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 17843 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17843 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18252 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17864 0funcg 50269 df-termc 50657 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 50734 prsthinc 50648 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 50762 df-mndtc 50762 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 50758 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17887 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 50750 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 50775 oppgoppchom 50774 oppgoppcid 50776 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17957 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17945 invisoinvl 17966 |
| [Adamek] p. 28 | Example 3.13 | idinv 17965 idiso 17964 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17950 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17924 df-iso 17925 dfiso2 17948 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17931 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17982 cicerALT 50230 |
| [Adamek] p. 29 | Definition 3.15 | cic 17975 df-cic 17972 |
| [Adamek] p. 29 | Definition 3.17 | df-func 18034 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17946 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17947 isoco 17953 |
| [Adamek] p. 30 | Remark 3.19 | df-func 18034 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 18057 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 50488 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 18050 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 50758 discthing 50645 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 50602 prsthinc 50648 thincciso 50637 thincciso2 50639 thincciso3 50640 thinccisod 50638 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 50762 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 18064 cofucla 50280 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 50346 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18287 catcisoi 50584 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18342 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 18083 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 18082 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18342 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 18107 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 18113 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 18112 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18327 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18327 |
| [Adamek] p. 39 | Remark 3.42 | 2oppf 50316 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 50307 funcoppc 18051 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18275 elcatchom 50581 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 18101 fthoppf 50348 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 18100 fulloppf 50347 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18284 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 50269 df-catc 18275 |
| [Adamek] p. 45 | Exercise 3G | incat 50785 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 50788 nelsubc3 50255 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 50335 imasubc2 50336 imasubc3 50340 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 18014 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 18015 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 50255 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 18026 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17988 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 50344 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 50343 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 50345 ressffth 18116 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 50786 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 18122 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 18143 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 18147 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 18123 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 18149 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 50269 df-inito 18160 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 50269 df-termc 50657 initc 50275 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21786 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 18161 oppctermo 50420 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 18188 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 18192 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 50421 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 18162 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21787 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 18195 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17923 |
| [Adamek] p. 107 | Example 7.20(7) | thincinv 50653 |
| [Adamek] p. 108 | Example 7.25(4) | thincsect2 50652 |
| [Adamek] p. 110 | Example 7.33(9) | thincmon 50617 |
| [Adamek] p. 110 | Proposition 7.35 | sectmon 17958 |
| [Adamek] p. 112 | Proposition 7.42 | sectepi 17960 |
| [Adamek] p. 185 | Section 10.67 | updjud 10016 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 50829 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 50829 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 50829 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 50830 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 50830 |
| [Adamek] p. 478 | Item Rng | df-ringc 20899 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 49736 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 49758 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14717 df-pfx 14822 df-substr 14790 df-word 14660 lencl 14679 wrd0 14685 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 25028 df-nmoo 31348 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32756 hmopidmchi 32754 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32804 pjcmul2i 32805 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 32521 unoplin 32523 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 32522 unopadj2 32541 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 32616 lnopunii 32615 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32689 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 28314 |
| [Alling] p. 184 | Axiom B | bdayfo 28035 |
| [Alling] p. 184 | Axiom O | ltsso 28034 |
| [Alling] p. 184 | Axiom SD | nodense 28050 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 28142 |
| [Alling] p. 185 | Theorem | conway 28166 |
| [Alling] p. 185 | Axiom FE | noeta 28101 |
| [Alling] p. 186 | Theorem 4 | lesrec 28186 lesrecd 28187 |
| [Alling], p. 2 | Definition | rp-brsslt 44500 |
| [Alling], p. 3 | Note | nla0001 44503 nla0002 44501 nla0003 44502 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11495 addcan2d 11515 addcan2i 11505 addcand 11514 addcani 11504 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11548 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11607 negsubd 11676 negsubi 11637 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11609 negnegd 11661 negnegi 11629 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11750 subdid 11773 subdii 11766 subdir 11751 subdird 11774 subdiri 11767 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11490 mul01d 11510 mul01i 11501 mul02 11489 mul02d 11509 mul02i 11500 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11954 mulcan2d 11951 mulcand 11950 mulcani 11956 |
| [Apostol] p. 18 | Theorem I.8 | receu 11962 xreceu 33531 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11991 divrecd 12097 divreci 12063 divreczi 12056 |
| [Apostol] p. 18 | Theorem I.10 | recrec 12015 recreci 12050 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11957 mul0ord 11965 mul0ori 11964 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11756 mul2negd 11772 mul2negi 11765 mulneg1 11753 mulneg1d 11770 mulneg1i 11763 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 12033 divadddivd 12138 divadddivi 12080 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 12018 divmuldivd 12135 divmuldivi 12078 rdivmuldivd 20644 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 12019 divdivdivd 12141 divdivdivi 12081 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 13145 rpaddcld 13180 rpmulcl 13146 rpmulcld 13181 |
| [Apostol] p. 20 | Axiom 8 | rpneg 13155 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 13158 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11437 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11910 ltadd1dd 11928 ltadd1i 11871 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12168 ltmul1a 12167 ltmul1i 12236 ltmul1ii 12246 ltmul2 12169 ltmul2d 13207 ltmul2dd 13221 ltmul2i 12239 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11837 msqgt0d 11884 msqgt0i 11854 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11839 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11823 lt0neg1d 11886 ltneg 11817 ltnegd 11895 ltnegi 11861 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11802 lt2addd 11940 lt2addi 11879 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 13122 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12164 recgt0d 12252 recgt0i 12223 recgt0ii 12224 |
