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 17760 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17760 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18169 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17781 0funcg 50013 df-termc 50401 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 50478 prsthinc 50392 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 50506 df-mndtc 50506 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 50502 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17804 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 50494 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 50519 oppgoppchom 50518 oppgoppcid 50520 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17874 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17862 invisoinvl 17883 |
| [Adamek] p. 28 | Example 3.13 | idinv 17882 idiso 17881 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17867 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17841 df-iso 17842 dfiso2 17865 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17848 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17899 cicerALT 49974 |
| [Adamek] p. 29 | Definition 3.15 | cic 17892 df-cic 17889 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17951 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17863 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17864 isoco 17870 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17951 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17974 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 50232 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17967 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 50502 discthing 50389 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 50346 prsthinc 50392 thincciso 50381 thincciso2 50383 thincciso3 50384 thinccisod 50382 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 50506 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17981 cofucla 50024 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 50090 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18204 catcisoi 50328 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18259 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 18000 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17999 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18259 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 18024 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 18030 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 18029 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18244 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18244 |
| [Adamek] p. 39 | Remark 3.42 | 2oppf 50060 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 50051 funcoppc 17968 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18192 elcatchom 50325 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 18018 fthoppf 50092 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 18017 fulloppf 50091 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18201 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 50013 df-catc 18192 |
| [Adamek] p. 45 | Exercise 3G | incat 50529 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 50532 nelsubc3 49999 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 50079 imasubc2 50080 imasubc3 50084 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17931 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17932 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 49999 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17943 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17905 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 50088 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 50087 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 50089 ressffth 18033 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 50530 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 18039 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 18060 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 18064 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 18040 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 18066 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 50013 df-inito 18077 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 50013 df-termc 50401 initc 50019 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21696 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 18078 oppctermo 50164 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 18105 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 18109 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 50165 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 18079 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21697 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 18112 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17840 |
| [Adamek] p. 107 | Example 7.20(7) | thincinv 50397 |
| [Adamek] p. 108 | Example 7.25(4) | thincsect2 50396 |
| [Adamek] p. 110 | Example 7.33(9) | thincmon 50361 |
| [Adamek] p. 110 | Proposition 7.35 | sectmon 17875 |
| [Adamek] p. 112 | Proposition 7.42 | sectepi 17877 |
| [Adamek] p. 185 | Section 10.67 | updjud 9942 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 50573 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 50573 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 50573 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 50574 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 50574 |
| [Adamek] p. 478 | Item Rng | df-ringc 20812 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 49480 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 49502 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14638 df-pfx 14743 df-substr 14711 df-word 14581 lencl 14600 wrd0 14606 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24938 df-nmoo 31227 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32635 hmopidmchi 32633 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32683 pjcmul2i 32684 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 32400 unoplin 32402 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 32401 unopadj2 32420 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 32495 lnopunii 32494 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32568 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 28193 |
| [Alling] p. 184 | Axiom B | bdayfo 27914 |
| [Alling] p. 184 | Axiom O | ltsso 27913 |
| [Alling] p. 184 | Axiom SD | nodense 27929 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 28021 |
| [Alling] p. 185 | Theorem | conway 28045 |
| [Alling] p. 185 | Axiom FE | noeta 27980 |
| [Alling] p. 186 | Theorem 4 | lesrec 28065 lesrecd 28066 |
| [Alling], p. 2 | Definition | rp-brsslt 44265 |
| [Alling], p. 3 | Note | nla0001 44268 nla0002 44266 nla0003 44267 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11421 addcan2d 11441 addcan2i 11431 addcand 11440 addcani 11430 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11474 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11533 negsubd 11602 negsubi 11563 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11535 negnegd 11587 negnegi 11555 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11674 subdid 11697 subdii 11690 subdir 11675 subdird 11698 subdiri 11691 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11416 mul01d 11436 mul01i 11427 mul02 11415 mul02d 11435 mul02i 11426 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11878 mulcan2d 11875 mulcand 11874 mulcani 11880 |
| [Apostol] p. 18 | Theorem I.8 | receu 11886 xreceu 33369 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11915 divrecd 12021 divreci 11987 divreczi 11980 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11939 recreci 11974 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11881 mul0ord 11889 mul0ori 11888 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11680 mul2negd 11696 mul2negi 11689 mulneg1 11677 mulneg1d 11694 mulneg1i 11687 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11957 divadddivd 12062 divadddivi 12004 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11942 divmuldivd 12059 divmuldivi 12002 rdivmuldivd 20558 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11943 divdivdivd 12065 divdivdivi 12005 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 13068 rpaddcld 13103 rpmulcl 13069 rpmulcld 13104 |
| [Apostol] p. 20 | Axiom 8 | rpneg 13078 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 13081 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11363 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11834 ltadd1dd 11852 ltadd1i 11795 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12092 ltmul1a 12091 ltmul1i 12160 ltmul1ii 12170 ltmul2 12093 ltmul2d 13130 ltmul2dd 13144 ltmul2i 12163 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11761 msqgt0d 11808 msqgt0i 11778 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11763 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11747 lt0neg1d 11810 ltneg 11741 ltnegd 11819 ltnegi 11785 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11726 lt2addd 11864 lt2addi 11803 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 13045 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12088 recgt0d 12176 recgt0i 12147 recgt0ii 12148 |
| [Apostol] p. 22 | Definition of integers | df-z 12619 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12274 |
| [Apostol] p. 22 | Definition of rationals | df-q 13001 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9427 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12527 |
| [Apostol] p. 26 | Theorem I.29 | arch 12528 archd 45996 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12727 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12529 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12999 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12998 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13253 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16433 zneo 12707 zneoALTV 48587 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26968 msqsqrtd 15532 resqrtth 15344 sqrtth 15454 sqrtthi 15460 sqsqrtd 15531 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12263 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12965 |
| [Apostol] p. 361 | Remark | crreczi 14294 |
| [Apostol] p. 363 | Remark | absgt0i 15489 |
| [Apostol] p. 363 | Example | abssubd 15545 abssubi 15493 |
| [ApostolNT] p. 7 | Remark | fmtno0 48445 fmtno1 48446 fmtno2 48455 fmtno3 48456 fmtno4 48457 fmtno5fac 48487 fmtnofz04prm 48482 |
| [ApostolNT] p. 7 | Definition | df-fmtno 48433 |
| [ApostolNT] p. 8 | Definition | df-ppi 27337 |
| [ApostolNT] p. 14 | Definition | df-dvds 16347 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16363 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16388 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16383 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16376 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16378 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16364 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16365 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16370 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16405 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16407 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16409 |
| [ApostolNT] p. 15 | Definition | df-gcd 16589 dfgcd2 16640 |
| [ApostolNT] p. 16 | Definition | isprm2 16776 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16747 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 17011 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16607 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16641 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16643 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16622 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16614 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16806 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16808 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 17024 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 17018 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16497 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16681 |
| [ApostolNT] p. 24 | Definition | df-mu 27338 |
| [ApostolNT] p. 25 | Definition | df-phi 16861 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27428 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16886 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16871 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16875 |
| [ApostolNT] p. 32 | Definition | df-vma 27335 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27430 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27453 |
| [ApostolNT] p. 38 | Remark | df-sgm 27339 |
| [ApostolNT] p. 38 | Definition | df-sgm 27339 |
| [ApostolNT] p. 75 | Definition | df-chp 27336 df-cht 27334 |
| [ApostolNT] p. 104 | Definition | congr 16758 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16350 |
| [ApostolNT] p. 106 | Definition | moddvds 16357 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16440 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16441 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13951 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13991 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14304 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16382 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16761 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17170 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16763 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16878 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16897 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16879 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27309 |
| [ApostolNT] p. 179 | Definition | df-lgs 27532 lgsprme0 27576 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27577 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27553 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27568 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27625 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27644 2lgsoddprm 27653 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27611 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27620 |
| [ApostolNT] p. 188 | Definition | df-lgs 27532 lgs1 27578 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27569 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27571 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27579 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27580 |
| [Baer] p. 40 | Property (b) | mapdord 42513 |
| [Baer] p. 40 | Property (c) | mapd11 42514 |
| [Baer] p. 40 | Property (e) | mapdin 42537 mapdlsm 42539 |
| [Baer] p. 40 | Property (f) | mapd0 42540 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 42500 mapd1o 42523 |
| [Baer] p. 41 | Property (g) | mapdat 42542 |
| [Baer] p. 44 | Part (1) | mapdpg 42581 |
| [Baer] p. 45 | Part (2) | hdmap1eq 42676 mapdheq 42603 mapdheq2 42604 mapdheq2biN 42605 |
| [Baer] p. 45 | Part (3) | baerlem3 42588 |
| [Baer] p. 46 | Part (4) | mapdheq4 42607 mapdheq4lem 42606 |
| [Baer] p. 46 | Part (5) | baerlem5a 42589 baerlem5abmN 42593 baerlem5amN 42591 baerlem5b 42590 baerlem5bmN 42592 |
| [Baer] p. 47 | Part (6) | hdmap1l6 42696 hdmap1l6a 42684 hdmap1l6e 42689 hdmap1l6f 42690 hdmap1l6g 42691 hdmap1l6lem1 42682 hdmap1l6lem2 42683 mapdh6N 42622 mapdh6aN 42610 mapdh6eN 42615 mapdh6fN 42616 mapdh6gN 42617 mapdh6lem1N 42608 mapdh6lem2N 42609 |
| [Baer] p. 48 | Part 9 | hdmapval 42703 |
| [Baer] p. 48 | Part 10 | hdmap10 42715 |
| [Baer] p. 48 | Part 11 | hdmapadd 42718 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 42692 mapdh6hN 42618 |
| [Baer] p. 48 | Part (7) | mapdh75cN 42628 mapdh75d 42629 mapdh75e 42627 mapdh75fN 42630 mapdh7cN 42624 mapdh7dN 42625 mapdh7eN 42623 mapdh7fN 42626 |
| [Baer] p. 48 | Part (8) | mapdh8 42663 mapdh8a 42650 mapdh8aa 42651 mapdh8ab 42652 mapdh8ac 42653 mapdh8ad 42654 mapdh8b 42655 mapdh8c 42656 mapdh8d 42658 mapdh8d0N 42657 mapdh8e 42659 mapdh8g 42660 mapdh8i 42661 mapdh8j 42662 |
| [Baer] p. 48 | Part (9) | mapdh9a 42664 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 42644 |
| [Baer] p. 49 | Part 12 | hdmap11 42723 hdmapeq0 42719 hdmapf1oN 42740 hdmapneg 42721 hdmaprnN 42739 hdmaprnlem1N 42724 hdmaprnlem3N 42725 hdmaprnlem3uN 42726 hdmaprnlem4N 42728 hdmaprnlem6N 42729 hdmaprnlem7N 42730 hdmaprnlem8N 42731 hdmaprnlem9N 42732 hdmapsub 42722 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 42743 hdmap14lem10 42752 hdmap14lem1a 42741 hdmap14lem2N 42744 hdmap14lem2a 42742 hdmap14lem3 42745 hdmap14lem8 42750 hdmap14lem9 42751 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 42753 hdmap14lem12 42754 hdmap14lem13 42755 hdmap14lem14 42756 hdmap14lem15 42757 hgmapval 42762 |
| [Baer] p. 50 | Part 15 | hgmapadd 42769 hgmapmul 42770 hgmaprnlem2N 42772 hgmapvs 42766 |
| [Baer] p. 50 | Part 16 | hgmaprnN 42776 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 42792 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 42793 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 42794 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 42795 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 42797 hgmapvv 42801 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 42796 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 42798 |
| [Baer] p. 111 | Line 15 | hdmapg 42805 hdmapglem7 42804 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26969 2irrexpqALT 27038 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 24 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2596 |
| [BellMachover] p. 460 | Notation | df-mo 2566 |
| [BellMachover] p. 460 | Definition | mo3 2591 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2734 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2738 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5244 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5255 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37810 sepex 5261 |
| [BellMachover] p. 466 | Problem | axpow2 5336 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5337 |
| [BellMachover] p. 466 | Axiom Union | axun2 7741 |
| [BellMachover] p. 468 | Definition | df-ord 6364 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6379 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6386 onelond 36781 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6381 |
| [BellMachover] p. 471 | Definition of N | df-om 7866 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7803 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6366 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9624 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7881 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9749 |
| [BellMachover] p. 478 | Definition | rankval2 9803 rankval2b 35608 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9767 r1ord3g 9764 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9571 |
| [BellMachover] p. 488 | Axiom AC | ac5 10482 dfac4 10128 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10116 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 40194 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32835 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32877 chirredi 32876 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32865 |
| [Beran] p. 3 | Definition of join | sshjval3 31836 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 32098 cmcm2i 32075 cmcm2ii 32080 cmt2N 40125 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 32099 lecmi 32084 lecmii 32085 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 32073 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 32102 cm2ji 32107 cm2mi 32108 |
| [Beran] p. 95 | Definition | df-sh 31689 issh2 31691 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31568 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31581 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31572 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 32310 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 32312 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 32311 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 32313 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31564 his1i 31582 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31565 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31566 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31567 |
| [Beran] p. 96 | Definition of norm | df-hnorm 31450 dfhnorm2 31604 normval 31606 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31666 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 31455 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31723 |
| [Beran] p. 96 | Definition of converge | df-hlim 31454 hlimi 31670 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31615 norm-i 31611 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31619 norm-ii 31620 normlem0 31591 normlem1 31592 normlem2 31593 normlem3 31594 normlem4 31595 normlem5 31596 normlem6 31597 normlem7 31598 normlem7tALT 31601 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31621 norm-iii 31622 |
| [Beran] p. 98 | Remark 3.4 | bcs 31663 bcsiALT 31661 bcsiHIL 31662 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31603 normpar 31637 normpari 31636 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31628 normpyth 31627 normpythi 31624 |
| [Beran] p. 99 | Remark | lnfn0 32529 lnfn0i 32524 lnop0 32448 lnop0i 32452 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32508 nmcfnex 32535 nmcfnexi 32533 nmcopex 32511 nmcopexi 32509 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32536 nmcfnlbi 32534 nmcoplb 32512 nmcoplbi 32510 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32538 lnfnconi 32537 lnopcon 32517 lnopconi 32516 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31638 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31635 norm3adifii 31630 norm3dif 31632 norm3difi 31629 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31783 pjhth 31875 pjhtheu 31876 pjpjhth 31907 pjpjhthi 31908 pjth 25671 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31888 ococi 31887 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32543 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32544 riesz4 32546 riesz4i 32545 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32561 cnlnadjeu 32560 cnlnadjeui 32559 cnlnadji 32558 cnlnadjlem1 32549 nmopadjlei 32570 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32573 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32572 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32574 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 32418 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32584 nmopcoadji 32583 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32575 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32585 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32582 pjadj2coi 32686 pjadjcoi 32643 |
| [Beran] p. 107 | Definition | df-ch 31703 isch2 31705 |
| [Beran] p. 107 | Remark 3.12 | choccl 31788 isch3 31723 occl 31786 ocsh 31765 shoccl 31787 shocsh 31766 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31890 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31814 |
| [Beran] p. 109 | Property (i) | pjadj2 32669 pjadj3 32670 pjadji 32167 pjadjii 32156 |
| [Beran] p. 109 | Property (ii) | pjidmco 32663 pjidmcoi 32659 pjidmi 32155 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32655 |
| [Beran] p. 111 | Remark | ho0val 32232 pjch1 32152 |
| [Beran] p. 111 | Definition | df-hfmul 32216 df-hfsum 32215 df-hodif 32214 df-homul 32213 df-hosum 32212 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 32153 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 32176 pjchi 31914 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31921 pjoc2i 31920 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 32162 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32647 pjssmii 32163 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32646 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32645 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32650 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32648 pjssge0ii 32164 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32649 pjdifnormii 32165 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1809 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1807 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1810 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1805 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34805 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34813 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34811 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34815 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34835 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34866 df-sitm 34844 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34866 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34843 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29506 isuhgrop 29528 isusgrop 29623 isuspgrop 29622 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 48779 df-subgr 29729 uhgrspan1 29764 uhgrspansubgr 29752 |
