 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 883 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 884 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 885 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 172 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 851 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 852 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 888 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 890 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 192 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 899 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 942 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 943 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 193 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 891 pm2.67 892 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 176 pm2.521g 174 pm2.521g2 175 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 898 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 974 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 900 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 203 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 975 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 976 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 933 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 931 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 973 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 977 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 84 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 932 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 109 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 993 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 469 pm3.2im 160 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 994 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 995 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 996 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 997 |
| [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 | pm3.35 802 |
| [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) | pm3.33 764 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 765 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 807 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 622 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 809 |
| [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 962 pm3.44 961 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 808 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 473 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 965 |
| [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 | pm4.14 806 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 832 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 222 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 805 bitr 804 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 563 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 904 pm4.25 905 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 460 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1009 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 870 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 468 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 921 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 633 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 917 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 637 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 978 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1088 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1007 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1053 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1024 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 998 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 1000 pm4.45 999 pm4.45im 827 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 984 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 853 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 545 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 983 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 986 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 987 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 988 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 989 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 985 pm4.56 990 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 991 pm4.57 992 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 404 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 856 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 397 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 849 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 405 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 850 |
| [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 | pm4.72 951 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 527 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 936 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 517 pm4.76 518 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 963 pm4.77 964 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 934 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1005 |
| [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 1025 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1026 |
| [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 pm4.87 843 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 823 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 946 pm5.11g 945 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 947 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 949 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 948 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1014 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1015 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1013 |
| [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 | pm5.21 824 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1016 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1049 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1050 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 901 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 572 |
| [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 1003 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 955 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 830 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 573 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 835 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 825 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 833 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 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 1006 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1019 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 950 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1002 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1020 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1021 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1029 |
| [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 1030 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 44456 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 44457 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1871 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 44458 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 44459 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 44460 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1894 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 44461 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 44462 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 44463 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 44464 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 44465 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 44467 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 44468 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 44469 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 44466 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2093 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 44472 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 44473 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2073 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2163 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1830 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1831 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 44474 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 44475 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 44476 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 44477 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 44479 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 44478 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1888 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 44481 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 44482 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 44480 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1829 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 44483 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 44484 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1847 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 44485 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2346 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1861 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 44490 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 44486 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 44487 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 44488 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 44489 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 44494 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 44491 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 44492 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 44493 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 44495 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2564 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 44505 pm13.13b 44506 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 44507 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3009 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3010 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3616 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 44513 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 44514 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 44508 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 44650 pm13.193 44509 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 44510 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 44511 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 44512 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 44519 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 44518 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 44517 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3799 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 44520 pm14.122b 44521 pm14.122c 44522 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 44523 pm14.123b 44524 pm14.123c 44525 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 44527 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 44526 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 44528 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6468 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 44529 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6469 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 44530 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 44532 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2628 eupickbi 2631 sbaniota 44533 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 44531 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2579 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 44534 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30387 df-fv 6495 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 9900 pm54.43lem 9899 |
| [Young] p. 141 | Definition of operator ordering | leop2 32111 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32117 idleop 32118 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 42926 |
| [vandenDries] p. 43 | Theorem 62 | pellex 42933 pellexlem1 42927 |