| [Apostol] p. 22 | Definition of integers | df-z 12695 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12350 |
| [Apostol] p. 22 | Definition of rationals | df-q 13077 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9447 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12603 |
| [Apostol] p. 26 | Theorem I.29 | arch 12604 archd 46253 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12803 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12605 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 13075 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 13074 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13330 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16510 zneo 12783 zneoALTV 48843 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 27059 msqsqrtd 15611 resqrtth 15423 sqrtth 15533 sqrtthi 15539 sqsqrtd 15610 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12339 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 13041 |
| [Apostol] p. 361 | Remark | crreczi 14373 |
| [Apostol] p. 363 | Remark | absgt0i 15568 |
| [Apostol] p. 363 | Example | abssubd 15624 abssubi 15572 |
| [ApostolNT] p. 7 | Remark | fmtno0 48701 fmtno1 48702 fmtno2 48711 fmtno3 48712 fmtno4 48713 fmtno5fac 48743 fmtnofz04prm 48738 |
| [ApostolNT] p. 7 | Definition | df-fmtno 48689 |
| [ApostolNT] p. 8 | Definition | df-ppi 27428 |
| [ApostolNT] p. 14 | Definition | df-dvds 16424 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16440 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16465 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16460 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16453 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16455 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16441 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16442 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16447 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16482 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16484 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16486 |
| [ApostolNT] p. 15 | Definition | df-gcd 16666 dfgcd2 16720 |
| [ApostolNT] p. 16 | Definition | isprm2 16858 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16829 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 17094 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16686 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16721 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16723 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16702 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16693 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16888 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16890 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 17107 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 17101 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16574 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16763 |
| [ApostolNT] p. 24 | Definition | df-mu 27429 |
| [ApostolNT] p. 25 | Definition | df-phi 16944 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27519 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16969 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16954 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16958 |
| [ApostolNT] p. 32 | Definition | df-vma 27426 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27521 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27544 |
| [ApostolNT] p. 38 | Remark | df-sgm 27430 |
| [ApostolNT] p. 38 | Definition | df-sgm 27430 |
| [ApostolNT] p. 75 | Definition | df-chp 27427 df-cht 27425 |
| [ApostolNT] p. 104 | Definition | congr 16840 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16427 |
| [ApostolNT] p. 106 | Definition | moddvds 16434 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16517 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16518 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 14029 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 14069 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14383 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16459 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16843 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17253 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16845 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16961 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16980 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16962 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27400 |
| [ApostolNT] p. 179 | Definition | df-lgs 27623 lgsprme0 27667 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27668 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27644 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27659 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27716 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27735 2lgsoddprm 27744 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27702 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27711 |
| [ApostolNT] p. 188 | Definition | df-lgs 27623 lgs1 27669 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27660 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27662 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27670 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27671 |
| [Baer] p. 40 | Property (b) | mapdord 42771 |
| [Baer] p. 40 | Property (c) | mapd11 42772 |
| [Baer] p. 40 | Property (e) | mapdin 42795 mapdlsm 42797 |
| [Baer] p. 40 | Property (f) | mapd0 42798 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 42758 mapd1o 42781 |
| [Baer] p. 41 | Property (g) | mapdat 42800 |
| [Baer] p. 44 | Part (1) | mapdpg 42839 |
| [Baer] p. 45 | Part (2) | hdmap1eq 42934 mapdheq 42861 mapdheq2 42862 mapdheq2biN 42863 |
| [Baer] p. 45 | Part (3) | baerlem3 42846 |
| [Baer] p. 46 | Part (4) | mapdheq4 42865 mapdheq4lem 42864 |
| [Baer] p. 46 | Part (5) | baerlem5a 42847 baerlem5abmN 42851 baerlem5amN 42849 baerlem5b 42848 baerlem5bmN 42850 |
| [Baer] p. 47 | Part (6) | hdmap1l6 42954 hdmap1l6a 42942 hdmap1l6e 42947 hdmap1l6f 42948 hdmap1l6g 42949 hdmap1l6lem1 42940 hdmap1l6lem2 42941 mapdh6N 42880 mapdh6aN 42868 mapdh6eN 42873 mapdh6fN 42874 mapdh6gN 42875 mapdh6lem1N 42866 mapdh6lem2N 42867 |
| [Baer] p. 48 | Part 9 | hdmapval 42961 |
| [Baer] p. 48 | Part 10 | hdmap10 42973 |
| [Baer] p. 48 | Part 11 | hdmapadd 42976 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 42950 mapdh6hN 42876 |
| [Baer] p. 48 | Part (7) | mapdh75cN 42886 mapdh75d 42887 mapdh75e 42885 mapdh75fN 42888 mapdh7cN 42882 mapdh7dN 42883 mapdh7eN 42881 mapdh7fN 42884 |
| [Baer] p. 48 | Part (8) | mapdh8 42921 mapdh8a 42908 mapdh8aa 42909 mapdh8ab 42910 mapdh8ac 42911 mapdh8ad 42912 mapdh8b 42913 mapdh8c 42914 mapdh8d 42916 mapdh8d0N 42915 mapdh8e 42917 mapdh8g 42918 mapdh8i 42919 mapdh8j 42920 |
| [Baer] p. 48 | Part (9) | mapdh9a 42922 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 42902 |
| [Baer] p. 49 | Part 12 | hdmap11 42981 hdmapeq0 42977 hdmapf1oN 42998 hdmapneg 42979 hdmaprnN 42997 hdmaprnlem1N 42982 hdmaprnlem3N 42983 hdmaprnlem3uN 42984 hdmaprnlem4N 42986 hdmaprnlem6N 42987 hdmaprnlem7N 42988 hdmaprnlem8N 42989 hdmaprnlem9N 42990 hdmapsub 42980 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 43001 hdmap14lem10 43010 hdmap14lem1a 42999 hdmap14lem2N 43002 hdmap14lem2a 43000 hdmap14lem3 43003 hdmap14lem8 43008 hdmap14lem9 43009 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 43011 hdmap14lem12 43012 hdmap14lem13 43013 hdmap14lem14 43014 hdmap14lem15 43015 hgmapval 43020 |
| [Baer] p. 50 | Part 15 | hgmapadd 43027 hgmapmul 43028 hgmaprnlem2N 43030 hgmapvs 43024 |
| [Baer] p. 50 | Part 16 | hgmaprnN 43034 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 43050 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 43051 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 43052 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 43053 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 43055 hgmapvv 43059 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 43054 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 43056 |
| [Baer] p. 111 | Line 15 | hdmapg 43063 hdmapglem7 43062 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 27060 2irrexpqALT 27129 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 24 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2594 |
| [BellMachover] p. 460 | Notation | df-mo 2564 |
| [BellMachover] p. 460 | Definition | mo3 2589 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2732 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2736 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5238 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5248 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 38054 sepex 5254 |
| [BellMachover] p. 466 | Problem | axpow2 5328 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5329 |
| [BellMachover] p. 466 | Axiom Union | axun2 7753 |