| [Bollobas] p. 3 | Definition | df-gric 48799 gricuspgr 48836 isuspgrim 48814 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29915 df-clnbgr 48737 df-cusgr 29873 df-nbgr 29794 fusgrmaxsize 29925 |
| [Bollobas] p. 4 | Definition | df-upwlks 49052 df-wlks 30060 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 30011 finsumvtxdgeven 30013 fusgr1th 30012 fusgrvtxdgonume 30015 vtxdgoddnumeven 30014 |
| [Bollobas] p. 5 | Notation | df-pths 30179 |
| [Bollobas] p. 5 | Definition | df-crcts 30253 df-cycls 30254 df-trls 30155 df-wlkson 30061 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29517 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 49117 df-cllaw 49103 df-mgm 18734 df-mgm2 49136 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 49118 df-asslaw 49105 df-sgrp 18825 df-sgrp2 49138 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 49137 df-comlaw 49104 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18841 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33468 mndlactf1o 33472 mndractf1 33470 mndractf1o 33473 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20378 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20292 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 34145 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 34149 assarrginv 34148 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 34190 fldextrspunfld 34188 fldextrspunlem1 34187 fldextrspunlem2 34189 fldextrspunlsp 34186 fldextrspunlsplem 34185 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 33949 dfufd2 33962 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7291 fcofo 7292 |
| [BourbakiTop1] p. | Remark | xnegmnf 13264 xnegpnf 13263 |
| [BourbakiTop1] p. | Remark | rexneg 13265 |
| [BourbakiTop1] p. | Remark 3 | ust0 24450 ustfilxp 24443 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24320 |
| [BourbakiTop1] p. | Criterion | ishmeo 23989 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24513 iducn 24512 snfil 24094 |
| [BourbakiTop1] p. | Example 2 | neifil 24110 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 24297 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24533 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 34469 |
| [BourbakiTop1] p. | Paragraph 3 | infil 24093 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24505 df-ust 24431 filintn0 24091 filn0 24092 istgp 24307 ucnprima 24511 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24516 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24527 df-usp 24487 df-utop 24461 trust 24459 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 34368 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23345 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23498 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24436 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24439 |
| [BourbakiTop1] p. | Property V_ii | innei 23354 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23362 neissex 23356 |
| [BourbakiTop1] p. | Proposition 1 | neips 23342 neiss 23338 ucncn 24514 ustund 24452 ustuqtop 24476 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23496 neiptopreu 23362 utop2nei 24480 utop3cls 24481 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24521 uspreg 24503 utopreg 24482 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23921 imasncls 23922 imasnopn 23920 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 24230 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24438 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24440 |
| [BourbakiTop1] p. | Property V_iii | elnei 23340 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24532 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24437 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24441 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23616 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 24076 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 23123 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 34365 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 46892 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 46894 stoweid 46893 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 46831 stoweidlem10 46840 stoweidlem14 46844 stoweidlem15 46845 stoweidlem35 46865 stoweidlem36 46866 stoweidlem37 46867 stoweidlem38 46868 stoweidlem40 46870 stoweidlem41 46871 stoweidlem43 46873 stoweidlem44 46874 stoweidlem46 46876 stoweidlem5 46835 stoweidlem50 46880 stoweidlem52 46882 stoweidlem53 46883 stoweidlem55 46885 stoweidlem56 46886 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 46853 stoweidlem24 46854 stoweidlem27 46857 stoweidlem28 46858 stoweidlem30 46860 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 46864 stoweidlem59 46889 stoweidlem60 46890 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 46875 stoweidlem49 46879 stoweidlem7 46837 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 46861 stoweidlem39 46869 stoweidlem42 46872 stoweidlem48 46878 stoweidlem51 46881 stoweidlem54 46884 stoweidlem57 46887 stoweidlem58 46888 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 46855 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 46847 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 46841 stoweidlem13 46843 stoweidlem26 46856 stoweidlem61 46891 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 46848 |
| [Bruck] p. 1 | Section I.1 | df-clintop 49117 df-mgm 18734 df-mgm2 49136 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18825 df-sgrp2 49138 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 19166 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5191 |
| [Church] p. 129 | Section II.24 | df-ifp 1079 dfifp2 1080 |
| [Clemente] p. 10 | Definition IT | natded 30884 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30884 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30884 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30884 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30884 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30884 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30884 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30884 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30884 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30884 |
| [Clemente] p. 14 | Proof 5.11 | natded 30884 |
| [Clemente] p. 14 | Definition E` `n | natded 30884 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30886 ex-natded5.2 30885 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30889 ex-natded5.3 30888 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30891 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30893 ex-natded5.7 30892 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30895 ex-natded5.8 30894 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30897 ex-natded5.13 30896 |
| [Clemente] p. 32 | Definition I` `n | natded 30884 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30884 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30884 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30884 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30898 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30899 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30901 ex-natded9.26 30900 |
| [Cohen] p. 301 | Remark | relogoprlem 26829 |
| [Cohen] p. 301 | Property 2 | relogmul 26830 relogmuld 26863 |
| [Cohen] p. 301 | Property 3 | relogdiv 26831 relogdivd 26864 |
| [Cohen] p. 301 | Property 4 | relogexp 26834 |
| [Cohen] p. 301 | Property 1a | log1 26823 |
| [Cohen] p. 301 | Property 1b | loge 26824 |
| [Cohen4] p. 348 | Observation | relogbcxpb 27025 |
| [Cohen4] p. 349 | Property | relogbf 27029 |
| [Cohen4] p. 352 | Definition | elogb 27008 |
| [Cohen4] p. 361 | Property 2 | relogbmul 27015 |
| [Cohen4] p. 361 | Property 3 | logbrec 27020 relogbdiv 27017 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 27013 |
| [Cohen4] p. 361 | Property 6 | relogbexp 27018 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 27006 |
| [Cohen4] p. 361 | Property 1(b) | logb1 27007 |
| [Cohen4] p. 367 | Property | logbchbase 27009 |
| [Cohen4] p. 377 | Property 2 | logblt 27022 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34798 sxbrsigalem4 34800 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18649 acsinfd 18648 acsinfdimd 18650 acsmap2d 18647 acsmapd 18646 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34803 |
| [Connell] p. 57 | Definition | df-scmat 22717 df-scmatalt 49331 |
| [Conway] p. 4 | Definition | lesrec 28065 lesrecd 28066 |
| [Conway] p. 5 | Definition | addsval 28228 addsval2 28229 df-adds 28226 df-muls 28373 df-negs 28287 |
| [Conway] p. 7 | Theorem | 0lt1s 28078 |
| [Conway] p. 12 | Theorem 12 | pw2cut2 28728 |
| [Conway] p. 16 | Theorem 0(i) | sltsright 28127 |
| [Conway] p. 16 | Theorem 0(ii) | sltsleft 28126 |
| [Conway] p. 16 | Theorem 0(iii) | lesid 28004 |
| [Conway] p. 17 | Theorem 3 | addsass 28271 addsassd 28272 addscom 28232 addscomd 28233 addsrid 28230 addsridd 28231 |
| [Conway] p. 17 | Definition | df-0s 28073 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 28310 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 28307 negsidd 28308 |
| [Conway] p. 18 | Theorem 5 | leadds1 28255 leadds1d 28261 |
| [Conway] p. 18 | Definition | df-1s 28074 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 28302 negscld 28303 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 28246 |
| [Conway] p. 19 | Note | mulsunif2 28436 |
| [Conway] p. 19 | Theorem 7 | addsdi 28421 addsdid 28422 addsdird 28423 mulnegs1d 28426 mulnegs2d 28427 mulsass 28432 mulsassd 28433 mulscom 28405 mulscomd 28406 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28400 mulscld 28401 |
| [Conway] p. 19 | Theorem 8(iii) | lemulsd 28404 ltmuls 28402 ltmulsd 28403 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28410 mulsgt0d 28411 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28484 |
| [Conway] p. 23 | Theorem 11 | eqcuts3 28070 |
| [Conway] p. 24 | Definition | df-reno 28756 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28765 remulscl 28768 renegscl 28764 |
| [Conway] p. 27 | Definition | df-ons 28518 elons2 28524 |
| [Conway] p. 27 | Theorem 14 | ltonsex 28528 |
| [Conway] p. 28 | Theorem 15 | oncutlt 28530 onswe 28538 |
| [Conway] p. 29 | Remark | madebday 28166 newbday 28168 oldbday 28167 |
| [Conway] p. 29 | Definition | df-made 28093 df-new 28095 df-old 28094 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13924 |
| [Crawley] p. 1 | Definition of poset | df-poset 18405 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 40261 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 41065 dalaw 40761 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 42836 |
| [Crawley] p. 111 | Definition of set W | df-watsN 40865 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 40981 df-ldil 40979 isldil 40985 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 40980 df-trnN 40982 isltrn 40994 ltrnu 40996 |
| [Crawley] p. 112 | Lemma A | cdlema1N 40666 cdlema2N 40667 exatleN 40279 |
| [Crawley] p. 112 | Lemma B | 1cvrat 40351 cdlemb 40669 cdlemb2 40916 cdlemb3 41481 idltrn 41025 l1cvat 39930 lhpat 40918 lhpat2 40920 lshpat 39931 ltrnel 41014 ltrnmw 41026 |
| [Crawley] p. 112 | Lemma C | cdlemc1 41066 cdlemc2 41067 ltrnnidn 41049 trlat 41044 trljat1 41041 trljat2 41042 trljat3 41043 trlne 41060 trlnidat 41048 trlnle 41061 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 40866 |
| [Crawley] p. 113 | Lemma C | cdlemc 41072 cdlemc3 41068 cdlemc4 41069 |
| [Crawley] p. 113 | Lemma D | cdlemd 41082 cdlemd1 41073 cdlemd2 41074 cdlemd3 41075 cdlemd4 41076 cdlemd5 41077 cdlemd6 41078 cdlemd7 41079 cdlemd8 41080 cdlemd9 41081 cdleme31sde 41260 cdleme31se 41257 cdleme31se2 41258 cdleme31snd 41261 cdleme32a 41316 cdleme32b 41317 cdleme32c 41318 cdleme32d 41319 cdleme32e 41320 cdleme32f 41321 cdleme32fva 41312 cdleme32fva1 41313 cdleme32fvcl 41315 cdleme32le 41322 cdleme48fv 41374 cdleme4gfv 41382 cdleme50eq 41416 cdleme50f 41417 cdleme50f1 41418 cdleme50f1o 41421 cdleme50laut 41422 cdleme50ldil 41423 cdleme50lebi 41415 cdleme50rn 41420 cdleme50rnlem 41419 cdlemeg49le 41386 cdlemeg49lebilem 41414 |
| [Crawley] p. 113 | Lemma E | cdleme 41435 cdleme00a 41084 cdleme01N 41096 cdleme02N 41097 cdleme0a 41086 cdleme0aa 41085 cdleme0b 41087 cdleme0c 41088 cdleme0cp 41089 cdleme0cq 41090 cdleme0dN 41091 cdleme0e 41092 cdleme0ex1N 41098 cdleme0ex2N 41099 cdleme0fN 41093 cdleme0gN 41094 cdleme0moN 41100 cdleme1 41102 cdleme10 41129 cdleme10tN 41133 cdleme11 41145 cdleme11a 41135 cdleme11c 41136 cdleme11dN 41137 cdleme11e 41138 cdleme11fN 41139 cdleme11g 41140 cdleme11h 41141 cdleme11j 41142 cdleme11k 41143 cdleme11l 41144 cdleme12 41146 cdleme13 41147 cdleme14 41148 cdleme15 41153 cdleme15a 41149 cdleme15b 41150 cdleme15c 41151 cdleme15d 41152 cdleme16 41160 cdleme16aN 41134 cdleme16b 41154 cdleme16c 41155 cdleme16d 41156 cdleme16e 41157 cdleme16f 41158 cdleme16g 41159 cdleme19a 41178 cdleme19b 41179 cdleme19c 41180 cdleme19d 41181 cdleme19e 41182 cdleme19f 41183 cdleme1b 41101 cdleme2 41103 cdleme20aN 41184 cdleme20bN 41185 cdleme20c 41186 cdleme20d 41187 cdleme20e 41188 cdleme20f 41189 cdleme20g 41190 cdleme20h 41191 cdleme20i 41192 cdleme20j 41193 cdleme20k 41194 cdleme20l 41197 cdleme20l1 41195 cdleme20l2 41196 cdleme20m 41198 cdleme20y 41177 cdleme20zN 41176 cdleme21 41212 cdleme21d 41205 cdleme21e 41206 cdleme22a 41215 cdleme22aa 41214 cdleme22b 41216 cdleme22cN 41217 cdleme22d 41218 cdleme22e 41219 cdleme22eALTN 41220 cdleme22f 41221 cdleme22f2 41222 cdleme22g 41223 cdleme23a 41224 cdleme23b 41225 cdleme23c 41226 cdleme26e 41234 cdleme26eALTN 41236 cdleme26ee 41235 cdleme26f 41238 cdleme26f2 41240 cdleme26f2ALTN 41239 cdleme26fALTN 41237 cdleme27N 41244 cdleme27a 41242 cdleme27cl 41241 cdleme28c 41247 cdleme3 41112 cdleme30a 41253 cdleme31fv 41265 cdleme31fv1 41266 cdleme31fv1s 41267 cdleme31fv2 41268 cdleme31id 41269 cdleme31sc 41259 cdleme31sdnN 41262 cdleme31sn 41255 cdleme31sn1 41256 cdleme31sn1c 41263 cdleme31sn2 41264 cdleme31so 41254 cdleme35a 41323 cdleme35b 41325 cdleme35c 41326 cdleme35d 41327 cdleme35e 41328 cdleme35f 41329 cdleme35fnpq 41324 cdleme35g 41330 cdleme35h 41331 cdleme35h2 41332 cdleme35sn2aw 41333 cdleme35sn3a 41334 cdleme36a 41335 cdleme36m 41336 cdleme37m 41337 cdleme38m 41338 cdleme38n 41339 cdleme39a 41340 cdleme39n 41341 cdleme3b 41104 cdleme3c 41105 cdleme3d 41106 cdleme3e 41107 cdleme3fN 41108 cdleme3fa 41111 cdleme3g 41109 cdleme3h 41110 cdleme4 41113 cdleme40m 41342 cdleme40n 41343 cdleme40v 41344 cdleme40w 41345 cdleme41fva11 41352 cdleme41sn3aw 41349 cdleme41sn4aw 41350 cdleme41snaw 41351 cdleme42a 41346 cdleme42b 41353 cdleme42c 41347 cdleme42d 41348 cdleme42e 41354 cdleme42f 41355 cdleme42g 41356 cdleme42h 41357 cdleme42i 41358 cdleme42k 41359 cdleme42ke 41360 cdleme42keg 41361 cdleme42mN 41362 cdleme42mgN 41363 cdleme43aN 41364 cdleme43bN 41365 cdleme43cN 41366 cdleme43dN 41367 cdleme5 41115 cdleme50ex 41434 cdleme50ltrn 41432 cdleme51finvN 41431 cdleme51finvfvN 41430 cdleme51finvtrN 41433 cdleme6 41116 cdleme7 41124 cdleme7a 41118 cdleme7aa 41117 cdleme7b 41119 cdleme7c 41120 cdleme7d 41121 cdleme7e 41122 cdleme7ga 41123 cdleme8 41125 cdleme8tN 41130 cdleme9 41128 cdleme9a 41126 cdleme9b 41127 cdleme9tN 41132 cdleme9taN 41131 cdlemeda 41173 cdlemedb 41172 cdlemednpq 41174 cdlemednuN 41175 cdlemefr27cl 41278 cdlemefr32fva1 41285 cdlemefr32fvaN 41284 cdlemefrs32fva 41275 cdlemefrs32fva1 41276 cdlemefs27cl 41288 cdlemefs32fva1 41298 cdlemefs32fvaN 41297 cdlemesner 41171 cdlemeulpq 41095 |
| [Crawley] p. 114 | Lemma E | 4atex 40951 4atexlem7 40950 cdleme0nex 41165 cdleme17a 41161 cdleme17c 41163 cdleme17d 41373 cdleme17d1 41164 cdleme17d2 41370 cdleme18a 41166 cdleme18b 41167 cdleme18c 41168 cdleme18d 41170 cdleme4a 41114 |
| [Crawley] p. 115 | Lemma E | cdleme21a 41200 cdleme21at 41203 cdleme21b 41201 cdleme21c 41202 cdleme21ct 41204 cdleme21f 41207 cdleme21g 41208 cdleme21h 41209 cdleme21i 41210 cdleme22gb 41169 |
| [Crawley] p. 116 | Lemma F | cdlemf 41438 cdlemf1 41436 cdlemf2 41437 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 41442 cdlemg16 41532 cdlemg28 41579 cdlemg28a 41568 cdlemg28b 41578 cdlemg3a 41472 cdlemg42 41604 cdlemg43 41605 cdlemg44 41608 cdlemg44a 41606 cdlemg46 41610 cdlemg47 41611 cdlemg9 41509 ltrnco 41594 ltrncom 41613 tgrpabl 41626 trlco 41602 |
| [Crawley] p. 116 | Definition of G | df-tgrp 41618 |
| [Crawley] p. 117 | Lemma G | cdlemg17 41552 cdlemg17b 41537 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 41631 df-edring 41632 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 41635 |
| [Crawley] p. 118 | Remark | tendopltp 41655 |
| [Crawley] p. 118 | Lemma H | cdlemh 41692 cdlemh1 41690 cdlemh2 41691 |
| [Crawley] p. 118 | Lemma I | cdlemi 41695 cdlemi1 41693 cdlemi2 41694 |
| [Crawley] p. 118 | Lemma J | cdlemj1 41696 cdlemj2 41697 cdlemj3 41698 tendocan 41699 |
| [Crawley] p. 118 | Lemma K | cdlemk 41849 cdlemk1 41706 cdlemk10 41718 cdlemk11 41724 cdlemk11t 41821 cdlemk11ta 41804 cdlemk11tb 41806 cdlemk11tc 41820 cdlemk11u-2N 41764 cdlemk11u 41746 cdlemk12 41725 cdlemk12u-2N 41765 cdlemk12u 41747 cdlemk13-2N 41751 cdlemk13 41727 cdlemk14-2N 41753 cdlemk14 41729 cdlemk15-2N 41754 cdlemk15 41730 cdlemk16-2N 41755 cdlemk16 41732 cdlemk16a 41731 cdlemk17-2N 41756 cdlemk17 41733 cdlemk18-2N 41761 cdlemk18-3N 41775 cdlemk18 41743 cdlemk19-2N 41762 cdlemk19 41744 cdlemk19u 41845 cdlemk1u 41734 cdlemk2 41707 cdlemk20-2N 41767 cdlemk20 41749 cdlemk21-2N 41766 cdlemk21N 41748 cdlemk22-3 41776 cdlemk22 41768 cdlemk23-3 41777 cdlemk24-3 41778 cdlemk25-3 41779 cdlemk26-3 41781 cdlemk26b-3 41780 cdlemk27-3 41782 cdlemk28-3 41783 cdlemk29-3 41786 cdlemk3 41708 cdlemk30 41769 cdlemk31 41771 cdlemk32 41772 cdlemk33N 41784 cdlemk34 41785 cdlemk35 41787 cdlemk36 41788 cdlemk37 41789 cdlemk38 41790 cdlemk39 41791 cdlemk39u 41843 cdlemk4 41709 cdlemk41 41795 cdlemk42 41816 cdlemk42yN 41819 cdlemk43N 41838 cdlemk45 41822 cdlemk46 41823 cdlemk47 41824 cdlemk48 41825 cdlemk49 41826 cdlemk5 41711 cdlemk50 41827 cdlemk51 41828 cdlemk52 41829 cdlemk53 41832 cdlemk54 41833 cdlemk55 41836 cdlemk55u 41841 cdlemk56 41846 cdlemk5a 41710 cdlemk5auN 41735 cdlemk5u 41736 cdlemk6 41712 cdlemk6u 41737 cdlemk7 41723 cdlemk7u-2N 41763 cdlemk7u 41745 cdlemk8 41713 cdlemk9 41714 cdlemk9bN 41715 cdlemki 41716 cdlemkid 41811 cdlemkj-2N 41757 cdlemkj 41738 cdlemksat 41721 cdlemksel 41720 cdlemksv 41719 cdlemksv2 41722 cdlemkuat 41741 cdlemkuel-2N 41759 cdlemkuel-3 41773 cdlemkuel 41740 cdlemkuv-2N 41758 cdlemkuv2-2 41760 cdlemkuv2-3N 41774 cdlemkuv2 41742 cdlemkuvN 41739 cdlemkvcl 41717 cdlemky 41801 cdlemkyyN 41837 tendoex 41850 |
| [Crawley] p. 120 | Remark | dva1dim 41860 |
| [Crawley] p. 120 | Lemma L | cdleml1N 41851 cdleml2N 41852 cdleml3N 41853 cdleml4N 41854 cdleml5N 41855 cdleml6 41856 cdleml7 41857 cdleml8 41858 cdleml9 41859 dia1dim 41936 |
| [Crawley] p. 120 | Lemma M | dia11N 41923 diaf11N 41924 dialss 41921 diaord 41922 dibf11N 42036 djajN 42012 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 41907 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 41993 dia2dimlem1 41939 dia2dimlem2 41940 dia2dimlem3 41941 dia2dimlem4 41942 dia2dimlem5 41943 diaf1oN 42005 diarnN 42004 dvheveccl 41987 dvhopN 41991 |
| [Crawley] p. 121 | Lemma N | cdlemn 42087 cdlemn10 42081 cdlemn11 42086 cdlemn11a 42082 cdlemn11b 42083 cdlemn11c 42084 cdlemn11pre 42085 cdlemn2 42070 cdlemn2a 42071 cdlemn3 42072 cdlemn4 42073 cdlemn4a 42074 cdlemn5 42076 cdlemn5pre 42075 cdlemn6 42077 cdlemn7 42078 cdlemn8 42079 cdlemn9 42080 diclspsn 42069 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 42048 |
| [Crawley] p. 122 | Lemma N | dih11 42140 dihf11 42142 dihjust 42092 dihjustlem 42091 dihord 42139 dihord1 42093 dihord10 42098 dihord11b 42097 dihord11c 42099 dihord2 42102 dihord2a 42094 dihord2b 42095 dihord2cN 42096 dihord2pre 42100 dihord2pre2 42101 dihordlem6 42088 dihordlem7 42089 dihordlem7b 42090 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 42105 dihfval 42106 dihval 42107 |
| [Diestel] p. 3 | Definition | df-gric 48799 df-grim 48796 isuspgrim 48814 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29873 df-nbgr 29794 |
| [Diestel] p. 3 | Definition by | df-grisom 48795 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 48779 df-subgr 29729 uhgrspan1 29764 uhgrspansubgr 29752 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 30015 vtxdgoddnumeven 30014 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29517 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 34376 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 34388 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 34380 zarcls1 34381 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 34391 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 34394 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 34397 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3905 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9629 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8831 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9637 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9988 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10566 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5266 |
| [Enderton] p. 19 | Definition | df-tp 4592 |
| [Enderton] p. 26 | Exercise 5 | unissb 4904 |
| [Enderton] p. 26 | Exercise 10 | pwel 5350 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5552 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5043 iinin2 5042 iinun2 5035 iunin1 5034 iunin1f 33032 iunin2 5033 uniin1 5037 uniin2 5038 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5041 iundif2 5036 |
| [Enderton] p. 32 | Exercise 20 | unineq 4237 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5062 |
| [Enderton] p. 33 | Exercise 25 | iununi 5063 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5070 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7773 iunpwss 5071 |
| [Enderton] p. 36 | Definition | opthwiener 5495 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5429 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4909 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5450 rnex 7910 rnexg 7902 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5902 rnuni 6144 |
| [Enderton] p. 42 | Definition of a function | dffun7 6564 dffun8 6565 |
| [Enderton] p. 43 | Definition of function value | funfv2 6970 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6606 |
| [Enderton] p. 44 | Definition (d) | dfima2 6062 dfima3 6063 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6979 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10478 ac7g 10479 df-ac 10122 dfac2 10137 dfac2a 10135 dfac2b 10136 dfac3 10127 dfac7 10138 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7246 |
| [Enderton] p. 52 | Definition | df-map 8831 |
| [Enderton] p. 53 | Exercise 21 | coass 6266 |
| [Enderton] p. 53 | Exercise 27 | dmco 6255 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6613 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6102 |
| [Enderton] p. 54 | Remark | ixpf 8930 ixpssmap 8942 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8908 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10488 ac9s 10498 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 39444 erref 8720 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 39447 erthi 8756 |
| [Enderton] p. 57 | Definition | df-ec 8701 |
| [Enderton] p. 58 | Definition | df-qs 8705 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8701 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5898 |
| [Enderton] p. 68 | Definition of successor | df-suc 6367 |
| [Enderton] p. 71 | Definition | df-tr 5217 dftr4 5222 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6443 unisucg 6442 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6443 unisucg 6442 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5232 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5234 trintALT 45705 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8595 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8597 onasuc 8518 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7419 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8596 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8598 onmsuc 8519 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8613 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8600 nnacom 8608 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8614 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8615 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8617 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8601 nnmsucr 8616 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8629 |
| [Enderton] p. 129 | Definition | df-en 8956 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7370 |
| [Enderton] p. 133 | Exercise 1 | xpomen 10021 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16305 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9204 |
| [Enderton] p. 135 | Corollary 6C | php3 9206 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9203 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9235 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9237 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9166 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9170 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9142 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10185 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10186 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10181 dju1en 10177 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9313 unifi 9314 unifi2 9315 |
| [Enderton] p. 144 | Corollary 6K | undif2 4434 unfi 9168 unfi2 9283 |
| [Enderton] p. 145 | Figure 38 | ffoss 7946 |
| [Enderton] p. 145 | Definition | df-dom 8957 |
| [Enderton] p. 146 | Example 1 | domen 8970 domeng 8971 |
| [Enderton] p. 146 | Example 3 | nndomo 9215 nnsdom 9636 nnsdomg 9272 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10189 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9143 xpdom1 9077 xpdom1g 9075 xpdom2g 9074 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9149 |
| [Enderton] p. 151 | Theorem 6M | zorn 10512 zorng 10509 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10497 dfac5 10134 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10587 |
| [Enderton] p. 164 | Example | infdif 10213 |
| [Enderton] p. 168 | Definition | df-po 5567 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6477 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6409 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6476 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6417 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7838 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7783 |
| [Enderton] p. 194 | Remark | onprc 7780 |
| [Enderton] p. 194 | Exercise 16 | suc11 6471 |
| [Enderton] p. 197 | Definition | df-card 9947 |
| [Enderton] p. 197 | Theorem 7P | carden 10562 |
| [Enderton] p. 200 | Exercise 25 | tfis 7854 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9761 |
| [Enderton] p. 202 | Definition | df-r1 9749 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9771 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9852 rankval4b 35609 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9588 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9842 rankprb 9836 rankpw 9828 rankpwi 9808 rankuniss 9851 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9600 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9601 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10116 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 10082 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10096 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8333 |
| [Enderton] p. 222 | Definition | df-kard 35678 |
| [Enderton] p. 222 | Definition of kard | karden 9901 kardex 9899 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8588 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8590 |
| [Enderton] p. 240 | Exercise 25 | oarec 8552 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10254 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17734 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17676 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18645 mrieqv2d 17731 mrieqvd 17730 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17735 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17740 mreexexlem2d 17737 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18651 mreexfidimd 17742 |
| [Frege1879] p. 11 | Statement | df3or2 44610 |
| [Frege1879] p. 12 | Statement | df3an2 44611 dfxor4 44608 dfxor5 44609 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 44632 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 44633 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 44637 |
| [Frege1879] p. 31 | Proposition 4 | frege4 44641 |
| [Frege1879] p. 32 | Proposition 5 | frege5 44642 |
| [Frege1879] p. 33 | Proposition 6 | frege6 44648 |
| [Frege1879] p. 34 | Proposition 7 | frege7 44650 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 44651 axfrege8 44649 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 91 wl-luk-pm2.04 38201 |
| [Frege1879] p. 35 | Proposition 9 | frege9 44654 |
| [Frege1879] p. 36 | Proposition 10 | frege10 44662 |
| [Frege1879] p. 36 | Proposition 11 | frege11 44656 |
| [Frege1879] p. 37 | Proposition 12 | frege12 44655 |
| [Frege1879] p. 37 | Proposition 13 | frege13 44664 |
| [Frege1879] p. 37 | Proposition 14 | frege14 44665 |
| [Frege1879] p. 38 | Proposition 15 | frege15 44668 |
| [Frege1879] p. 38 | Proposition 16 | frege16 44658 |
| [Frege1879] p. 39 | Proposition 17 | frege17 44663 |
| [Frege1879] p. 39 | Proposition 18 | frege18 44660 |
| [Frege1879] p. 39 | Proposition 19 | frege19 44666 |
| [Frege1879] p. 40 | Proposition 20 | frege20 44670 |
| [Frege1879] p. 40 | Proposition 21 | frege21 44669 |
| [Frege1879] p. 41 | Proposition 22 | frege22 44661 |
| [Frege1879] p. 42 | Proposition 23 | frege23 44667 |
| [Frege1879] p. 42 | Proposition 24 | frege24 44657 |
| [Frege1879] p. 42 | Proposition 25 | frege25 44659 rp-frege25 44647 |
| [Frege1879] p. 42 | Proposition 26 | frege26 44652 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 44672 |
| [Frege1879] p. 43 | Proposition 27 | frege27 44653 |
| [Frege1879] p. 43 | Proposition 28 | con3 154 |
| [Frege1879] p. 43 | Proposition 29 | frege29 44673 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 44676 axfrege31 44675 |
| [Frege1879] p. 44 | Proposition 30 | frege30 44674 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 131 |
| [Frege1879] p. 44 | Proposition 32 | frege32 44677 |
| [Frege1879] p. 44 | Proposition 33 | frege33 44678 |
| [Frege1879] p. 45 | Proposition 34 | frege34 44679 |
| [Frege1879] p. 45 | Proposition 35 | frege35 44680 |
| [Frege1879] p. 45 | Proposition 36 | frege36 44681 |
| [Frege1879] p. 46 | Proposition 37 | frege37 44682 |
| [Frege1879] p. 46 | Proposition 38 | frege38 44683 |
| [Frege1879] p. 46 | Proposition 39 | frege39 44684 |
| [Frege1879] p. 46 | Proposition 40 | frege40 44685 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 44687 axfrege41 44686 |
| [Frege1879] p. 47 | Proposition 41 | notnot 143 |
| [Frege1879] p. 47 | Proposition 42 | frege42 44688 |
| [Frege1879] p. 47 | Proposition 43 | frege43 44689 |
| [Frege1879] p. 47 | Proposition 44 | frege44 44690 |
| [Frege1879] p. 47 | Proposition 45 | frege45 44691 |
| [Frege1879] p. 48 | Proposition 46 | frege46 44692 |
| [Frege1879] p. 48 | Proposition 47 | frege47 44693 |
| [Frege1879] p. 49 | Proposition 48 | frege48 44694 |
| [Frege1879] p. 49 | Proposition 49 | frege49 44695 |
| [Frege1879] p. 49 | Proposition 50 | frege50 44696 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 44699 ax-frege52c 44730 frege52aid 44700 frege52b 44731 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 44704 ax-frege54c 44734 frege54b 44735 |
| [Frege1879] p. 50 | Proposition 51 | frege51 44697 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3744 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 44702 frege53aid 44701 frege53b 44732 frege53c 44756 |
| [Frege1879] p. 50 | Proposition 54 | biid 264 eqid 2762 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 44710 frege55aid 44707 frege55b 44739 frege55c 44760 frege55cor1a 44711 frege55lem2a 44709 frege55lem2b 44738 frege55lem2c 44759 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 44713 frege56aid 44712 frege56b 44740 frege56c 44761 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 44717 ax-frege58b 44743 frege58bid 44744 frege58c 44763 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 44715 frege57aid 44714 frege57b 44741 frege57c 44762 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3755 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 44719 frege59b 44746 frege59c 44764 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 44720 frege60b 44747 frege60c 44765 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 44721 frege61b 44748 frege61c 44766 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 44722 frege62b 44749 frege62c 44767 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 44723 frege63b 44750 frege63c 44768 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 44724 frege64b 44751 frege64c 44769 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 44725 frege65b 44752 frege65c 44770 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 44726 frege66b 44753 frege66c 44771 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 44727 frege67b 44754 frege67c 44772 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 44728 frege68b 44755 frege68c 44773 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 44774 |
| [Frege1879] p. 58 | Proposition 70 | frege70 44775 |
| [Frege1879] p. 59 | Proposition 71 | frege71 44776 |
| [Frege1879] p. 59 | Proposition 72 | frege72 44777 |
| [Frege1879] p. 59 | Proposition 73 | frege73 44778 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 44781 |
| [Frege1879] p. 60 | Proposition 74 | frege74 44779 |
| [Frege1879] p. 60 | Proposition 75 | frege75 44780 |
| [Frege1879] p. 62 | Proposition 77 | frege77 44782 frege77d 44588 |
| [Frege1879] p. 63 | Proposition 78 | frege78 44783 |
| [Frege1879] p. 63 | Proposition 79 | frege79 44784 |
| [Frege1879] p. 63 | Proposition 80 | frege80 44785 |
| [Frege1879] p. 63 | Proposition 81 | frege81 44786 frege81d 44589 |
| [Frege1879] p. 64 | Proposition 82 | frege82 44787 |
| [Frege1879] p. 65 | Proposition 83 | frege83 44788 frege83d 44590 |
| [Frege1879] p. 65 | Proposition 84 | frege84 44789 |
| [Frege1879] p. 66 | Proposition 85 | frege85 44790 |
| [Frege1879] p. 66 | Proposition 86 | frege86 44791 |
| [Frege1879] p. 66 | Proposition 87 | frege87 44792 frege87d 44592 |
| [Frege1879] p. 67 | Proposition 88 | frege88 44793 |
| [Frege1879] p. 68 | Proposition 89 | frege89 44794 |
| [Frege1879] p. 68 | Proposition 90 | frege90 44795 |
| [Frege1879] p. 68 | Proposition 91 | frege91 44796 frege91d 44593 |
| [Frege1879] p. 69 | Proposition 92 | frege92 44797 |
| [Frege1879] p. 70 | Proposition 93 | frege93 44798 |
| [Frege1879] p. 70 | Proposition 94 | frege94 44799 |
| [Frege1879] p. 70 | Proposition 95 | frege95 44800 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 44804 |
| [Frege1879] p. 71 | Proposition 96 | frege96 44801 frege96d 44591 |
| [Frege1879] p. 71 | Proposition 97 | frege97 44802 frege97d 44594 |
| [Frege1879] p. 71 | Proposition 98 | frege98 44803 frege98d 44595 |
| [Frege1879] p. 72 | Proposition 100 | frege100 44805 |
| [Frege1879] p. 72 | Proposition 101 | frege101 44806 |
| [Frege1879] p. 72 | Proposition 102 | frege102 44807 frege102d 44596 |
| [Frege1879] p. 73 | Proposition 103 | frege103 44808 |
| [Frege1879] p. 73 | Proposition 104 | frege104 44809 |
| [Frege1879] p. 73 | Proposition 105 | frege105 44810 |
| [Frege1879] p. 73 | Proposition 106 | frege106 44811 frege106d 44597 |
| [Frege1879] p. 74 | Proposition 107 | frege107 44812 |
| [Frege1879] p. 74 | Proposition 108 | frege108 44813 frege108d 44598 |
| [Frege1879] p. 74 | Proposition 109 | frege109 44814 frege109d 44599 |
| [Frege1879] p. 75 | Proposition 110 | frege110 44815 |
| [Frege1879] p. 75 | Proposition 111 | frege111 44816 frege111d 44601 |
| [Frege1879] p. 76 | Proposition 112 | frege112 44817 |
| [Frege1879] p. 76 | Proposition 113 | frege113 44818 |
| [Frege1879] p. 76 | Proposition 114 | frege114 44819 frege114d 44600 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 44820 |
| [Frege1879] p. 77 | Proposition 116 | frege116 44821 |
| [Frege1879] p. 78 | Proposition 117 | frege117 44822 |
| [Frege1879] p. 78 | Proposition 118 | frege118 44823 |
| [Frege1879] p. 78 | Proposition 119 | frege119 44824 |
| [Frege1879] p. 78 | Proposition 120 | frege120 44825 |
| [Frege1879] p. 79 | Proposition 121 | frege121 44826 |
| [Frege1879] p. 79 | Proposition 122 | frege122 44827 frege122d 44602 |
| [Frege1879] p. 79 | Proposition 123 | frege123 44828 |
| [Frege1879] p. 80 | Proposition 124 | frege124 44829 frege124d 44603 |
| [Frege1879] p. 81 | Proposition 125 | frege125 44830 |
| [Frege1879] p. 81 | Proposition 126 | frege126 44831 frege126d 44604 |
| [Frege1879] p. 82 | Proposition 127 | frege127 44832 |
| [Frege1879] p. 83 | Proposition 128 | frege128 44833 |
| [Frege1879] p. 83 | Proposition 129 | frege129 44834 frege129d 44605 |
| [Frege1879] p. 84 | Proposition 130 | frege130 44835 |
| [Frege1879] p. 85 | Proposition 131 | frege131 44836 frege131d 44606 |
| [Frege1879] p. 86 | Proposition 132 | frege132 44837 |
| [Frege1879] p. 86 | Proposition 133 | frege133 44838 frege133d 44607 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 47143 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 47466 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 47166 |
| [Fremlin1] p. 14 | Definition 112A | ismea 47281 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 47301 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 47292 meadjunre 47306 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 47293 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 47294 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 47290 meaiunle 47299 meaiunlelem 47298 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 47311 meaiuninc2 47312 meaiuninc3 47315 meaiuninc3v 47314 meaiunincf 47313 meaiuninclem 47310 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 47317 meaiininc2 47318 meaiininclem 47316 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 47336 caragendifcl 47344 caratheodory 47358 omelesplit 47348 |
| [Fremlin1] p. 19 | Definition 113A | isome 47324 isomennd 47361 isomenndlem 47360 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 47346 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 47365 voncmpl 47451 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 47328 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 47353 carageniuncllem1 47351 carageniuncllem2 47352 caragenuncl 47343 caragenuncllem 47342 caragenunicl 47354 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 47362 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 47356 caratheodorylem2 47357 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 47365 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 47424 hoidmv1lelem1 47421 hoidmv1lelem2 47422 hoidmv1lelem3 47423 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 47468 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 47424 hoidmvle 47430 hoidmvlelem1 47425 hoidmvlelem2 47426 hoidmvlelem3 47427 hoidmvlelem4 47428 hoidmvlelem5 47429 hsphoidmvle2 47415 hsphoif 47406 hsphoival 47409 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 47378 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 47386 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 47413 hoidmvn0val 47414 hoidmvval 47407 hoidmvval0 47417 hoidmvval0b 47420 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 47418 hsphoidmvle 47416 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 47367 df-voln 47369 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 47434 ovn0 47396 ovn0lem 47395 ovnf 47393 ovnome 47403 ovnssle 47391 ovnsslelem 47390 ovnsupge0 47387 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 47433 ovnhoilem1 47431 ovnhoilem2 47432 vonhoi 47497 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 47450 hoidifhspf 47448 hoidifhspval 47438 hoidifhspval2 47445 hoidifhspval3 47449 hspmbl 47459 hspmbllem1 47456 hspmbllem2 47457 hspmbllem3 47458 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 47451 vonmea 47404 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 47402 ovnsubadd2 47476 ovnsubadd2lem 47475 ovnsubaddlem1 47400 ovnsubaddlem2 47401 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 47461 hoimbl2 47495 hoimbllem 47460 hspdifhsp 47446 opnvonmbl 47464 opnvonmbllem2 47463 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 47466 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 47509 iccvonmbllem 47508 ioovonmbl 47507 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 47515 vonicclem2 47514 vonioo 47512 vonioolem2 47511 vonn0icc 47518 vonn0icc2 47522 vonn0ioo 47517 vonn0ioo2 47520 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 47519 snvonmbl 47516 vonct 47523 vonsn 47521 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 47189 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 47188 subsaliuncllem 47187 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 47555 salpreimalegt 47539 salpreimaltle 47556 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 47558 issmff 47564 issmflem 47557 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 47575 issmflelem 47574 smfpreimale 47584 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 47586 issmfgtlem 47585 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 47526 issmf 47558 issmff 47564 issmfge 47600 issmfgelem 47599 issmfgt 47586 issmfgtlem 47585 issmfle 47575 issmflelem 47574 issmflem 47557 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 47537 salpreimagtlt 47560 salpreimalelt 47559 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 47600 issmfgelem 47599 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 47583 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 47581 cnfsmf 47570 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 47597 decsmflem 47596 incsmf 47572 incsmflem 47571 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 47531 pimconstlt1 47532 smfconst 47579 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 47595 smfaddlem1 47593 smfaddlem2 47594 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 47626 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 47625 smfmullem1 47621 smfmullem2 47622 smfmullem3 47623 smfmullem4 47624 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 47627 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 47630 smfpimbor1lem2 47629 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 47632 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 47620 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 47619 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 47628 smfresal 47618 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 47607 smflim2 47636 smflimlem1 47601 smflimlem2 47602 smflimlem3 47603 smflimlem4 47604 smflimlem5 47605 smflimlem6 47606 smflimmpt 47640 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 47644 smfsuplem1 47641 smfsuplem2 47642 smfsuplem3 47643 smfsupmpt 47645 smfsupxr 47646 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 47648 smfinflem 47647 smfinfmpt 47649 |
| [Fremlin1] p. 39 | Remark 121G | smflim 47607 smflim2 47636 smflimmpt 47640 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 47638 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 47668 smfdivdmmbl2 47671 smfinfdmmbl 47679 smfinfdmmbllem 47678 smfsupdmmbl 47675 smfsupdmmbllem 47674 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 47658 smflimsuplem2 47651 smflimsuplem6 47655 smflimsuplem7 47656 smflimsuplem8 47657 smflimsupmpt 47659 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 47661 smfliminflem 47660 smfliminfmpt 47662 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 47526 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 47672 fsupdm2 47673 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 47663 adddmmbl2 47664 finfdm 47676 finfdm2 47677 fsupdm 47672 fsupdm2 47673 muldmmbl 47665 muldmmbl2 47666 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 47676 finfdm2 47677 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25768 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25811 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25821 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 38449 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 38452 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9620 inf1 9604 inf2 9605 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10923 enqer 10933 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10928 df-nq 10924 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10920 df-plq 10926 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7654 df-mpq 10921 df-mq 10927 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10929 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10987 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10988 ltbtwnnq 10990 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10983 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10984 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10991 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10993 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 11005 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 11007 |
| [Gleason] p. 122 | Definition | df-1p 10994 |
| [Gleason] p. 122 | Remark (1) | prub 11006 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 11045 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10997 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 11044 psslinpr 11043 supexpr 11066 suplem1pr 11064 suplem2pr 11065 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 11030 addclprlem1 11028 addclprlem2 11029 df-plp 10995 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 11034 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 11033 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 11046 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 11055 ltexprlem1 11048 ltexprlem2 11049 ltexprlem3 11050 ltexprlem4 11051 ltexprlem5 11052 ltexprlem6 11053 ltexprlem7 11054 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 11057 ltaprlem 11056 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 11058 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 11059 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10996 mulclpr 11032 mulclprlem 11031 reclem2pr 11060 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 11041 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 11036 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 11035 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 11040 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 11063 reclem3pr 11061 reclem4pr 11062 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 11067 enrer 11075 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 11072 df-1r 11073 df-nr 11068 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 11070 df-plr 11069 negexsr 11114 recexsr 11119 recexsrlem 11115 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 11071 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12240 creur 12239 cru 12237 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11200 axcnre 11176 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15204 crimd 15321 crimi 15282 crre 15203 crred 15320 crrei 15281 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15206 remimd 15287 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15373 absval2d 15537 absval2i 15487 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15230 cjaddd 15309 cjaddi 15277 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15231 cjmuld 15310 cjmuli 15278 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15229 cjcjd 15288 cjcji 15260 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15228 cjreb 15212 cjrebd 15291 cjrebi 15263 cjred 15315 rere 15211 rereb 15209 rerebd 15290 rerebi 15262 rered 15313 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15237 addcjd 15301 addcji 15272 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15327 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15368 abscjd 15542 abscji 15491 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15378 abs00d 15538 abs00i 15488 absne0d 15539 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15411 releabsd 15543 releabsi 15492 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15383 absmuld 15546 absmuli 15494 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15371 sqabsaddi 15495 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15420 abstrid 15548 abstrii 15498 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14128 exp0 14131 expp1 14134 expp1d 14213 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26917 cxpaddd 26955 expadd 14170 expaddd 14214 expaddz 14172 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26926 cxpmuld 26975 expmul 14173 expmuld 14215 expmulz 14174 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26923 mulcxpd 26966 mulexp 14167 mulexpd 14227 mulexpz 14168 |