| [BellMachover] p. 468 | Definition | df-ord 6365 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6380 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6387 onelond 37023 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6382 |
| [BellMachover] p. 471 | Definition of N | df-om 7878 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7815 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6367 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9644 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7893 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9769 |
| [BellMachover] p. 478 | Definition | rankval2 9828 rankval2b 9836 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9790 r1ord3g 9787 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9591 |
| [BellMachover] p. 488 | Axiom AC | ac5 10556 dfac4 10202 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10190 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 40452 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32956 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32998 chirredi 32997 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32986 |
| [Beran] p. 3 | Definition of join | sshjval3 31957 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 32219 cmcm2i 32196 cmcm2ii 32201 cmt2N 40383 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 32220 lecmi 32205 lecmii 32206 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 32194 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 32223 cm2ji 32228 cm2mi 32229 |
| [Beran] p. 95 | Definition | df-sh 31810 issh2 31812 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31689 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31702 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31693 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 32431 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 32433 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 32432 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 32434 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31685 his1i 31703 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31686 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31687 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31688 |
| [Beran] p. 96 | Definition of norm | df-hnorm 31571 dfhnorm2 31725 normval 31727 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31787 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 31576 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31844 |
| [Beran] p. 96 | Definition of converge | df-hlim 31575 hlimi 31791 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31736 norm-i 31732 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31740 norm-ii 31741 normlem0 31712 normlem1 31713 normlem2 31714 normlem3 31715 normlem4 31716 normlem5 31717 normlem6 31718 normlem7 31719 normlem7tALT 31722 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31742 norm-iii 31743 |
| [Beran] p. 98 | Remark 3.4 | bcs 31784 bcsiALT 31782 bcsiHIL 31783 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31724 normpar 31758 normpari 31757 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31749 normpyth 31748 normpythi 31745 |
| [Beran] p. 99 | Remark | lnfn0 32650 lnfn0i 32645 lnop0 32569 lnop0i 32573 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32629 nmcfnex 32656 nmcfnexi 32654 nmcopex 32632 nmcopexi 32630 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32657 nmcfnlbi 32655 nmcoplb 32633 nmcoplbi 32631 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32659 lnfnconi 32658 lnopcon 32638 lnopconi 32637 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31759 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31756 norm3adifii 31751 norm3dif 31753 norm3difi 31750 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31904 pjhth 31996 pjhtheu 31997 pjpjhth 32028 pjpjhthi 32029 pjth 25761 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 32009 ococi 32008 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32664 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32665 riesz4 32667 riesz4i 32666 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32682 cnlnadjeu 32681 cnlnadjeui 32680 cnlnadji 32679 cnlnadjlem1 32670 nmopadjlei 32691 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32694 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32693 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32695 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 32539 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32705 nmopcoadji 32704 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32696 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32706 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32703 pjadj2coi 32807 pjadjcoi 32764 |
| [Beran] p. 107 | Definition | df-ch 31824 isch2 31826 |
| [Beran] p. 107 | Remark 3.12 | choccl 31909 isch3 31844 occl 31907 ocsh 31886 shoccl 31908 shocsh 31887 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 32011 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31935 |
| [Beran] p. 109 | Property (i) | pjadj2 32790 pjadj3 32791 pjadji 32288 pjadjii 32277 |
| [Beran] p. 109 | Property (ii) | pjidmco 32784 pjidmcoi 32780 pjidmi 32276 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32776 |
| [Beran] p. 111 | Remark | ho0val 32353 pjch1 32273 |
| [Beran] p. 111 | Definition | df-hfmul 32337 df-hfsum 32336 df-hodif 32335 df-homul 32334 df-hosum 32333 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 32274 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 32297 pjchi 32035 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 32042 pjoc2i 32041 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 32283 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32768 pjssmii 32284 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32767 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32766 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32771 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32769 pjssge0ii 32285 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32770 pjdifnormii 32286 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1808 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1806 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1809 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1804 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34967 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34975 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34973 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34977 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34997 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 35028 df-sitm 35006 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 35028 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 35005 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29627 isuhgrop 29649 isusgrop 29744 isuspgrop 29743 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 49035 df-subgr 29850 uhgrspan1 29885 uhgrspansubgr 29873 |
| [Bollobas] p. 3 | Definition | df-gric 49055 gricuspgr 49092 isuspgrim 49070 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 30036 df-clnbgr 48993 df-cusgr 29994 df-nbgr 29915 fusgrmaxsize 30046 |
| [Bollobas] p. 4 | Definition | df-upwlks 49308 df-wlks 30181 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 30132 finsumvtxdgeven 30134 fusgr1th 30133 fusgrvtxdgonume 30136 vtxdgoddnumeven 30135 |
| [Bollobas] p. 5 | Notation | df-pths 30300 |
| [Bollobas] p. 5 | Definition | df-crcts 30374 df-cycls 30375 df-trls 30276 df-wlkson 30182 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29638 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 49373 df-cllaw 49359 df-mgm 18817 df-mgm2 49392 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 49374 df-asslaw 49361 df-sgrp 18909 df-sgrp2 49394 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 49393 df-comlaw 49360 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18925 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33630 mndlactf1o 33634 mndractf1 33632 mndractf1o 33635 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20462 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20376 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 34308 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 34312 assarrginv 34311 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 34353 fldextrspunfld 34351 fldextrspunlem1 34350 fldextrspunlem2 34352 fldextrspunlsp 34349 fldextrspunlsplem 34348 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 34112 dfufd2 34125 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7295 fcofo 7296 |
| [BourbakiTop1] p. | Remark | xnegmnf 13341 xnegpnf 13340 |
| [BourbakiTop1] p. | Remark | rexneg 13342 |
| [BourbakiTop1] p. | Remark 3 | ust0 24540 ustfilxp 24533 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24410 |
| [BourbakiTop1] p. | Criterion | ishmeo 24079 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24603 iducn 24602 snfil 24184 |