| [Gleason] p. 140 | Exercise 1 | znnen 16304 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13565 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15721 rlimadd 15732 rlimdiv 15735 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15723 rlimsub 15733 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15722 rlimmul 15734 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15726 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15672 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15693 climcj 15694 climim 15696 climre 15695 rlimabs 15698 rlimcj 15699 rlimim 15701 rlimre 15700 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11275 df-xr 11274 ltxr 13168 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15560 limsupval 15563 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15759 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15768 caucvgb 15769 caucvgbf 46319 caucvgr 15765 climcau 15760 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15905 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15974 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15425 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13891 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21583 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24573 xmet0 24572 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24589 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24580 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24582 mstri 24699 xmettri 24581 xmstri 24698 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24612 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23878 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25542 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24770 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 25096 addcn2 15683 mulcn 25098 mulcn2 15685 subcn 25097 subcn2 15684 |
| [Gleason] p. 295 | Remark | bcval3 14372 bcval4 14373 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14387 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14370 df-bc 14369 |
| [Gleason] p. 296 | Remark | bcn0 14376 bcnn 14378 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15921 |
| [Gleason] p. 308 | Equation 2 | ef0 16181 |
| [Gleason] p. 308 | Equation 3 | efcj 16182 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16188 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16193 |
| [Gleason] p. 310 | Equation 14 | sinadd 16256 |
| [Gleason] p. 310 | Equation 15 | cosadd 16257 |
| [Gleason] p. 311 | Equation 17 | sincossq 16268 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16273 sinbnd 16272 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14282 sqeqori 14280 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16162 |
| [Godowski] p. 730 | Equation SF | goeqi 32755 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 32150 |
| [Golan] p. 1 | Remark | srgisid 20352 |
| [Golan] p. 1 | Definition | df-srg 20330 |
| [Golan] p. 149 | Definition | df-slmd 33643 |
| [Gonshor] p. 7 | Definition | df-cuts 28026 |
| [Gonshor] p. 9 | Theorem 2.5 | lesrec 28065 lesrecd 28066 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 28186 cofcut1d 28187 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 28188 cofcut2d 28189 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 28190 cofcutr1d 28191 cofcutr2d 28192 |
| [Gonshor] p. 13 | Definition | df-adds 28226 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 28242 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 28268 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28396 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28416 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28724 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28726 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28725 |
| [Gonshor] p. 39 | Theorem 4.4(b) | elreno2 28761 |
| [Gonshor] p. 95 | Theorem 6.1 | addbday 28284 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36741 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17674 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17676 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 49105 df-cllaw 49103 df-comlaw 49104 |
| [Hall] p. 2 | Section 1.2 | df-clintop 49117 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 49138 |
| [Halmos] p. 28 | Partition ` ` | df-parts 39618 dfmembpart2 39623 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32547 riesz2 32548 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 32423 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32655 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32667 elpjidm 32666 pjnmopi 32630 |
| [Halmos] p. 44 | Remark | pjinormi 32169 pjinormii 32158 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32671 pjrn 32189 pjrni 32184 pjvec 32178 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 32209 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32636 hmopidmpji 32634 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32673 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32662 pjocvec 32179 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32651 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32654 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32657 pjssdif2i 32656 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 32337 |
| [Hamilton] p. 28 | Definition 2.1 | ax-1 6 |
| [Hamilton] p. 31 | Example 2.7(a) | idALT 24 |
| [Hamilton] p. 73 | Rule 1 | ax-mp 5 |
| [Hamilton] p. 74 | Rule 2 | ax-gen 1828 |
| [Hatcher] p. 25 | Definition | df-phtpc 25224 df-phtpy 25203 |
| [Hatcher] p. 26 | Definition | df-pco 25237 df-pi1 25240 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 25227 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 25282 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22716 df-dmatalt 49330 |
| [Helfgott] p. 2 | Theorem | tgoldbach 48735 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 48720 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 48732 bgoldbtbnd 48727 bgoldbtbnd 48727 tgblthelfgott 48733 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 35152 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 35153 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 35167 hgt750lemb 35166 hgt750leme 35168 hgt750lemf 35163 hgt750lemg 35164 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 48729 tgoldbachgt 35173 tgoldbachgtALTV 48730 tgoldbachgtd 35172 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 35154 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30975 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 19072 grpoideu 30991 mndideu 18851 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 19102 grpoinveu 31001 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 19133 grpo2inv 31013 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 19145 grpoinvop 31015 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 19167 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1801 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1802 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1804 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32902 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32915 cdj3i 32923 cdj3lem1 32916 cdjreui 32914 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32913 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 42836 |
| [Holland95] p. 14 | Line 15 | hgmapvs 42766 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 42788 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 42789 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 42786 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 42792 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 42711 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 42806 |
| [Holland95] p. 204 | Definition of involution | df-srng 21010 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 40378 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 42403 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 42356 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 40808 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 42252 poml4N 40828 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 42343 pexmidALTN 40853 pexmidN 40844 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 42408 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 39999 ldualset 40000 |
| [Holland95] p. 222 | Item 1 | df-lines 40376 df-pointsN 40377 |
| [Holland95] p. 222 | Item 2 | df-polarityN 40778 |
| [Holland95] p. 223 | Remark | ispsubcl2N 40822 omllaw4 40121 pol1N 40785 polcon3N 40792 |
| [Holland95] p. 223 | Definition | df-psubclN 40810 |
| [Holland95] p. 223 | Equation for polarity | polval2N 40781 |
| [Holmes] p. 40 | Definition | df-xrn 39130 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31566 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32664 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 32445 eigre 32317 eigrei 32316 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 32446 eigorth 32320 eigorthi 32319 |
| [Hughes] p. 137 | Remark (ii) | eigposi 32318 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30790 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30786 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30787 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30788 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30806 frgrregorufr0 30805 frgrregorufrg 30807 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30813 frrusgrord 30822 frrusgrord0 30821 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30559 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30796 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30799 frgrwopreg2 30800 frgrwopregasn 30797 frgrwopregbsn 30798 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30802 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30816 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30819 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30557 numclwlk1 30852 numclwlk1lem1 30850 numclwlk1lem2 30851 numclwwlk1 30842 numclwwlk8 30873 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30793 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 30238 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30828 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30854 numclwwlkovh0 30853 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30862 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 30449 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30866 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30869 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30872 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30884 natded 30884 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30884 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30884 natded 30884 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30884 |
| [Jech] p. 4 | Definition of class | cv 1569 cvjust 2756 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10591 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10589 alephmul 10590 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10588 infmap2 10222 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9799 |
| [Jech] p. 72 | Equation 9.3 | df-scott 9871 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9852 rankval4b 35609 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9896 |
| [Jech] p. 78 | Note | opthprc 5723 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 43758 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 43846 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 43847 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 43770 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 43774 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 43775 rmyp1 43776 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 43777 rmym1 43778 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 43768 rmx1 43769 rmxluc 43779 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 43772 rmy1 43773 rmyluc 43780 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 43782 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 43783 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 43803 jm2.17b 43804 jm2.17c 43805 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 43836 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 43840 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 43831 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 43806 jm2.24nn 43802 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 43845 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 43851 rmygeid 43807 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 43863 |
| [Juillerat] p. 11 | Section *5 | etransc 47113 etransclem47 47111 etransclem48 47112 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 47108 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 47110 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 47096 |
| [Juillerat] p. 13 | Proof | etransclem35 47099 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 47102 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 47088 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 47105 |
| [Juillerat] p. 14 | Proof | etransclem23 47087 |
| [KalishMontague] p. 81 | Note 1 | ax-6 2000 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2045 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2050 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2040 cbvaliw 2039 wl-cbvmotv 38278 wl-motae 38280 wl-moteq 38279 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 2019 spimw 2003 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2066 spw 2067 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31998 chabs1i 32000 chabs2 31999 chabs2i 32001 chjass 32015 chjassi 31968 latabs1 18567 latabs2 18568 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32820 ela 32821 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32765 cvrval2 40149 |
| [Kalmbach] p. 16 | Definition | df-ol 40053 df-oml 40054 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 32066 cmbri 32072 cmtvalN 40086 df-cm 32065 df-cmtN 40052 |
| [Kalmbach] p. 22 | Remark | omllaw5N 40122 pjoml5 32095 pjoml5i 32070 |
| [Kalmbach] p. 22 | Definition | pjoml2 32093 pjoml2i 32067 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 32096 cmcmi 32074 cmcmii 32079 cmtcomN 40124 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 40120 omlsi 31886 pjoml 31918 pjomli 31917 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 40119 |
| [Kalmbach] p. 23 | Remark | cmbr2i 32078 cmcm3 32097 cmcm3i 32076 cmcm3ii 32081 cmcm4i 32077 cmt3N 40126 cmt4N 40127 cmtbr2N 40128 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 32090 cmbr3i 32082 cmtbr3N 40129 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 32100 fh1i 32103 fh2 32101 fh2i 32104 omlfh1N 40133 |
| [Kalmbach] p. 65 | Remark | chjatom 32839 chslej 31980 chsleji 31940 shslej 31862 shsleji 31852 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31977 chocini 31936 chsupcl 31822 chsupval2 31892 h0elch 31737 helch 31725 hsupval2 31891 ocin 31778 ococss 31775 shococss 31776 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31794 |
| [Kalmbach] p. 66 | Remark | df-pjh 31877 pjssmi 32647 pjssmii 32163 |
| [Kalmbach] p. 67 | Lemma 3 | osum 32127 osumi 32124 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32682 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32882 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32792 |
| [Kalmbach] p. 140 | Remark | hatomic 32842 hatomici 32841 hatomistici 32844 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 40194 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32863 lsatexch 39918 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32837 cvlcvr1 40214 cvr1 40285 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32856 cvexchi 32851 cvrexch 40295 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32846 hlrelat 40277 hlrelat5N 40276 lrelat 39889 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21332 lsmsatcv 39885 spansncv 32135 spansncvi 32134 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 39904 spansncv2 32775 |
| [Kalmbach] p. 266 | Definition | df-st 32693 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 32331 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10658 fpwwe2 10655 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10659 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10666 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10661 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10663 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10676 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10680 gchxpidm 10681 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10692 gchhar 10691 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10220 unxpwdom 9564 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10682 |
| [Kreyszig] p. 3 | Property M1 | metcl 24562 xmetcl 24561 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24569 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24802 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11959 muleqadd 11885 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24668 |
| [Kreyszig] p. 19 | Remark | mopntopon 24669 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24728 mopnm 24674 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24726 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24731 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24772 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23487 lmmbr 25490 lmmbr2 25491 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23609 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25545 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25508 iscmet2 25526 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25548 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23691 metelcls 25537 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25538 metcld2 25539 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25331 lmodvneg1 21093 nvinv 31121 vcm 31058 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25327 lmod0vs 21083 slmd0vs 33666 vc0 31056 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 21084 slmdvs0 33667 vcz 31057 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 31173 ngpmet 24833 nrmmetd 24804 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 31168 imsdval2 31169 ncvspds 25393 ngpds 24834 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24819 nvnd 31170 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24848 nmge0 24847 nvge0 31155 nvz 31151 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24854 nvabs 31154 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 31283 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 31227 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 31289 blocni 31287 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 31288 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25436 ipeq0 21855 ipz 31201 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25448 pythi 31332 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 31336 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25470 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15947 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25668 minveco 31366 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 31232 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25561 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 31355 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32605 leopg 32604 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32623 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 31400 |
| [Kulpa] p. 547 | Theorem | poimir 38404 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 38403 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 38402 |
| [Kulpa] p. 548 | Theorem | broucube 38405 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 38397 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 38398 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2414 axnul 5266 |
| [Kunen] p. 11 | Axiom 3 | axnul 5266 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 5248 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8840 mapvalg 8838 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10527 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7940 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9749 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9791 r1elssi 9790 |
| [Kunen] p. 107 | Exercise 4 | rankop 9843 rankopb 9837 rankuni 9848 rankxplim 9864 rankxpsuc 9867 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 45779 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 45787 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 45786 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 45788 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 45793 rexabso 45794 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 45800 n0abso 45801 ssabso 45799 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 45802 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 45812 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 45807 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 45810 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 45811 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 45806 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 45818 wfaxpr 45823 wfaxreg 45825 wfaxrep 45819 wfaxsep 45820 wfaxun 45824 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 45809 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 45822 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 45818 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 45817 omelaxinf2 45814 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 45827 wfaxinf2 45826 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 45840 permaxext 45830 permaxinf2 45838 permaxnul 45833 permaxpow 45834 permaxpr 45835 permaxrep 45831 permaxsep 45832 permaxun 45836 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 45828 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 45839 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4967 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 34177 |
| [Lang] p. | Definition | df-rn 5670 |
| [Lang] p. 3 | Statement | lidrideqd 18767 mndbn0 18857 |
| [Lang] p. 3 | Definition | df-mnd 18841 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18793 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18954 |
| [Lang] p. 5 | Equation | gsumreidx 20048 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 49099 |
| [Lang] p. 6 | Example | nn0mnd 49096 |
| [Lang] p. 6 | Equation | gsumxp2 20111 |
| [Lang] p. 6 | Statement | cycsubm 19334 |
| [Lang] p. 6 | Definition | mulgnn0gsum 19207 |
| [Lang] p. 6 | Observation | mndlsmidm 19801 |
| [Lang] p. 7 | Definition | dfgrp2e 19091 |
| [Lang] p. 30 | Definition | df-tocyc 33549 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33594 |
| [Lang] p. 32 | Property (b) | cyc3conja 33599 cycpmconjv 33584 |
| [Lang] p. 53 | Definition | df-cat 17760 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18190 cat1lem 18189 |
| [Lang] p. 54 | Definition | df-iso 17842 |
| [Lang] p. 57 | Definition | df-inito 18077 df-termo 18078 |
| [Lang] p. 58 | Example | irinitoringc 21696 |
| [Lang] p. 58 | Statement | initoeu1 18104 termoeu1 18111 |
| [Lang] p. 62 | Definition | df-func 17951 |
| [Lang] p. 65 | Definition | df-nat 18039 |
| [Lang] p. 83 | Definition of "ring with unit" | dfring2 20433 |
| [Lang] p. 91 | Note | df-ringc 20812 |
| [Lang] p. 92 | Statement | mxidlprm 33875 |
| [Lang] p. 92 | Definition | isprmidlc 21539 |
| [Lang] p. 128 | Remark | dsmmlmod 21962 |
| [Lang] p. 129 | Proof | lincscm 49362 lincscmcl 49364 lincsum 49361 lincsumcl 49363 |
| [Lang] p. 129 | Statement | lincolss 49366 |
| [Lang] p. 129 | Observation | dsmmfi 21955 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 34139 qusdimsum 34140 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 34120 |
| [Lang] p. 147 | Definition | snlindsntor 49403 |
| [Lang] p. 504 | Statement | mat1 22673 matring 22669 |
| [Lang] p. 504 | Definition | df-mamu 22617 |
| [Lang] p. 505 | Statement | mamuass 22628 mamutpos 22684 matassa 22670 mattposvs 22681 tposmap 22683 |
| [Lang] p. 513 | Definition | mdet1 22827 mdetf 22821 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22920 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22813 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22837 |
| [Lang] p. 515 | Definition | df-minmar1 22861 smadiadetr 22901 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22836 mdetralt 22834 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22849 |
| [Lang] p. 518 | Definition | df-madu 22860 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22871 madurid 22870 matinv 22903 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 23119 |
| [Lang], p. 190 | Chapter 6 | vieta 34092 |
| [Lang], p. 224 | Proposition 1.1 | extdgfialg 34206 finextalg 34210 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 34175 fedgmul 34143 |
| [Lang], p. 225 | Proposition 1.4 | algextdeg 34237 |
| [Lang], p. 561 | Remark | chpmatply1 23061 |
| [Lang], p. 561 | Definition | df-chpmat 23056 |
| [Lang2] p. 3 | Notations | df-ind 12246 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 45160 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 45155 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 45161 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5266 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2741 wl-df.clab 38263 |
| [Levy] p. 59 | Definition | df-ttrcl 9690 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9736 |
| [Levy] p. 338 | Axiom | df-clel 2837 df-cleq 2754 wl-df.cleq 38264 |
| [Levy] p. 338 | Axiom. See also comments under ~ df-clab , ~ df-cleq , and ~ eqabb . Alternate characterizations | wl-df.clel 38267 |
| [Levy] p. 357 | Definition extends to class variables a relation already valid for set variables, and is therefore conservative. This only sketches the conservativity arguement; for details see Appendix | wl-df.clel 38267 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2837 df-cleq 2754 wl-df.cleq 38264 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2741 wl-df.clab 38263 |
| [Levy] p. 358 | Axiom | df-clab 2741 wl-df.clab 38263 |
| [Levy58] p. 2 | Definition I | isfin1-3 10391 |
| [Levy58] p. 2 | Definition II | df-fin2 10291 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10290 |
| [Levy58] p. 2 | Definition III | df-fin3 10293 |
| [Levy58] p. 3 | Definition V | df-fin5 10294 |
| [Levy58] p. 3 | Definition IV | df-fin4 10292 |
| [Levy58] p. 4 | Definition VI | df-fin6 10295 |
| [Levy58] p. 4 | Definition VII | df-fin7 10296 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10420 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27923 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27934 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27966 nosupbnd1 27951 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27968 nosupbnd2 27953 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27972 noetasuplem4 27973 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27969 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1801 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1802 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1804 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32890 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32894 mdsymi 32893 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32888 mdsymlem6 32890 mdsymlem7 32891 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32892 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32795 ssdmd2 32796 ssmd1 32793 ssmd2 32794 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32791 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32763 df-md 32762 mdbr 32776 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32813 mdslj1i 32801 mdslj2i 32802 mdslle1i 32799 mdslle2i 32800 mdslmd1i 32811 mdslmd2i 32812 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32803 mdsl2bi 32805 mdsl2i 32804 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32817 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32814 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32815 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32792 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32797 mdsl3 32798 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32816 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32911 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 40196 hlrelat1 40275 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 39914 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32818 cvmdi 32806 cvnbtwn4 32771 cvrnbtwn4 40154 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32819 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 40215 cvp 32857 cvrp 40291 lcvp 39915 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32881 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32880 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 40208 hlexch4N 40267 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32883 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 40318 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 40624 atpsubN 40628 df-pointsN 40377 pointpsubN 40626 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 40379 pmap11 40637 pmaple 40636 pmapsub 40643 pmapval 40632 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 40640 pmap1N 40642 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 40645 pmapglb2N 40646 pmapglb2xN 40647 pmapglbx 40644 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 40727 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 40352 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 40671 paddclN 40717 paddidm 40716 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 40353 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 40713 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 40352 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 40353 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19806 lsmmod2 19807 lssats 39887 shatomici 32840 shatomistici 32843 shmodi 31872 shmodsi 31871 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32782 mdsymlem7 32891 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 32071 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31975 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32897 |
| [Margaris] p. 40 | Rule C | exlimiv 1963 |
| [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 402 df-ex 1813 df-or 862 dfbi2 480 |
| [Margaris] p. 51 | Theorem 1 | idALT 24 |
| [Margaris] p. 56 | Theorem 3 | conventions 30881 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 45739 |
| [Margaris] p. 60 | Theorem 8 | jcn 163 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 45740 |
| [Margaris] p. 79 | Rule C | exinst01 45450 exinst11 45451 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 2009 19.2g 2226 r19.2z 4458 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2240 rr19.3v 3624 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2196 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1859 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1814 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2219 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2243 19.9h 2321 exlimd 2256 exlimdh 2325 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2199 excomim 2200 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2359 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30882 conventions-labels 30882 conventions-labels 30882 conventions-labels 30882 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1860 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 45204 albi 1851 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2263 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2264 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 45206 exbi 1880 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2267 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 45203 2alimdv 1951 alimd 2250 alimdh 1850 alimdv 1949 ax-4 1842 ralimdaa 3265 ralimdv 3178 ralimdva 3176 ralimdvva 3211 sbcimdv 3810 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2245 19.21h 2322 19.21t 2244 19.21vv 45202 alrimd 2253 alrimdd 2252 alrimdh 1896 alrimdv 1962 alrimi 2251 alrimih 1857 alrimiv 1960 alrimivv 1961 bj-alrimdh 37327 hbralrimi 3154 r19.21be 3257 r19.21bi 3256 ralrimd 3269 ralrimdv 3162 ralrimdva 3164 ralrimdvv 3208 ralrimdvva 3219 ralrimi 3262 ralrimia 3263 ralrimiv 3155 ralrimiva 3156 ralrimivv 3205 ralrimivva 3207 ralrimivvva 3210 ralrimivw 3160 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 45205 2eximdv 1952 bj-exim 37342 exim 1867 eximd 2254 eximdh 1897 eximdv 1950 rexim 3105 reximd2a 3274 reximdai 3266 reximdd 45982 reximddv 3180 reximddv2 3223 reximddv3 3181 reximdv 3179 reximdv2 3174 reximdva 3177 reximdvai 3175 reximdvva 3212 reximi2 3097 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2249 19.23bi 2229 19.23h 2323 19.23t 2248 exlimdv 1966 exlimdvv 1967 exlimexi 45349 exlimiv 1963 exlimivv 1965 rexlimd3 45978 rexlimdv 3163 rexlimdv3a 3169 rexlimdva 3165 rexlimdva2 3167 rexlimdvaa 3166 rexlimdvv 3220 rexlimdvva 3221 rexlimdvvva 3222 rexlimdvw 3170 rexlimiv 3158 rexlimiva 3157 rexlimivv 3206 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 2024 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1913 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1903 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2265 r19.27z 4469 r19.27zv 4470 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2266 19.28vv 45212 r19.28z 4461 r19.28zf 45993 r19.28zv 4465 rr19.28v 3625 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1906 r19.29d2r 3151 r19.29imd 3129 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1914 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2272 19.31vv 45210 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2271 r19.32 47988 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 45208 19.33 1917 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 2025 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1910 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2268 19.36vv 45209 r19.36zv 4471 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2270 19.37vv 45211 r19.37zv 4466 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1872 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 2023 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1920 19.40 1919 r19.40 3130 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2273 19.41rg 45375 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2274 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1915 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2275 r19.44zv 4468 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2276 r19.45zv 4467 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2637 |
| [Mayet] p. 370 | Remark | jpi 32752 largei 32749 stri 32739 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32694 ishst 32696 |
| [Mayet3] p. 10 | Theorem | hstrbi 32748 hstri 32747 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 32210 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 32211 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32760 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31814 chsupcl 31822 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32842 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32836 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32863 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 40858 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18579 latj32 18577 latjass 18575 |
| [Megill] p. 444 | Axiom C5 | ax-5 1943 ax5ALT 39782 |
| [Megill] p. 444 | Section 7 | conventions 30881 |
| [Megill] p. 445 | Lemma L12 | aecom-o 39776 ax-c11n 39763 axc11n 2457 |
| [Megill] p. 446 | Lemma L17 | equtrr 2055 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 39771 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 39803 hbnae 2463 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2512 sbid 2292 sbidd-misc 50647 sbidd 50646 |
| [Megill] p. 448 | Remark 9.6 | axc14 2494 |
| [Megill] p. 448 | Scheme C4' | ax-c4 39759 |
| [Megill] p. 448 | Scheme C5' | ax-c5 39758 sp 2221 |
| [Megill] p. 448 | Scheme C6' | ax-11 2194 |
| [Megill] p. 448 | Scheme C7' | ax-c7 39760 |
| [Megill] p. 448 | Scheme C8' | ax-7 2041 |
| [Megill] p. 448 | Scheme C9' | ax-c9 39765 |
| [Megill] p. 448 | Scheme C10' | ax-6 2000 ax-c10 39761 |
| [Megill] p. 448 | Scheme C11' | ax-c11 39762 |
| [Megill] p. 448 | Scheme C12' | ax-8 2147 |
| [Megill] p. 448 | Scheme C13' | ax-9 2155 |
| [Megill] p. 448 | Scheme C14' | ax-c14 39766 |
| [Megill] p. 448 | Scheme C15' | ax-c15 39764 |
| [Megill] p. 448 | Scheme C16' | ax-c16 39767 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 39779 dral1 2470 dral2-o 39805 dral2 2469 drex1 2472 drex2 2473 drsb1 2526 drsb2 2302 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2209 sbequ 2120 sbid2v 2540 |
| [Megill] p. 450 | Example in Appendix | hba1-o 39772 hba1 2328 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 47782 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 24 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3829 rspsbca 3830 stdpc4 2105 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 39759 ra4 3836 stdpc5 2246 |
| [Mendelson] p. 81 | Rule C | exlimiv 1963 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2061 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2287 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3741 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5495 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4351 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4352 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 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 4091 |
| [Mendelson] p. 231 | Definition of union | dfun3 4225 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5430 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4867 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5550 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4578 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5551 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4894 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5811 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6270 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7777 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6367 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8586 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9141 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 9062 xpsneng 9063 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9069 xpcomeng 9070 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9072 |
| [Mendelson] p. 255 | Definition | brsdom 8983 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9065 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8833 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 9047 mapsnend 9046 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9147 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9146 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8892 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 9050 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9066 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10184 djucomen 10183 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10188 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10182 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8521 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8548 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10570 |
| [Mendelson] p. 281 | Definition | df-r1 9749 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9798 |
| [Mendelson] p. 287 | Axiom system MK | ru 3741 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30740 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30775 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30777 vdgn1frgrv3 30778 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30779 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30772 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30765 2pthfrgrrn 30763 2pthfrgrrn2 30764 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31734 |
| [Monk1] p. 22 | Remark | conventions 30881 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30881 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4187 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5767 ssrelf 33090 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5768 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5172 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6263 coi2 6264 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5908 rn0 5914 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 5869 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5677 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5917 rnxp 6167 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5758 xp0 5759 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6077 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6074 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7914 imaexg 7913 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6071 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7071 funfvop 7046 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6936 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6947 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6583 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7254 dff13f 7255 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7221 funrnex 7954 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7247 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6227 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4927 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 8006 df-1st 7989 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 8007 df-2nd 7990 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9839 ranksnb 9812 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9840 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9841 rankunb 9835 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9823 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9749 r1val2 9822 |
| [Monk1] p. 117 | Lemma | zorn2 10511 zorn2g 10508 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9994 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10572 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9989 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1842 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2041 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2215 ax-c15 39764 ax12v2 2217 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 39759 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2194 |
| [Monk2] p. 109 | Lemma 15 | equvini 2486 equvinv 2062 eqvinop 5467 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1943 ax5ALT 39782 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2178 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2194 |
| [Monk2] p. 114 | Lemma 21 | sp 2221 |
| [Monk2] p. 114 | Lemma 22 | axc4 2353 hba1-o 39772 hba1 2328 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2190 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2212 nfra2 3363 nfra2w 3300 |
| [Moore] p. 53 | Part I | df-mre 17674 |
| [Munkres] p. 77 | Example 2 | distop 23224 indistop 23231 indistopon 23230 |
| [Munkres] p. 77 | Example 3 | fctop 23233 fctop2 23234 |
| [Munkres] p. 77 | Example 4 | cctop 23235 |
| [Munkres] p. 78 | Definition of basis | df-bases 23175 isbasis3g 23178 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17532 tgval2 23185 |
| [Munkres] p. 79 | Remark | tgcl 23198 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 23192 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 23216 tgss3 23215 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 23217 basgen2 23218 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 38105 topdifinfeq 38106 topdifinffin 38104 topdifinfindis 38102 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23389 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 23267 topcld 23264 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 23268 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 23270 |
| [Munkres] p. 94 | Definition of closure | clsval 23266 |
| [Munkres] p. 94 | Definition of interior | ntrval 23265 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 23304 elcls 23302 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 23312 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23377 neindisj 23346 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23379 |
| [Munkres] p. 97 | Definition of limit point | islp2 23374 lpval 23368 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23544 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23456 iscn 23464 iscn2 23467 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23509 cncnp2 23510 cncnpi 23507 df-cnp 23457 iscnp 23466 iscnp2 23468 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24773 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25543 |
| [Nathanson] p. 123 | Remark | reprgt 35131 reprinfz1 35132 reprlt 35129 |
| [Nathanson] p. 123 | Definition | df-repr 35119 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 35151 |
| [Nathanson] p. 123 | Proposition | breprexp 35143 breprexpnat 35144 itgexpif 35116 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32586 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 48728 |
| [Pfenning] p. 17 | Definition XM | natded 30884 |
| [Pfenning] p. 17 | Definition NNC | natded 30884 notnotrd 134 |
| [Pfenning] p. 17 | Definition ` `C | natded 30884 |
| [Pfenning] p. 18 | Rule" | natded 30884 |
| [Pfenning] p. 18 | Definition /\I | natded 30884 |
| [Pfenning] p. 18 | Definition ` `E | natded 30884 natded 30884 natded 30884 natded 30884 natded 30884 |
| [Pfenning] p. 18 | Definition ` `I | natded 30884 natded 30884 natded 30884 natded 30884 natded 30884 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30884 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30884 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30884 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30884 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30884 |
| [Pfenning] p. 127 | Definition =E | natded 30884 |
| [Pfenning] p. 127 | Definition =I | natded 30884 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25434 df-dip 31183 dip0l 31200 ip0l 21853 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25475 ipval 31185 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 31196 ipcj 21851 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25437 dipdir 31324 ipdir 21856 ipdiri 31312 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 31192 nmsq 25426 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 31307 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 31309 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 31310 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25443 dipass 31327 ipass 21862 ipassi 31323 |
| [Prugovecki] p. 186 | Definition of bra | braval 32426 df-bra 32332 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 32333 kbval 32436 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32864 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 40763 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32878 atcvat4i 32879 cvrat3 40317 cvrat4 40318 lsatcvat3 39927 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32764 cvrval 40144 df-cv 32761 df-lcv 39894 lspsncv0 21337 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 40775 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 40776 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2741 rabid 3435 rabidd 45989 wl-df.clab 38263 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2314 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2754 wl-df.cleq 38264 |
| [Quine] p. 19 | Definition 2.9 | conventions 30881 df-v 3455 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2901 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2898 abid2f 2954 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2311 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2122 sbalex 2280 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2837 wl-df.clel 38267 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2762 eqid1 30948 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2769 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3743 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3744 dfsbcq2 3745 |
| [Quine] p. 43 | Theorem 6.8 | vex 3457 |
| [Quine] p. 43 | Theorem 6.9 | isset 3467 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3548 spcgv 3553 spcimgf 3516 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3755 spsbcd 3756 |
| [Quine] p. 44 | Theorem 6.12 | elex 3474 |
| [Quine] p. 44 | Theorem 6.13 | elab 3636 elabg 3633 elabgf 3631 |
| [Quine] p. 44 | Theorem 6.14 | noel 4287 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4681 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4590 df-sn 4588 |
| [Quine] p. 49 | Theorem 7.4 | snss 4748 snssg 4747 |
| [Quine] p. 49 | Theorem 7.5 | prss 4784 prssg 4783 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4726 prid1g 4724 prid2 4727 prid2g 4725 snid 4626 snidg 4624 |