| [BourbakiTop1] p. | Example 2 | neifil 24200 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 24387 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24623 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 34632 |
| [BourbakiTop1] p. | Paragraph 3 | infil 24183 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24595 df-ust 24521 filintn0 24181 filn0 24182 istgp 24397 ucnprima 24601 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24606 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24617 df-usp 24577 df-utop 24551 trust 24549 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 34531 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23435 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23588 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24526 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24529 |
| [BourbakiTop1] p. | Property V_ii | innei 23444 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23452 neissex 23446 |
| [BourbakiTop1] p. | Proposition 1 | neips 23432 neiss 23428 ucncn 24604 ustund 24542 ustuqtop 24566 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23586 neiptopreu 23452 utop2nei 24570 utop3cls 24571 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24611 uspreg 24593 utopreg 24572 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 24011 imasncls 24012 imasnopn 24010 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 24320 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24528 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24530 |
| [BourbakiTop1] p. | Property V_iii | elnei 23430 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24622 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24527 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24531 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23706 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 24166 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 23213 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 34528 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 47148 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 47150 stoweid 47149 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 47087 stoweidlem10 47096 stoweidlem14 47100 stoweidlem15 47101 stoweidlem35 47121 stoweidlem36 47122 stoweidlem37 47123 stoweidlem38 47124 stoweidlem40 47126 stoweidlem41 47127 stoweidlem43 47129 stoweidlem44 47130 stoweidlem46 47132 stoweidlem5 47091 stoweidlem50 47136 stoweidlem52 47138 stoweidlem53 47139 stoweidlem55 47141 stoweidlem56 47142 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 47109 stoweidlem24 47110 stoweidlem27 47113 stoweidlem28 47114 stoweidlem30 47116 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 47120 stoweidlem59 47145 stoweidlem60 47146 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 47131 stoweidlem49 47135 stoweidlem7 47093 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 47117 stoweidlem39 47125 stoweidlem42 47128 stoweidlem48 47134 stoweidlem51 47137 stoweidlem54 47140 stoweidlem57 47143 stoweidlem58 47144 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 47111 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 47103 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 47097 stoweidlem13 47099 stoweidlem26 47112 stoweidlem61 47147 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 47104 |
| [Bruck] p. 1 | Section I.1 | df-clintop 49373 df-mgm 18817 df-mgm2 49392 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18909 df-sgrp2 49394 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 19250 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5186 |
| [Church] p. 129 | Section II.24 | df-ifp 1079 dfifp2 1080 |
| [Clemente] p. 10 | Definition IT | natded 31005 |
| [Clemente] p. 10 | Definition I` `m,n | natded 31005 |
| [Clemente] p. 11 | Definition E=>m,n | natded 31005 |
| [Clemente] p. 11 | Definition I=>m,n | natded 31005 |
| [Clemente] p. 11 | Definition E` `(1) | natded 31005 |
| [Clemente] p. 11 | Definition E` `(2) | natded 31005 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 31005 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 31005 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 31005 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 31005 |
| [Clemente] p. 14 | Proof 5.11 | natded 31005 |
| [Clemente] p. 14 | Definition E` `n | natded 31005 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 31007 ex-natded5.2 31006 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 31010 ex-natded5.3 31009 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 31012 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 31014 ex-natded5.7 31013 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 31016 ex-natded5.8 31015 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 31018 ex-natded5.13 31017 |
| [Clemente] p. 32 | Definition I` `n | natded 31005 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 31005 |
| [Clemente] p. 32 | Definition E` `n,t | natded 31005 |
| [Clemente] p. 32 | Definition I` `n,t | natded 31005 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 31019 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 31020 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 31022 ex-natded9.26 31021 |
| [Cohen] p. 301 | Remark | relogoprlem 26920 |
| [Cohen] p. 301 | Property 2 | relogmul 26921 relogmuld 26954 |
| [Cohen] p. 301 | Property 3 | relogdiv 26922 relogdivd 26955 |
| [Cohen] p. 301 | Property 4 | relogexp 26925 |
| [Cohen] p. 301 | Property 1a | log1 26914 |
| [Cohen] p. 301 | Property 1b | loge 26915 |
| [Cohen4] p. 348 | Observation | relogbcxpb 27116 |
| [Cohen4] p. 349 | Property | relogbf 27120 |
| [Cohen4] p. 352 | Definition | elogb 27099 |
| [Cohen4] p. 361 | Property 2 | relogbmul 27106 |
| [Cohen4] p. 361 | Property 3 | logbrec 27111 relogbdiv 27108 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 27104 |
| [Cohen4] p. 361 | Property 6 | relogbexp 27109 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 27097 |
| [Cohen4] p. 361 | Property 1(b) | logb1 27098 |
| [Cohen4] p. 367 | Property | logbchbase 27100 |
| [Cohen4] p. 377 | Property 2 | logblt 27113 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34960 sxbrsigalem4 34962 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18732 acsinfd 18731 acsinfdimd 18733 acsmap2d 18730 acsmapd 18729 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34965 |
| [Connell] p. 57 | Definition | df-scmat 22807 df-scmatalt 49587 |
| [Conway] p. 4 | Definition | lesrec 28186 lesrecd 28187 |
| [Conway] p. 5 | Definition | addsval 28349 addsval2 28350 df-adds 28347 df-muls 28494 df-negs 28408 |
| [Conway] p. 7 | Theorem | 0lt1s 28199 |
| [Conway] p. 12 | Theorem 12 | pw2cut2 28849 |
| [Conway] p. 16 | Theorem 0(i) | sltsright 28248 |
| [Conway] p. 16 | Theorem 0(ii) | sltsleft 28247 |
| [Conway] p. 16 | Theorem 0(iii) | lesid 28125 |
| [Conway] p. 17 | Theorem 3 | addsass 28392 addsassd 28393 addscom 28353 addscomd 28354 addsrid 28351 addsridd 28352 |
| [Conway] p. 17 | Definition | df-0s 28194 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 28431 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 28428 negsidd 28429 |
| [Conway] p. 18 | Theorem 5 | leadds1 28376 leadds1d 28382 |
| [Conway] p. 18 | Definition | df-1s 28195 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 28423 negscld 28424 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 28367 |
| [Conway] p. 19 | Note | mulsunif2 28557 |
| [Conway] p. 19 | Theorem 7 | addsdi 28542 addsdid 28543 addsdird 28544 mulnegs1d 28547 mulnegs2d 28548 mulsass 28553 mulsassd 28554 mulscom 28526 mulscomd 28527 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28521 mulscld 28522 |
| [Conway] p. 19 | Theorem 8(iii) | lemulsd 28525 ltmuls 28523 ltmulsd 28524 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28531 mulsgt0d 28532 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28605 |
| [Conway] p. 23 | Theorem 11 | eqcuts3 28191 |
| [Conway] p. 24 | Definition | df-reno 28877 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28886 remulscl 28889 renegscl 28885 |
| [Conway] p. 27 | Definition | df-ons 28639 elons2 28645 |
| [Conway] p. 27 | Theorem 14 | ltonsex 28649 |
| [Conway] p. 28 | Theorem 15 | oncutlt 28651 onswe 28659 |
| [Conway] p. 29 | Remark | madebday 28287 newbday 28289 oldbday 28288 |
| [Conway] p. 29 | Definition | df-made 28214 df-new 28216 df-old 28215 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 14002 |
| [Crawley] p. 1 | Definition of poset | df-poset 18488 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 40519 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 41323 dalaw 41019 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 43094 |
| [Crawley] p. 111 | Definition of set W | df-watsN 41123 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 41239 df-ldil 41237 isldil 41243 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 41238 df-trnN 41240 isltrn 41252 ltrnu 41254 |
| [Crawley] p. 112 | Lemma A | cdlema1N 40924 cdlema2N 40925 exatleN 40537 |
| [Crawley] p. 112 | Lemma B | 1cvrat 40609 cdlemb 40927 cdlemb2 41174 cdlemb3 41739 idltrn 41283 l1cvat 40188 lhpat 41176 lhpat2 41178 lshpat 40189 ltrnel 41272 ltrnmw 41284 |