| [Quine] p. 51 | Theorem 7.12 | snex 5408 |
| [Quine] p. 51 | Theorem 7.13 | prex 5407 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4889 unisnALT 45750 unisng 4888 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4893 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4902 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4899 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6507 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 47976 dfiota2 6494 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 47985 iotaval 6511 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6517 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6513 |
| [Quine] p. 58 | Definition 9.1 | df-op 4594 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5507 opabidw 5506 opelopab 5525 opelopaba 5518 opelopabaf 5527 opelopabf 5528 opelopabg 5521 opelopabga 5515 opelopabgf 5523 oprabid 7448 oprabidw 7447 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5665 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5667 |
| [Quine] p. 64 | Definition 9.15 | df-id 5554 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6602 |
| [Quine] p. 65 | Theorem 10.4 | funi 6569 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6590 funsng 6588 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6539 |
| [Quine] p. 65 | Definition 10.2 | args 6092 dffv4 6879 |
| [Quine] p. 68 | Definition 10.11 | conventions 30881 df-fv 6545 fv2 6877 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14338 nn0opth2i 14337 nn0opthi 14336 omopthi 8652 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8402 |
| [Quine] p. 232 | Equation i | carddom 10565 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6624 funimaexg 6623 |
| [Quine] p. 331 | Axiom system NF | ru 3741 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31566 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 31183 polid 31641 polid2i 31639 polidi 31640 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 31295 |
| [ReedSimon] p. 195 | Remark | lnophm 32501 lnophmi 32500 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32614 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32616 leopmuli 32615 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32619 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 32334 leoppos 32608 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32618 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32607 |
| [Ribenboim] p. 181 | Remark | nprmdvdsfacm1 48529 |
| [Ribenboim], p. 181 | Statement | ppivalnn 48537 |
| [Roman] p. 4 | Definition | df-dmat 22716 df-dmatalt 49330 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20292 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20378 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 49417 |
| [Roman] p. 112 | Note | isldepslvec2 49417 ldepsnlinc 49440 zlmodzxznm 49429 |
| [Roman] p. 112 | Example | zlmodzxzequa 49428 zlmodzxzequap 49431 zlmodzxzldep 49436 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 23119 |
| [Rosenlicht] p. 80 | Theorem | heicant 38406 |
| [Rosser] p. 281 | Definition | df-op 4594 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 35155 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 35156 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 49298 pmtr3ncom 19606 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19602 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19545 cayleyth 19546 |
| [Rudin] p. 164 | Equation 27 | efcan 16186 |
| [Rudin] p. 164 | Equation 30 | efzval 16194 |
| [Rudin] p. 167 | Equation 48 | absefi 16288 |
| [Russell1905] p. 482 | Example of "the father | dfalseu2 50767 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 200 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1804 |
| [Sanford] p. 39 | Rule 4 | mptxor 1802 |
| [Sanford] p. 40 | Rule 1 | mptnan 1801 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6113 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6116 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6112 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6110 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17674 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17675 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17675 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17677 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10142 |
| [Schechter] p. 141 | Definition (MC) | dfac11 43905 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10451 axdc3 10459 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20380 isrngo 38649 |
| [Schechter] p. 276 | Remark 11.6.e | span0 32024 |
| [Schechter] p. 276 | Definition of span | df-span 31791 spanval 31815 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 23222 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6386 onelond 36781 onelord 44094 ordelon 6385 ordelord 6383 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 44095 sucidg 6445 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6417 onsuc 7812 ord0 6416 ordsuci 7810 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 44096 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5220 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 43871 elon2 6372 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6367 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5562 epelg 5560 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9575 epirron 44097 ordirr 6379 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 44099 oneptr 44098 ontr1 6409 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6405 oneptri 44100 ordtri3or 6394 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8491 ord0eln0 6418 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6431 onsucss 44109 trsucss 6452 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7817 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6458 ordnbtwn 6457 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 44111 ordnexbtwnsuc 44110 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10406 onsucf1lem 44112 onsucf1o 44115 onsucf1olem 44113 onsucrn 44114 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 44116 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7844 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 44105 ordne0gt0 44104 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 44107 limnsuc 44108 onsucelab 44106 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9625 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7859 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9628 ordom 7875 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9629 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8631 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7782 ssorduni 7781 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8521 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9632 limom 7881 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8458 df1o2 8465 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8506 oa0suclim 44118 oalim 8522 oasuc 8514 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8507 om0suclim 44119 omlim 8523 omsuc 8516 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8512 oe0m1 8511 oe0suclim 44120 oelim 8524 oesuc 8517 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 44072 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 44122 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 44123 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 44124 limexissupab 44126 limiun 44125 limuni 6424 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8528 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8532 om1om1r 44127 om1r 8533 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8525 oaomoecl 44121 oecl 8527 omcl 8526 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 44074 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8534 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8535 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 44128 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 44129 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8602 nnamecl 44130 nnecl 8604 nnmcl 8603 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 44131 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8542 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8543 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8550 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 44133 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 44134 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 44136 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8549 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 44140 omword1 8563 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 44139 oaordnrex 44138 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 44135 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 44141 omword2 8564 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 44142 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 44143 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 44144 omordi 8556 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8558 omord2com 44145 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 44146 df-2o 8459 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 44149 oewordi 8582 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 44150 oeworde 8584 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 44151 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 44152 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 44148 omnord1ex 44147 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 44153 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 44155 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 44159 oenord1ex 44158 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 44160 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8551 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 44154 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8569 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8570 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 44162 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8588 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 44163 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 44164 cantnfub2 44165 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 44168 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 29372 axtgcgrrflx 28804 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 29373 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 29374 axtgcgrid 28805 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28790 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 29385 axtgsegcon 28806 df-trkgcb 28792 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 29396 axtg5seg 28807 df-trkgcb 28792 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 29397 axtgbtwnid 28808 df-trkgb 28791 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 29399 axtgpasch 28809 df-trkgb 28791 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 29418 df-trkg2d 35175 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28812 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28813 df-trkg2d 35175 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 29421 axtgeucl 28814 df-trkge 28793 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 29434 axtgcont 28811 axtgcont1 28810 df-trkgb 28791 |
| [Schwabhauser] p. 24 | Theorem A10 | prlngmo 29312 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 36569 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 36571 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 36574 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 36578 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 36579 tgcgrcomimp 28819 tgcgrcoml 28821 tgcgrcomr 28820 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 36584 tgcgrtriv 28826 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 36588 tg5segofs 35186 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 35183 df-ofs 36565 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 36590 tgcgrextend 28827 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 36592 tgsegconeq 28828 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36604 btwntriv2 36594 tgbtwntriv2 28830 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 36595 tgbtwncom 28831 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36598 tgbtwntriv1 28834 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36599 tgbtwnswapid 28835 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36605 btwnintr 36601 tgbtwnexch2 28839 tgbtwnintr 28836 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36607 btwnexch3 36602 tgbtwnexch 28841 tgbtwnexch3 28837 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36606 tgbtwnouttr 28840 tgbtwnouttr2 28838 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 29417 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36609 tgbtwndiff 28849 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28842 trisegint 36610 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36626 tgifscgr 28851 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28901 colrot1 28902 colrot2 28903 lncom 28970 lnrot1 28971 lnrot2 28972 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36622 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36627 tgcgrsub 28852 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36637 tgcgrxfr 28861 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28860 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36623 df-cgrg 28854 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28854 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36638 tgbtwnxfr 28873 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36644 colinearperm2 36646 colinearperm3 36645 colinearperm4 36647 colinearperm5 36648 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28876 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36621 tgellng 28896 tglng 28889 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36649 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36657 lnxfr 28909 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36658 lnext 28910 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36662 tgfscgr 28911 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36663 lncgr 28912 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36624 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36665 lnid 28913 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36666 tgidinside 28914 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36683 tgbtwnconn1 28918 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36684 tgbtwnconn2 28919 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36685 tgbtwnconn3 28920 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36691 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36689 legov 28928 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28929 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28942 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36692 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36694 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36696 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36697 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36698 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36695 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36700 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28930 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28932 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28933 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28934 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28935 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36707 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36708 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36703 df-outsideof 36702 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36704 ishlg 28948 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28953 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28955 outsideofrflx 36709 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28949 hlcomd 28950 outsideofcom 36710 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28956 outsideoftr 36711 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreq 28965 hlcgreu 28964 outsideofeu 36713 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36720 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36721 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36714 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36729 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36730 tglineelsb2 28980 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36732 linerflx1 36731 linerflx2 36733 tglinecom 28983 tglinerflx1 28981 tglinerflx2 28982 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36735 tglinethru 28984 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36719 tglng 28889 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28937 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36738 tglinethrueu 28987 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36739 tglineineq 28991 tglineinsn 28992 tglineinteq 28994 tglineintmo 28990 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28998 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28999 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 29000 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 29018 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 29014 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 29006 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 29005 ismir 29011 mirbtwn 29010 mircgr 29009 mirfv 29008 mirval 29007 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 29016 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 29017 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 29018 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 29021 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 29022 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 29027 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 29024 mirbtwni 29023 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 29025 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 29037 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 29041 symquadmid 29184 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 29038 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 29039 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 29040 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 29043 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 29044 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 29053 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 29049 israg 29052 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 29054 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 29055 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 29057 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 29058 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 29059 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 29060 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 29061 ragncol 29064 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 29062 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 29068 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 29072 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 29069 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 29051 isperp 29067 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 29070 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 29077 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 29086 colperpexlem2 29087 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 29089 colperpexlem3 29088 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 29094 midex 29093 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 29091 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 29100 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 29095 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 29104 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 29107 opphllem6 29108 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 29110 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28809 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 29113 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 29121 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 29116 hpgbr 29118 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 29123 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 29122 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 29124 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 29125 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 29126 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 29127 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 29128 |
| [Schwabhauser] p. 74 | Lemma 9.22 | lnincplng 29142 |
| [Schwabhauser] p. 74 | Theorem 9.21 | plngcp 29144 |
| [Schwabhauser] p. 74 | Theorem 9.24 | plngrot 29148 |
| [Schwabhauser] p. 74 | Definition 9.20 | df-plng 29132 elplng 29138 |
| [Schwabhauser] p. 75 | Theorem 9.25 | lnssplng 29150 lnssplng1 29151 |
| [Schwabhauser] p. 76 | Theorem 9.26 | plng3p 29155 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 29169 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 29159 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 29173 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 29174 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 29175 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 29176 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 29177 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 29180 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 29182 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 29160 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 29183 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 29187 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 29188 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 29189 lnperpexs 29190 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 29191 trgcopyeu 29193 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 29218 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 29196 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 29205 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 29203 cgrahl2 29204 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 29206 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 29207 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 29209 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 29210 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 29214 cgrahl 29215 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 29219 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 29220 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 29221 acopyeu 29222 |
| [Schwabhauser] p. 98 | Theorem 11.16 | ragcgra 29223 |
| [Schwabhauser] p. 98 | Theorem 11.17 | cgrarag 29224 |
| [Schwabhauser] p. 98 | Theorem 11.18 | ragsupplcgra 29225 |
| [Schwabhauser] p. 99 | Theorem 11.19 | ragraghl 29226 |
| [Schwabhauser] p. 99 | Theorem 11.20 | perpeq 29228 |
| [Schwabhauser] p. 99 | Theorem 11.22 | tgaaddcpbl 29232 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 29240 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 29244 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 29237 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 29252 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 29245 isleag 29246 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 29280 tgsas1 29279 tgsas2 29281 tgsas3 29282 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 29284 tgasa1 29283 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 29285 tgsss2 29286 tgsss3 29287 |
| [Schwabhauser] p. 121 | Definition 12.2 | df-prlng 29295 |
| [Schwabhauser] p. 122 | Theorem 12.4 | prlngref 29298 |
| [Schwabhauser] p. 122 | Theorem 12.5 | prlngsym 29299 |
| [Schwabhauser] p. 122 | Theorem 12.6 | prlnghpg 29304 |
| [Schwabhauser] p. 122 | Theorem 12.7 | dfprlng2 29305 dfprlng3 29306 |
| [Schwabhauser] p. 122 | Theorem 12.9 | perpprlng 29308 |
| [Schwabhauser] p. 122 | Theorem 12.10 | prlngex 29309 |
| [Schwabhauser] p. 123 | Theorem 12.11 | prlngmo 29312 prlngmo2 29314 |
| [Schwabhauser] p. 124 | Theorem 12.13 | prlngeu 29313 |
| [Schwabhauser] p. 124 | Theorem 12.14 | prlngpln4 29316 |
| [Schwabhauser] p. 124 | Theorem 12.15 | prlngplngtr 29317 |
| [Schwabhauser] p. 125 | Theorem 12.16 | prlnginn0 29318 |
| [Schwabhauser] p. 125 | Theorem 12.17 | prlngmid2 29319 |
| [Schwabhauser] p. 126 | Theorem 12.18 | symquadprlng 29320 |
| [Schwabhauser] p. 126 | Theorem 12.19 | prlngsymquad 29322 prlngsymquadopp 29323 |