| [Crawley] p. 112 | Lemma C | cdlemc1 41324 cdlemc2 41325 ltrnnidn 41307 trlat 41302 trljat1 41299 trljat2 41300 trljat3 41301 trlne 41318 trlnidat 41306 trlnle 41319 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 41124 |
| [Crawley] p. 113 | Lemma C | cdlemc 41330 cdlemc3 41326 cdlemc4 41327 |
| [Crawley] p. 113 | Lemma D | cdlemd 41340 cdlemd1 41331 cdlemd2 41332 cdlemd3 41333 cdlemd4 41334 cdlemd5 41335 cdlemd6 41336 cdlemd7 41337 cdlemd8 41338 cdlemd9 41339 cdleme31sde 41518 cdleme31se 41515 cdleme31se2 41516 cdleme31snd 41519 cdleme32a 41574 cdleme32b 41575 cdleme32c 41576 cdleme32d 41577 cdleme32e 41578 cdleme32f 41579 cdleme32fva 41570 cdleme32fva1 41571 cdleme32fvcl 41573 cdleme32le 41580 cdleme48fv 41632 cdleme4gfv 41640 cdleme50eq 41674 cdleme50f 41675 cdleme50f1 41676 cdleme50f1o 41679 cdleme50laut 41680 cdleme50ldil 41681 cdleme50lebi 41673 cdleme50rn 41678 cdleme50rnlem 41677 cdlemeg49le 41644 cdlemeg49lebilem 41672 |
| [Crawley] p. 113 | Lemma E | cdleme 41693 cdleme00a 41342 cdleme01N 41354 cdleme02N 41355 cdleme0a 41344 cdleme0aa 41343 cdleme0b 41345 cdleme0c 41346 cdleme0cp 41347 cdleme0cq 41348 cdleme0dN 41349 cdleme0e 41350 cdleme0ex1N 41356 cdleme0ex2N 41357 cdleme0fN 41351 cdleme0gN 41352 cdleme0moN 41358 cdleme1 41360 cdleme10 41387 cdleme10tN 41391 cdleme11 41403 cdleme11a 41393 cdleme11c 41394 cdleme11dN 41395 cdleme11e 41396 cdleme11fN 41397 cdleme11g 41398 cdleme11h 41399 cdleme11j 41400 cdleme11k 41401 cdleme11l 41402 cdleme12 41404 cdleme13 41405 cdleme14 41406 cdleme15 41411 cdleme15a 41407 cdleme15b 41408 cdleme15c 41409 cdleme15d 41410 cdleme16 41418 cdleme16aN 41392 cdleme16b 41412 cdleme16c 41413 cdleme16d 41414 cdleme16e 41415 cdleme16f 41416 cdleme16g 41417 cdleme19a 41436 cdleme19b 41437 cdleme19c 41438 cdleme19d 41439 cdleme19e 41440 cdleme19f 41441 cdleme1b 41359 cdleme2 41361 cdleme20aN 41442 cdleme20bN 41443 cdleme20c 41444 cdleme20d 41445 cdleme20e 41446 cdleme20f 41447 cdleme20g 41448 cdleme20h 41449 cdleme20i 41450 cdleme20j 41451 cdleme20k 41452 cdleme20l 41455 cdleme20l1 41453 cdleme20l2 41454 cdleme20m 41456 cdleme20y 41435 cdleme20zN 41434 cdleme21 41470 cdleme21d 41463 cdleme21e 41464 cdleme22a 41473 cdleme22aa 41472 cdleme22b 41474 cdleme22cN 41475 cdleme22d 41476 cdleme22e 41477 cdleme22eALTN 41478 cdleme22f 41479 cdleme22f2 41480 cdleme22g 41481 cdleme23a 41482 cdleme23b 41483 cdleme23c 41484 cdleme26e 41492 cdleme26eALTN 41494 cdleme26ee 41493 cdleme26f 41496 cdleme26f2 41498 cdleme26f2ALTN 41497 cdleme26fALTN 41495 cdleme27N 41502 cdleme27a 41500 cdleme27cl 41499 cdleme28c 41505 cdleme3 41370 cdleme30a 41511 cdleme31fv 41523 cdleme31fv1 41524 cdleme31fv1s 41525 cdleme31fv2 41526 cdleme31id 41527 cdleme31sc 41517 cdleme31sdnN 41520 cdleme31sn 41513 cdleme31sn1 41514 cdleme31sn1c 41521 cdleme31sn2 41522 cdleme31so 41512 cdleme35a 41581 cdleme35b 41583 cdleme35c 41584 cdleme35d 41585 cdleme35e 41586 cdleme35f 41587 cdleme35fnpq 41582 cdleme35g 41588 cdleme35h 41589 cdleme35h2 41590 cdleme35sn2aw 41591 cdleme35sn3a 41592 cdleme36a 41593 cdleme36m 41594 cdleme37m 41595 cdleme38m 41596 cdleme38n 41597 cdleme39a 41598 cdleme39n 41599 cdleme3b 41362 cdleme3c 41363 cdleme3d 41364 cdleme3e 41365 cdleme3fN 41366 cdleme3fa 41369 cdleme3g 41367 cdleme3h 41368 cdleme4 41371 cdleme40m 41600 cdleme40n 41601 cdleme40v 41602 cdleme40w 41603 cdleme41fva11 41610 cdleme41sn3aw 41607 cdleme41sn4aw 41608 cdleme41snaw 41609 cdleme42a 41604 cdleme42b 41611 cdleme42c 41605 cdleme42d 41606 cdleme42e 41612 cdleme42f 41613 cdleme42g 41614 cdleme42h 41615 cdleme42i 41616 cdleme42k 41617 cdleme42ke 41618 cdleme42keg 41619 cdleme42mN 41620 cdleme42mgN 41621 cdleme43aN 41622 cdleme43bN 41623 cdleme43cN 41624 cdleme43dN 41625 cdleme5 41373 cdleme50ex 41692 cdleme50ltrn 41690 cdleme51finvN 41689 cdleme51finvfvN 41688 cdleme51finvtrN 41691 cdleme6 41374 cdleme7 41382 cdleme7a 41376 cdleme7aa 41375 cdleme7b 41377 cdleme7c 41378 cdleme7d 41379 cdleme7e 41380 cdleme7ga 41381 cdleme8 41383 cdleme8tN 41388 cdleme9 41386 cdleme9a 41384 cdleme9b 41385 cdleme9tN 41390 cdleme9taN 41389 cdlemeda 41431 cdlemedb 41430 cdlemednpq 41432 cdlemednuN 41433 cdlemefr27cl 41536 cdlemefr32fva1 41543 cdlemefr32fvaN 41542 cdlemefrs32fva 41533 cdlemefrs32fva1 41534 cdlemefs27cl 41546 cdlemefs32fva1 41556 cdlemefs32fvaN 41555 cdlemesner 41429 cdlemeulpq 41353 |
| [Crawley] p. 114 | Lemma E | 4atex 41209 4atexlem7 41208 cdleme0nex 41423 cdleme17a 41419 cdleme17c 41421 cdleme17d 41631 cdleme17d1 41422 cdleme17d2 41628 cdleme18a 41424 cdleme18b 41425 cdleme18c 41426 cdleme18d 41428 cdleme4a 41372 |
| [Crawley] p. 115 | Lemma E | cdleme21a 41458 cdleme21at 41461 cdleme21b 41459 cdleme21c 41460 cdleme21ct 41462 cdleme21f 41465 cdleme21g 41466 cdleme21h 41467 cdleme21i 41468 cdleme22gb 41427 |
| [Crawley] p. 116 | Lemma F | cdlemf 41696 cdlemf1 41694 cdlemf2 41695 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 41700 cdlemg16 41790 cdlemg28 41837 cdlemg28a 41826 cdlemg28b 41836 cdlemg3a 41730 cdlemg42 41862 cdlemg43 41863 cdlemg44 41866 cdlemg44a 41864 cdlemg46 41868 cdlemg47 41869 cdlemg9 41767 ltrnco 41852 ltrncom 41871 tgrpabl 41884 trlco 41860 |
| [Crawley] p. 116 | Definition of G | df-tgrp 41876 |
| [Crawley] p. 117 | Lemma G | cdlemg17 41810 cdlemg17b 41795 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 41889 df-edring 41890 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 41893 |
| [Crawley] p. 118 | Remark | tendopltp 41913 |
| [Crawley] p. 118 | Lemma H | cdlemh 41950 cdlemh1 41948 cdlemh2 41949 |
| [Crawley] p. 118 | Lemma I | cdlemi 41953 cdlemi1 41951 cdlemi2 41952 |
| [Crawley] p. 118 | Lemma J | cdlemj1 41954 cdlemj2 41955 cdlemj3 41956 tendocan 41957 |
| [Crawley] p. 118 | Lemma K | cdlemk 42107 cdlemk1 41964 cdlemk10 41976 cdlemk11 41982 cdlemk11t 42079 cdlemk11ta 42062 cdlemk11tb 42064 cdlemk11tc 42078 cdlemk11u-2N 42022 cdlemk11u 42004 cdlemk12 41983 cdlemk12u-2N 42023 cdlemk12u 42005 cdlemk13-2N 42009 cdlemk13 41985 cdlemk14-2N 42011 cdlemk14 41987 cdlemk15-2N 42012 cdlemk15 41988 cdlemk16-2N 42013 cdlemk16 41990 cdlemk16a 41989 cdlemk17-2N 42014 cdlemk17 41991 cdlemk18-2N 42019 cdlemk18-3N 42033 cdlemk18 42001 cdlemk19-2N 42020 cdlemk19 42002 cdlemk19u 42103 cdlemk1u 41992 cdlemk2 41965 cdlemk20-2N 42025 cdlemk20 42007 cdlemk21-2N 42024 cdlemk21N 42006 cdlemk22-3 42034 cdlemk22 42026 cdlemk23-3 42035 cdlemk24-3 42036 cdlemk25-3 42037 cdlemk26-3 42039 cdlemk26b-3 42038 cdlemk27-3 42040 cdlemk28-3 42041 cdlemk29-3 42044 cdlemk3 41966 cdlemk30 42027 cdlemk31 42029 cdlemk32 42030 cdlemk33N 42042 cdlemk34 42043 cdlemk35 42045 cdlemk36 42046 cdlemk37 42047 cdlemk38 42048 cdlemk39 42049 cdlemk39u 42101 cdlemk4 41967 cdlemk41 42053 cdlemk42 42074 cdlemk42yN 42077 cdlemk43N 42096 cdlemk45 42080 cdlemk46 42081 cdlemk47 42082 cdlemk48 42083 cdlemk49 42084 cdlemk5 41969 cdlemk50 42085 cdlemk51 42086 cdlemk52 42087 cdlemk53 42090 cdlemk54 42091 cdlemk55 42094 cdlemk55u 42099 cdlemk56 42104 cdlemk5a 41968 cdlemk5auN 41993 cdlemk5u 41994 cdlemk6 41970 cdlemk6u 41995 cdlemk7 41981 cdlemk7u-2N 42021 cdlemk7u 42003 cdlemk8 41971 cdlemk9 41972 cdlemk9bN 41973 cdlemki 41974 cdlemkid 42069 cdlemkj-2N 42015 cdlemkj 41996 cdlemksat 41979 cdlemksel 41978 cdlemksv 41977 cdlemksv2 41980 cdlemkuat 41999 cdlemkuel-2N 42017 cdlemkuel-3 42031 cdlemkuel 41998 cdlemkuv-2N 42016 cdlemkuv2-2 42018 cdlemkuv2-3N 42032 cdlemkuv2 42000 cdlemkuvN 41997 cdlemkvcl 41975 cdlemky 42059 cdlemkyyN 42095 tendoex 42108 |
| [Crawley] p. 120 | Remark | dva1dim 42118 |
| [Crawley] p. 120 | Lemma L | cdleml1N 42109 cdleml2N 42110 cdleml3N 42111 cdleml4N 42112 cdleml5N 42113 cdleml6 42114 cdleml7 42115 cdleml8 42116 cdleml9 42117 dia1dim 42194 |
| [Crawley] p. 120 | Lemma M | dia11N 42181 diaf11N 42182 dialss 42179 diaord 42180 dibf11N 42294 djajN 42270 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 42165 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 42251 dia2dimlem1 42197 dia2dimlem2 42198 dia2dimlem3 42199 dia2dimlem4 42200 dia2dimlem5 42201 diaf1oN 42263 diarnN 42262 dvheveccl 42245 dvhopN 42249 |
| [Crawley] p. 121 | Lemma N | cdlemn 42345 cdlemn10 42339 cdlemn11 42344 cdlemn11a 42340 cdlemn11b 42341 cdlemn11c 42342 cdlemn11pre 42343 cdlemn2 42328 cdlemn2a 42329 cdlemn3 42330 cdlemn4 42331 cdlemn4a 42332 cdlemn5 42334 cdlemn5pre 42333 cdlemn6 42335 cdlemn7 42336 cdlemn8 42337 cdlemn9 42338 diclspsn 42327 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 42306 |
| [Crawley] p. 122 | Lemma N | dih11 42398 dihf11 42400 dihjust 42350 dihjustlem 42349 dihord 42397 dihord1 42351 dihord10 42356 dihord11b 42355 dihord11c 42357 dihord2 42360 dihord2a 42352 dihord2b 42353 dihord2cN 42354 dihord2pre 42358 dihord2pre2 42359 dihordlem6 42346 dihordlem7 42347 dihordlem7b 42348 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 42363 dihfval 42364 dihval 42365 |
| [Diestel] p. 3 | Definition | df-gric 49055 df-grim 49052 isuspgrim 49070 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29994 df-nbgr 29915 |
| [Diestel] p. 3 | Definition by | df-grisom 49051 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 49035 df-subgr 29850 uhgrspan1 29885 uhgrspansubgr 29873 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 30136 vtxdgoddnumeven 30135 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29638 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 34539 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 34551 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 34543 zarcls1 34544 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 34554 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 34557 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 34560 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 4047 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9649 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8850 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9657 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 10062 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10640 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5258 |
| [Enderton] p. 19 | Definition | df-tp 4588 |
| [Enderton] p. 26 | Exercise 5 | unissb 4900 |
| [Enderton] p. 26 | Exercise 10 | pwel 5342 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5543 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5038 iinin2 5037 iinun2 5030 iunin1 5029 iunin1f 33195 iunin2 5028 uniin1 5032 uniin2 5033 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5036 iundif2 5031 |
| [Enderton] p. 32 | Exercise 20 | unineq 4233 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5057 |
| [Enderton] p. 33 | Exercise 25 | iununi 5058 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5065 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7785 iunpwss 5066 |
| [Enderton] p. 36 | Definition | opthwiener 5486 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5417 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4905 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5438 rnex 7922 rnexg 7914 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5895 rnuni 6139 |
| [Enderton] p. 42 | Definition of a function | dffun7 6567 dffun8 6568 |
| [Enderton] p. 43 | Definition of function value | funfv2 6973 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6609 |
| [Enderton] p. 44 | Definition (d) | dfima2 6057 dfima3 6058 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6982 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10552 ac7g 10553 df-ac 10196 dfac2 10211 dfac2a 10209 dfac2b 10210 dfac3 10201 dfac7 10212 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7250 |
| [Enderton] p. 52 | Definition | df-map 8850 |
| [Enderton] p. 53 | Exercise 21 | coass 6267 |
| [Enderton] p. 53 | Exercise 27 | dmco 6256 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6616 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6054 |
| [Enderton] p. 54 | Remark | ixpf 8949 ixpssmap 8961 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8927 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10562 ac9s 10572 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 39702 erref 8739 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 39705 erthi 8775 |
| [Enderton] p. 57 | Definition | df-ec 8720 |
| [Enderton] p. 58 | Definition | df-qs 8724 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8720 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5891 |
| [Enderton] p. 68 | Definition of successor | df-suc 6368 |
| [Enderton] p. 71 | Definition | df-tr 5212 dftr4 5217 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6444 unisucg 6443 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6444 unisucg 6443 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5227 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5229 trintALT 45939 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8614 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8616 onasuc 8537 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7423 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8615 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8617 onmsuc 8538 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8632 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8619 nnacom 8627 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8633 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8634 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8636 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8620 nnmsucr 8635 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8648 |
| [Enderton] p. 129 | Definition | df-en 8975 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7374 |
| [Enderton] p. 133 | Exercise 1 | xpomen 10095 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16382 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9223 |
| [Enderton] p. 135 | Corollary 6C | php3 9225 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9222 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9254 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9256 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9185 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9189 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9161 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10259 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10260 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10255 dju1en 10251 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9333 unifi 9334 unifi2 9335 |
| [Enderton] p. 144 | Corollary 6K | undif2 4430 unfi 9187 unfi2 9303 |
| [Enderton] p. 145 | Figure 38 | ffoss 7958 |
| [Enderton] p. 145 | Definition | df-dom 8976 |
| [Enderton] p. 146 | Example 1 | domen 8989 domeng 8990 |
| [Enderton] p. 146 | Example 3 | nndomo 9234 nnsdom 9656 nnsdomg 9292 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10263 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9162 xpdom1 9096 xpdom1g 9094 xpdom2g 9093 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9168 |
| [Enderton] p. 151 | Theorem 6M | zorn 10586 zorng 10583 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10571 dfac5 10208 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10661 |
| [Enderton] p. 164 | Example | infdif 10287 |
| [Enderton] p. 168 | Definition | df-po 5558 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6478 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6410 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6477 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6418 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7850 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7795 |
| [Enderton] p. 194 | Remark | onprc 7792 |
| [Enderton] p. 194 | Exercise 16 | suc11 6472 |
| [Enderton] p. 197 | Definition | df-card 10021 |
| [Enderton] p. 197 | Theorem 7P | carden 10636 |
| [Enderton] p. 200 | Exercise 25 | tfis 7866 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9784 |
| [Enderton] p. 202 | Definition | df-r1 9769 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9794 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9885 rankval4b 9881 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9608 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9872 rankprb 9866 rankpw 9857 rankpwi 9833 rankuniss 9884 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9620 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9621 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10190 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 10156 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10170 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8350 |
| [Enderton] p. 222 | Definition | df-kard 35867 |
| [Enderton] p. 222 | Definition of kard | karden 9960 kardex 9958 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8607 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8609 |
| [Enderton] p. 240 | Exercise 25 | oarec 8571 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10328 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17817 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17759 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18728 mrieqv2d 17814 mrieqvd 17813 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17818 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17823 mreexexlem2d 17820 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18734 mreexfidimd 17825 |
| [Frege1879] p. 11 | Statement | df3or2 44844 |
| [Frege1879] p. 12 | Statement | df3an2 44845 dfxor4 44842 dfxor5 44843 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 44866 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 44867 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 44871 |
| [Frege1879] p. 31 | Proposition 4 | frege4 44875 |
| [Frege1879] p. 32 | Proposition 5 | frege5 44876 |
| [Frege1879] p. 33 | Proposition 6 | frege6 44882 |
| [Frege1879] p. 34 | Proposition 7 | frege7 44884 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 44885 axfrege8 44883 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 91 wl-luk-pm2.04 38444 |
| [Frege1879] p. 35 | Proposition 9 | frege9 44888 |
| [Frege1879] p. 36 | Proposition 10 | frege10 44896 |
| [Frege1879] p. 36 | Proposition 11 | frege11 44890 |
| [Frege1879] p. 37 | Proposition 12 | frege12 44889 |
| [Frege1879] p. 37 | Proposition 13 | frege13 44898 |