| [Schwabhauser] p. 126 | Theorem 12.20 | quadcgrprlng 29324 |
| [Schwabhauser] p. 126 | Theorem 12.21 | tgaltai 29325 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27508 dchrsum 27506 dchrsum2 27505 sumdchr 27509 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27510 sum2dchr 27511 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 20199 ablfacrp2 20200 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27453 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27454 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27461 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27719 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27722 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27776 vmalogdivsum2 27775 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27766 dirith2 27765 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27764 rpvmasum 27763 rpvmasum2 27749 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27724 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27762 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27729 dchrisumlem1 27726 dchrisumlem2 27727 dchrisumlem3 27728 dchrisumlema 27725 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27732 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27761 dchrmusumlem 27759 dchrvmasumlem 27760 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27731 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27733 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27757 dchrisum0re 27750 dchrisumn0 27758 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27743 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27747 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27748 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27803 pntrsumbnd2 27804 pntrsumo1 27802 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27767 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27769 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27771 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27774 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27779 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27780 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27785 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27787 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27788 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27796 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27797 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27794 selberg3lem2 27795 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27798 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27792 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27805 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27806 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27807 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27821 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27833 pntlemb 27834 pntlemc 27832 pntlemd 27831 pntlemg 27835 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27833 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27825 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27830 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27833 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27846 pntleml 27848 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 34255 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 34242 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 34274 constrinvcl 34285 constrmulcl 34283 constrnegcl 34275 constrsqrtcl 34291 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 34261 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 34271 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 34293 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 34303 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4255 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4359 dif0 4330 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4450 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4432 |
| [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 4596 |
| [Stoll] p. 43 | Definition | uniiun 5021 |
| [Stoll] p. 44 | Definition | intiin 5022 |
| [Stoll] p. 45 | Definition | df-iin 4957 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4956 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 407 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4255 |
| [Strang] p. 242 | Section 6.3 | expgrowth 45161 |
| [Suppes] p. 22 | Theorem 2 | eq0 4300 eq0f 4297 |
| [Suppes] p. 22 | Theorem 4 | eqss 3949 eqssd 3951 eqssi 3950 |
| [Suppes] p. 23 | Theorem 5 | ss0 4355 ss0b 4354 |
| [Suppes] p. 23 | Theorem 6 | sstr 3942 sstrALT2 45659 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4054 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4056 |
| [Suppes] p. 23 | Theorem 9 | psstr 4059 |
| [Suppes] p. 23 | Theorem 10 | pssss 4049 |
| [Suppes] p. 25 | Theorem 12 | elin 3918 elun 4103 |
| [Suppes] p. 26 | Theorem 15 | inidm 4175 |
| [Suppes] p. 26 | Theorem 16 | in0 4348 |
| [Suppes] p. 27 | Theorem 23 | unidm 4107 |
| [Suppes] p. 27 | Theorem 24 | un0 4347 |
| [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 4328 |
| [Suppes] p. 29 | Theorem 33 | difin 4221 |
| [Suppes] p. 29 | Theorem 34 | indif 4229 |
| [Suppes] p. 29 | Theorem 35 | undif1 4433 |
| [Suppes] p. 29 | Theorem 36 | difun2 4440 |
| [Suppes] p. 29 | Theorem 37 | difin0 4431 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4429 |
| [Suppes] p. 29 | Theorem 39 | difundi 4239 |
| [Suppes] p. 29 | Theorem 40 | difindi 4241 |
| [Suppes] p. 30 | Theorem 41 | nalset 5275 |
| [Suppes] p. 39 | Theorem 61 | uniss 4878 |
| [Suppes] p. 39 | Theorem 65 | uniop 5496 |
| [Suppes] p. 41 | Theorem 70 | intsn 4947 |
| [Suppes] p. 42 | Theorem 71 | intpr 4945 intprg 4944 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5451 |
| [Suppes] p. 42 | Theorem 78 | intun 4943 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4994 dfiun2g 4992 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4995 |
| [Suppes] p. 47 | Theorem 86 | elpw 4564 elpw2 5303 elpw2g 5302 elpwg 4563 elpwgdedVD 45741 |
| [Suppes] p. 47 | Theorem 87 | pwid 4583 |
| [Suppes] p. 47 | Theorem 89 | pw0 4776 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4777 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5674 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5817 xpindir 5818 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5728 xpundir 5729 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9572 |
| [Suppes] p. 58 | Theorem 2 | relss 5766 |
| [Suppes] p. 59 | Theorem 4 | eldm 5888 eldm2 5889 eldm2g 5887 eldmg 5886 |
| [Suppes] p. 59 | Definition 3 | df-dm 5669 |
| [Suppes] p. 60 | Theorem 6 | dmin 5899 |
| [Suppes] p. 60 | Theorem 8 | rnun 6140 |
| [Suppes] p. 60 | Theorem 9 | rnin 6141 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5876 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5866 brcnvg 5863 |
| [Suppes] p. 62 | Equation 5 | elcnv 5860 elcnv2 5861 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6104 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6139 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6137 |
| [Suppes] p. 63 | Definition | dftrrels2 39409 |
| [Suppes] p. 63 | Theorem 20 | co02 6261 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5963 |
| [Suppes] p. 63 | Definition 7 | df-co 5668 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5873 |
| [Suppes] p. 64 | Theorem 27 | coass 6266 |
| [Suppes] p. 65 | Theorem 31 | resundi 5990 |
| [Suppes] p. 65 | Theorem 34 | elima 6065 elima2 6066 elima3 6067 elimag 6064 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6145 |
| [Suppes] p. 66 | Theorem 40 | dminss 6148 |
| [Suppes] p. 66 | Theorem 41 | imainss 6149 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6152 |
| [Suppes] p. 81 | Definition 34 | dfec2 8702 |
| [Suppes] p. 82 | Theorem 72 | elec 8746 elecALTV 39021 elecg 8744 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 39445 erth 8754 erth2 8755 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 39448 erdisj 8757 |
| [Suppes] p. 83 | Definition 35, | df-parts 39618 dfmembpart2 39623 |
| [Suppes] p. 89 | Theorem 96 | map0b 8893 |
| [Suppes] p. 89 | Theorem 97 | map0 8897 map0g 8894 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8898 mapsnd 8896 |
| [Suppes] p. 89 | Theorem 99 | mapss 8899 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 10074 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 10073 |
| [Suppes] p. 92 | Theorem 1 | enref 8994 enrefg 8993 |
| [Suppes] p. 92 | Theorem 2 | ensym 9012 ensymb 9011 ensymi 9013 |
| [Suppes] p. 92 | Theorem 3 | entr 9015 |
| [Suppes] p. 92 | Theorem 4 | unen 9055 |
| [Suppes] p. 94 | Theorem 15 | endom 8988 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 9009 |
| [Suppes] p. 94 | Theorem 17 | domtr 9016 |
| [Suppes] p. 95 | Theorem 18 | sbth 9098 |
| [Suppes] p. 97 | Theorem 23 | canth2 9131 canth2g 9132 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9102 df-sdom 8958 dfsdom2 9101 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9115 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9104 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9103 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9113 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8991 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9116 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9111 |
| [Suppes] p. 98 | Exercise 4 | fundmen 9041 fundmeng 9042 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9076 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9112 |
| [Suppes] p. 104 | Theorem 37 | fofi 9286 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9291 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9291 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10562 |
| [Suppes] p. 130 | Definition 3 | df-tr 5217 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7782 |
| [Suppes] p. 134 | Definition 6 | df-suc 6367 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7900 finds 7896 finds1 7899 finds2 7898 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9634 isfinite2 9271 isfiniteg 9273 unbnn 9269 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10930 df-ltpq 10922 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7862 tfinds 7859 tfinds2 7863 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8541 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8543 |
| [Suppes] p. 211 | Theorem 25 | oaass 8551 |
| [Suppes] p. 225 | Definition 8 | iscard2 9984 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10574 |
| [Suppes] p. 228 | Theorem 59 | harcard 9986 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 10072 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6414 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7795 onminsb 7796 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10584 |
| [Suppes] p. 229 | Theorem 65 | alephcard 10076 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 10083 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 10077 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9948 |
| [Suppes] p. 242 | Theorem 6 | weth 10500 |
| [Suppes] p. 242 | Theorem 8 | entric 10568 |
| [Suppes] p. 242 | Theorem 9 | carden 10562 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 36277 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 36281 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2734 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2754 wl-df.cleq 38264 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2837 wl-df.clel 38267 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2756 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2782 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7420 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3741 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5390 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4612 elpr2 4614 elpr2g 4613 elprg 4610 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4602 elsn2 4629 elsn2g 4628 elsng 4601 velsn 4603 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5447 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4597 sneqr 4803 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4608 dfsn2 4600 dfsn2ALT 4609 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7746 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5456 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5443 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5427 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7749 unexg 7748 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4655 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4871 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3909 df-un 3907 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4887 uniprg 4886 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5346 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4653 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6434 elsucg 6432 sstr2 3941 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4108 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4158 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4121 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4176 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4233 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4234 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3922 df-ss 3919 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4562 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4136 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3920 sseqin2 4172 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3956 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4185 inss2 4186 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 3998 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4881 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5428 sspwimp 45742 sspwimpALT 45749 sspwimpALT2 45752 sspwimpcf 45744 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5435 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5236 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3415 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5268 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3905 |
| [TakeutiZaring] p. 20 | Definition 5.14 | bj-dfnul2 37273 dfnul2 4285 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4328 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4303 n0f 4299 neq0 4302 neq0f 4298 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9571 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9714 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9729 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3455 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5281 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4353 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5289 ssexg 5288 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5284 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9583 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9575 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4317 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4085 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4249 undif3VD 45706 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4086 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4093 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3079 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3089 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7755 xpexg 7752 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5666 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6608 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6786 fun11 6611 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6550 svrelfun 6609 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5875 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5877 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5671 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5672 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5668 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6191 dfrel2 6186 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5675 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5796 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5803 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5816 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 6002 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5982 opelresi 5984 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 6009 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5998 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 6003 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6579 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6108 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6577 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6788 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2636 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30881 df-fv 6545 fv3 6900 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7925 cnvexg 7924 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7909 dmexg 7901 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7910 rnexg 7902 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 45278 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7920 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6895 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 48064 tz6.12-1-afv2 48131 tz6.12-1 6905 tz6.12-afv 48063 tz6.12-afv2 48130 tz6.12 6906 tz6.12c-afv2 48132 tz6.12c 6904 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 48127 tz6.12-2 6869 tz6.12i-afv2 48133 tz6.12i 6908 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6540 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6541 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6543 wfo 6535 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6542 wf1 6534 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6544 wf1o 6536 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 7026 eqfnfv2 7027 eqfnfv2f 7030 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6980 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7219 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7217 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6624 funimaexg 6623 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5108 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5568 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5620 dffr3 6099 eliniseg 6094 iniseg 6097 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5559 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5636 fr3nr 7774 frirr 5635 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5612 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7776 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5623 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5645 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6349 tz6.26i 6350 wefrc 5653 wereu2 5656 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6351 wfii 6352 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6546 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7333 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7334 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7340 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7341 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7342 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7346 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7353 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7355 |
| [TakeutiZaring] p. 35 | Notation | wtr 5216 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 45279 tz7.2 5642 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5221 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6374 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6382 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6383 ordelordALT 45362 ordelordALTVD 45691 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6389 ordelssne 6388 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6387 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6392 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7784 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7785 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6365 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6394 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 45374 ordon 7779 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7780 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7852 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6410 ontr2d 36782 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5218 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7794 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7830 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6468 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6467 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7781 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4902 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6367 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6444 sucidg 6445 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7812 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6458 ordnbtwn 6457 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7827 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6366 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7880 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7885 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7840 ordelsuc 7819 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7821 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7850 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7867 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7888 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7889 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7890 |
| [TakeutiZaring] p. 43 | Remark | omon 7877 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9617 omex 9625 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7875 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7895 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7892 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7893 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7870 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4925 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5235 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4926 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5312 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7797 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6413 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4911 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9642 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7792 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8367 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8389 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8390 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8391 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8398 tz7.44-2 8399 tz7.44-3 8400 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8359 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8354 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8338 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8437 tz7.49c 8438 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8435 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8434 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8436 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2682 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 10017 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 10018 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8522 oasuc 8514 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7860 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8525 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8506 oa0r 8528 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8526 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8538 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8610 nnaordi 8609 oaord 8537 oaordi 8536 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5012 uniss2 4905 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8540 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8545 oawordex 8547 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8602 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8639 |