| [Frege1879] p. 37 | Proposition 14 | frege14 44899 |
| [Frege1879] p. 38 | Proposition 15 | frege15 44902 |
| [Frege1879] p. 38 | Proposition 16 | frege16 44892 |
| [Frege1879] p. 39 | Proposition 17 | frege17 44897 |
| [Frege1879] p. 39 | Proposition 18 | frege18 44894 |
| [Frege1879] p. 39 | Proposition 19 | frege19 44900 |
| [Frege1879] p. 40 | Proposition 20 | frege20 44904 |
| [Frege1879] p. 40 | Proposition 21 | frege21 44903 |
| [Frege1879] p. 41 | Proposition 22 | frege22 44895 |
| [Frege1879] p. 42 | Proposition 23 | frege23 44901 |
| [Frege1879] p. 42 | Proposition 24 | frege24 44891 |
| [Frege1879] p. 42 | Proposition 25 | frege25 44893 rp-frege25 44881 |
| [Frege1879] p. 42 | Proposition 26 | frege26 44886 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 44906 |
| [Frege1879] p. 43 | Proposition 27 | frege27 44887 |
| [Frege1879] p. 43 | Proposition 28 | con3 154 |
| [Frege1879] p. 43 | Proposition 29 | frege29 44907 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 44910 axfrege31 44909 |
| [Frege1879] p. 44 | Proposition 30 | frege30 44908 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 131 |
| [Frege1879] p. 44 | Proposition 32 | frege32 44911 |
| [Frege1879] p. 44 | Proposition 33 | frege33 44912 |
| [Frege1879] p. 45 | Proposition 34 | frege34 44913 |
| [Frege1879] p. 45 | Proposition 35 | frege35 44914 |
| [Frege1879] p. 45 | Proposition 36 | frege36 44915 |
| [Frege1879] p. 46 | Proposition 37 | frege37 44916 |
| [Frege1879] p. 46 | Proposition 38 | frege38 44917 |
| [Frege1879] p. 46 | Proposition 39 | frege39 44918 |
| [Frege1879] p. 46 | Proposition 40 | frege40 44919 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 44921 axfrege41 44920 |
| [Frege1879] p. 47 | Proposition 41 | notnot 143 |
| [Frege1879] p. 47 | Proposition 42 | frege42 44922 |
| [Frege1879] p. 47 | Proposition 43 | frege43 44923 |
| [Frege1879] p. 47 | Proposition 44 | frege44 44924 |
| [Frege1879] p. 47 | Proposition 45 | frege45 44925 |
| [Frege1879] p. 48 | Proposition 46 | frege46 44926 |
| [Frege1879] p. 48 | Proposition 47 | frege47 44927 |
| [Frege1879] p. 49 | Proposition 48 | frege48 44928 |
| [Frege1879] p. 49 | Proposition 49 | frege49 44929 |
| [Frege1879] p. 49 | Proposition 50 | frege50 44930 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 44933 ax-frege52c 44964 frege52aid 44934 frege52b 44965 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 44938 ax-frege54c 44968 frege54b 44969 |
| [Frege1879] p. 50 | Proposition 51 | frege51 44931 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3740 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 44936 frege53aid 44935 frege53b 44966 frege53c 44990 |
| [Frege1879] p. 50 | Proposition 54 | biid 264 eqid 2760 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 44944 frege55aid 44941 frege55b 44973 frege55c 44994 frege55cor1a 44945 frege55lem2a 44943 frege55lem2b 44972 frege55lem2c 44993 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 44947 frege56aid 44946 frege56b 44974 frege56c 44995 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 44951 ax-frege58b 44977 frege58bid 44978 frege58c 44997 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 44949 frege57aid 44948 frege57b 44975 frege57c 44996 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3751 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 44953 frege59b 44980 frege59c 44998 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 44954 frege60b 44981 frege60c 44999 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 44955 frege61b 44982 frege61c 45000 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 44956 frege62b 44983 frege62c 45001 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 44957 frege63b 44984 frege63c 45002 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 44958 frege64b 44985 frege64c 45003 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 44959 frege65b 44986 frege65c 45004 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 44960 frege66b 44987 frege66c 45005 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 44961 frege67b 44988 frege67c 45006 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 44962 frege68b 44989 frege68c 45007 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 45008 |
| [Frege1879] p. 58 | Proposition 70 | frege70 45009 |
| [Frege1879] p. 59 | Proposition 71 | frege71 45010 |
| [Frege1879] p. 59 | Proposition 72 | frege72 45011 |
| [Frege1879] p. 59 | Proposition 73 | frege73 45012 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 45015 |
| [Frege1879] p. 60 | Proposition 74 | frege74 45013 |
| [Frege1879] p. 60 | Proposition 75 | frege75 45014 |
| [Frege1879] p. 62 | Proposition 77 | frege77 45016 frege77d 44822 |
| [Frege1879] p. 63 | Proposition 78 | frege78 45017 |
| [Frege1879] p. 63 | Proposition 79 | frege79 45018 |
| [Frege1879] p. 63 | Proposition 80 | frege80 45019 |
| [Frege1879] p. 63 | Proposition 81 | frege81 45020 frege81d 44823 |
| [Frege1879] p. 64 | Proposition 82 | frege82 45021 |
| [Frege1879] p. 65 | Proposition 83 | frege83 45022 frege83d 44824 |
| [Frege1879] p. 65 | Proposition 84 | frege84 45023 |
| [Frege1879] p. 66 | Proposition 85 | frege85 45024 |
| [Frege1879] p. 66 | Proposition 86 | frege86 45025 |
| [Frege1879] p. 66 | Proposition 87 | frege87 45026 frege87d 44826 |
| [Frege1879] p. 67 | Proposition 88 | frege88 45027 |
| [Frege1879] p. 68 | Proposition 89 | frege89 45028 |
| [Frege1879] p. 68 | Proposition 90 | frege90 45029 |
| [Frege1879] p. 68 | Proposition 91 | frege91 45030 frege91d 44827 |
| [Frege1879] p. 69 | Proposition 92 | frege92 45031 |
| [Frege1879] p. 70 | Proposition 93 | frege93 45032 |
| [Frege1879] p. 70 | Proposition 94 | frege94 45033 |
| [Frege1879] p. 70 | Proposition 95 | frege95 45034 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 45038 |
| [Frege1879] p. 71 | Proposition 96 | frege96 45035 frege96d 44825 |
| [Frege1879] p. 71 | Proposition 97 | frege97 45036 frege97d 44828 |
| [Frege1879] p. 71 | Proposition 98 | frege98 45037 frege98d 44829 |
| [Frege1879] p. 72 | Proposition 100 | frege100 45039 |
| [Frege1879] p. 72 | Proposition 101 | frege101 45040 |
| [Frege1879] p. 72 | Proposition 102 | frege102 45041 frege102d 44830 |
| [Frege1879] p. 73 | Proposition 103 | frege103 45042 |
| [Frege1879] p. 73 | Proposition 104 | frege104 45043 |
| [Frege1879] p. 73 | Proposition 105 | frege105 45044 |
| [Frege1879] p. 73 | Proposition 106 | frege106 45045 frege106d 44831 |
| [Frege1879] p. 74 | Proposition 107 | frege107 45046 |
| [Frege1879] p. 74 | Proposition 108 | frege108 45047 frege108d 44832 |
| [Frege1879] p. 74 | Proposition 109 | frege109 45048 frege109d 44833 |
| [Frege1879] p. 75 | Proposition 110 | frege110 45049 |
| [Frege1879] p. 75 | Proposition 111 | frege111 45050 frege111d 44835 |
| [Frege1879] p. 76 | Proposition 112 | frege112 45051 |
| [Frege1879] p. 76 | Proposition 113 | frege113 45052 |
| [Frege1879] p. 76 | Proposition 114 | frege114 45053 frege114d 44834 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 45054 |
| [Frege1879] p. 77 | Proposition 116 | frege116 45055 |
| [Frege1879] p. 78 | Proposition 117 | frege117 45056 |
| [Frege1879] p. 78 | Proposition 118 | frege118 45057 |
| [Frege1879] p. 78 | Proposition 119 | frege119 45058 |
| [Frege1879] p. 78 | Proposition 120 | frege120 45059 |
| [Frege1879] p. 79 | Proposition 121 | frege121 45060 |
| [Frege1879] p. 79 | Proposition 122 | frege122 45061 frege122d 44836 |
| [Frege1879] p. 79 | Proposition 123 | frege123 45062 |
| [Frege1879] p. 80 | Proposition 124 | frege124 45063 frege124d 44837 |
| [Frege1879] p. 81 | Proposition 125 | frege125 45064 |
| [Frege1879] p. 81 | Proposition 126 | frege126 45065 frege126d 44838 |
| [Frege1879] p. 82 | Proposition 127 | frege127 45066 |
| [Frege1879] p. 83 | Proposition 128 | frege128 45067 |
| [Frege1879] p. 83 | Proposition 129 | frege129 45068 frege129d 44839 |
| [Frege1879] p. 84 | Proposition 130 | frege130 45069 |
| [Frege1879] p. 85 | Proposition 131 | frege131 45070 frege131d 44840 |
| [Frege1879] p. 86 | Proposition 132 | frege132 45071 |
| [Frege1879] p. 86 | Proposition 133 | frege133 45072 frege133d 44841 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 47399 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 47722 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 47422 |
| [Fremlin1] p. 14 | Definition 112A | ismea 47537 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 47557 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 47548 meadjunre 47562 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 47549 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 47550 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 47546 meaiunle 47555 meaiunlelem 47554 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 47567 meaiuninc2 47568 meaiuninc3 47571 meaiuninc3v 47570 meaiunincf 47569 meaiuninclem 47566 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 47573 meaiininc2 47574 meaiininclem 47572 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 47592 caragendifcl 47600 caratheodory 47614 omelesplit 47604 |