| [TakeutiZaring] p. 60 | Remark | oancom 9633 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8550 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8607 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8542 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8509 omlim 8523 omsuc 8516 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8507 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8604 nnmcl 8603 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8623 nnmordi 8622 omord 8558 omordi 8556 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8559 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8627 omwordri 8562 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8529 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8532 om1r 8533 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8565 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8567 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8568 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8569 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8570 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8599 oe0 8512 oelim 8524 oesuc 8517 onesuc 8520 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8510 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8577 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8578 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8511 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8535 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8579 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8585 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8583 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8584 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8588 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8590 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9710 tz9.1 9711 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9749 r10 9753 r1lim 9757 r1limg 9756 r1suc 9755 r1sucg 9754 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9765 r1ord2 9766 r1ordg 9763 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9775 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9800 tz9.13 9776 tz9.13g 9777 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9750 rankval 9801 rankvalb 9782 rankvalg 9802 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9824 rankelb 9809 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9838 rankval3 9825 rankval3b 9811 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9814 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9780 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9819 rankr1c 9806 rankr1g 9817 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9820 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9834 rankssb 9833 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9827 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9826 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10480 dfac3 10127 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 10036 numth 10477 numth2 10476 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10557 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10558 cardid2 9961 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9968 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10562 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9967 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9952 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9973 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9965 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9151 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 9027 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9156 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9080 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9971 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10104 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9203 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9211 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10105 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9208 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10094 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 10072 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9980 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10221 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9295 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8959 isfi 8984 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9212 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10540 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9073 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10532 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10191 unxpdom 9232 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9982 cardsdomelir 9981 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9234 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 10020 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8831 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10573 infxpidm2 10023 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10212 infxp 10219 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9085 pw2f1o 9083 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9144 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10492 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10487 ac6s5 10496 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10554 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10555 uniimadomf 10556 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10279 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10274 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10258 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10255 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10262 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10269 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10278 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10594 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10256 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10281 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10103 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10102 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10114 alephfp2 10115 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10711 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10118 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10581 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10595 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10596 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 39758 |
| [Tarski] p. 67 | Scheme B5 | sp 2221 |
| [Tarski] p. 68 | Lemma 6 | avril1 30944 equid 2045 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2050 |
| [Tarski] p. 70 | Lemma 14 | spim 2418 spime 2420 spimew 2004 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2215 ax-c15 39764 ax12i 1999 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2122 |
| [Tarski] p. 75 | Axiom B7 | ax6v 2001 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1943 ax5ALT 39782 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2041 ax-8 2147 ax-9 2155 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28806 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28807 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28809 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28809 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28810 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16335 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 38410 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 38412 |
| [Weierstrass] p. 272 | Definition | df-mdet 22811 mdetuni 22848 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 917 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 882 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 883 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 933 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 983 |
| [WhiteheadRussell] p. 100 | Theorem *2.01 | pm2.01 190 |
| [WhiteheadRussell] p. 100 | Theorem *2.02 | ax-1 6 |
| [WhiteheadRussell] p. 100 | Theorem *2.03 | con2 136 |
| [WhiteheadRussell] p. 100 | Theorem *2.04 | pm2.04 91 wl-luk-pm2.04 38201 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 44642 imim2 59 wl-luk-imim2 38196 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 47909 imim1 84 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 910 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2689 syl 18 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 916 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 23 wl-luk-id 38199 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 908 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 143 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 911 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 131 notnotrALT2 45751 wl-luk-notnotr 38200 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 147 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 44672 axfrege28 44671 con3 154 |
| [WhiteheadRussell] p. 103 | Theorem *2.17 | ax-3 8 |
| [WhiteheadRussell] p. 103 | Theorem *2.18 | pm2.18 129 |
| [WhiteheadRussell] p. 104 | Theorem *2.2 | orc 881 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 938 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 124 wl-luk-pm2.21 38193 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 125 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 903 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 954 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 30882 pm2.27 43 wl-luk-pm2.27 38191 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 936 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 39121 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 937 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 985 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 986 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 984 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1104 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 920 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 921 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 957 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 57 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 895 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 896 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5 170 pm2.5g 169 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6 193 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 897 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 898 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 899 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 174 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 865 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 866 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 902 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 904 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 194 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 913 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 955 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 956 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 195 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 905 pm2.67 906 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 177 pm2.521g 175 pm2.521g2 176 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 912 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 988 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 914 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 206 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 989 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 990 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 947 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 945 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 987 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 991 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 85 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 946 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 110 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 1007 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 475 pm3.2im 161 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 1008 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 1009 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 1010 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 1011 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 477 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 465 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 408 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 815 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 454 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 455 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 488 simplim 168 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 490 simprim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 777 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 778 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 820 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 634 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 822 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 498 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 499 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 975 pm3.44 974 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 821 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 479 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 978 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34b 319 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 264 |
| [WhiteheadRussell] p. 117 | Theorem *4.11 | notbi 322 |
| [WhiteheadRussell] p. 117 | Theorem *4.12 | con2bi 356 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotb 318 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14 819 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 846 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 225 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 818 bitr 817 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 574 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 918 pm4.25 919 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 466 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1025 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 884 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 474 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 935 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 645 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 931 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 649 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 992 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1105 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1023 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1069 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1040 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 1012 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 1014 pm4.45 1013 pm4.45im 841 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 998 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 867 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 555 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 997 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 1000 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 1001 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 1002 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 1003 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 999 pm4.56 1004 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 1005 pm4.57 1006 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 410 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 870 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 403 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 863 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 411 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 864 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67 404 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 567 pm4.71d 571 pm4.71i 569 pm4.71r 568 pm4.71rd 572 pm4.71ri 570 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 964 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 537 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 950 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 527 pm4.76 528 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 976 pm4.77 977 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 948 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1021 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 398 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81 399 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 1041 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1042 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 350 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 351 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 354 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 392 impexp 456 pm4.87 857 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 836 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 959 pm5.11g 958 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 960 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 962 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 961 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1030 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1031 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1029 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbn 386 pm5.18 384 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 391 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 837 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1032 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1065 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1066 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 915 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 583 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 393 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 364 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6 1017 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 968 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 844 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 584 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 849 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 838 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 847 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 394 pm5.41 395 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 553 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 552 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 1022 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1035 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 963 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1016 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1036 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1037 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1045 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 369 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 273 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 1046 |
| [WhiteheadRussell] p. 145 | Theorem *10.3 | bj-alsyl 37324 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 45184 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 45185 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1903 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 45186 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 45187 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 45188 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1926 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 45189 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 45190 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 45191 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 45192 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 45193 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 45195 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 45196 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 45197 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 45194 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2127 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 45200 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 45201 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2107 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2197 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1862 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1863 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 45202 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 45203 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 45204 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 45205 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 45207 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 45206 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1920 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 45209 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 45210 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 45208 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1861 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 45211 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 45212 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1879 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 45213 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2377 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1893 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 45218 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 45214 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 45215 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 45216 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 45217 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 45222 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 45219 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 45220 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 45221 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 45223 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2596 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 45233 pm13.13b 45234 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 45235 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3038 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3039 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3623 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 45241 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 45242 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 45236 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 45377 pm13.193 45237 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 45238 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 45239 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 45240 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 45247 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 45246 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 45245 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3804 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 45248 pm14.122b 45249 pm14.122c 45250 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 45251 pm14.123b 45252 pm14.123c 45253 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 45255 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 45254 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 45256 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6518 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 45257 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6519 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 45258 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 45260 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2660 eupickbi 2663 sbaniota 45261 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 45259 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2611 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 45262 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30881 df-fv 6545 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 10009 pm54.43lem 10008 |
| [Young] p. 141 | Definition of operator ordering | leop2 32606 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32612 idleop 32613 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 43671 |
| [vandenDries] p. 43 | Theorem 62 | pellex 43678 pellexlem1 43672 |