| [Fremlin1] p. 19 | Definition 113A | isome 47580 isomennd 47617 isomenndlem 47616 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 47602 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 47621 voncmpl 47707 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 47584 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 47609 carageniuncllem1 47607 carageniuncllem2 47608 caragenuncl 47599 caragenuncllem 47598 caragenunicl 47610 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 47618 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 47612 caratheodorylem2 47613 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 47621 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 47680 hoidmv1lelem1 47677 hoidmv1lelem2 47678 hoidmv1lelem3 47679 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 47724 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 47680 hoidmvle 47686 hoidmvlelem1 47681 hoidmvlelem2 47682 hoidmvlelem3 47683 hoidmvlelem4 47684 hoidmvlelem5 47685 hsphoidmvle2 47671 hsphoif 47662 hsphoival 47665 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 47634 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 47642 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 47669 hoidmvn0val 47670 hoidmvval 47663 hoidmvval0 47673 hoidmvval0b 47676 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 47674 hsphoidmvle 47672 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 47623 df-voln 47625 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 47690 ovn0 47652 ovn0lem 47651 ovnf 47649 ovnome 47659 ovnssle 47647 ovnsslelem 47646 ovnsupge0 47643 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 47689 ovnhoilem1 47687 ovnhoilem2 47688 vonhoi 47753 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 47706 hoidifhspf 47704 hoidifhspval 47694 hoidifhspval2 47701 hoidifhspval3 47705 hspmbl 47715 hspmbllem1 47712 hspmbllem2 47713 hspmbllem3 47714 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 47707 vonmea 47660 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 47658 ovnsubadd2 47732 ovnsubadd2lem 47731 ovnsubaddlem1 47656 ovnsubaddlem2 47657 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 47717 hoimbl2 47751 hoimbllem 47716 hspdifhsp 47702 opnvonmbl 47720 opnvonmbllem2 47719 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 47722 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 47765 iccvonmbllem 47764 ioovonmbl 47763 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 47771 vonicclem2 47770 vonioo 47768 vonioolem2 47767 vonn0icc 47774 vonn0icc2 47778 vonn0ioo 47773 vonn0ioo2 47776 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 47775 snvonmbl 47772 vonct 47779 vonsn 47777 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 47445 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 47444 subsaliuncllem 47443 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 47811 salpreimalegt 47795 salpreimaltle 47812 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 47814 issmff 47820 issmflem 47813 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 47831 issmflelem 47830 smfpreimale 47840 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 47842 issmfgtlem 47841 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 47782 issmf 47814 issmff 47820 issmfge 47856 issmfgelem 47855 issmfgt 47842 issmfgtlem 47841 issmfle 47831 issmflelem 47830 issmflem 47813 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 47793 salpreimagtlt 47816 salpreimalelt 47815 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 47856 issmfgelem 47855 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 47839 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 47837 cnfsmf 47826 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 47853 decsmflem 47852 incsmf 47828 incsmflem 47827 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 47787 pimconstlt1 47788 smfconst 47835 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 47851 smfaddlem1 47849 smfaddlem2 47850 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 47882 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 47881 smfmullem1 47877 smfmullem2 47878 smfmullem3 47879 smfmullem4 47880 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 47883 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 47886 smfpimbor1lem2 47885 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 47888 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 47876 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 47875 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 47884 smfresal 47874 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 47863 smflim2 47892 smflimlem1 47857 smflimlem2 47858 smflimlem3 47859 smflimlem4 47860 smflimlem5 47861 smflimlem6 47862 smflimmpt 47896 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 47900 smfsuplem1 47897 smfsuplem2 47898 smfsuplem3 47899 smfsupmpt 47901 smfsupxr 47902 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 47904 smfinflem 47903 smfinfmpt 47905 |
| [Fremlin1] p. 39 | Remark 121G | smflim 47863 smflim2 47892 smflimmpt 47896 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 47894 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 47924 smfdivdmmbl2 47927 smfinfdmmbl 47935 smfinfdmmbllem 47934 smfsupdmmbl 47931 smfsupdmmbllem 47930 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 47914 smflimsuplem2 47907 smflimsuplem6 47911 smflimsuplem7 47912 smflimsuplem8 47913 smflimsupmpt 47915 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 47917 smfliminflem 47916 smfliminfmpt 47918 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 47782 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 47928 fsupdm2 47929 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 47919 adddmmbl2 47920 finfdm 47932 finfdm2 47933 fsupdm 47928 fsupdm2 47929 muldmmbl 47921 muldmmbl2 47922 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 47932 finfdm2 47933 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25858 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25901 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25911 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 38692 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 38695 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9640 inf1 9624 inf2 9625 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10997 enqer 11007 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 11002 df-nq 10998 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10994 df-plq 11000 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7658 df-mpq 10995 df-mq 11001 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 11003 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 11061 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 11062 ltbtwnnq 11064 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 11057 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 11058 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 11065 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 11067 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 11079 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 11081 |
| [Gleason] p. 122 | Definition | df-1p 11068 |
| [Gleason] p. 122 | Remark (1) | prub 11080 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 11119 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 11071 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 11118 psslinpr 11117 supexpr 11140 suplem1pr 11138 suplem2pr 11139 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 11104 addclprlem1 11102 addclprlem2 11103 df-plp 11069 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 11108 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 11107 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 11120 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 11129 ltexprlem1 11122 ltexprlem2 11123 ltexprlem3 11124 ltexprlem4 11125 ltexprlem5 11126 ltexprlem6 11127 ltexprlem7 11128 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 11131 ltaprlem 11130 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 11132 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 11133 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 11070 mulclpr 11106 mulclprlem 11105 reclem2pr 11134 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 11115 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 11110 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 11109 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 11114 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 11137 reclem3pr 11135 reclem4pr 11136 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 11141 enrer 11149 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 11146 df-1r 11147 df-nr 11142 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 11144 df-plr 11143 negexsr 11188 recexsr 11193 recexsrlem 11189 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 11145 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12316 creur 12315 cru 12313 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11274 axcnre 11250 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15283 crimd 15400 crimi 15361 crre 15282 crred 15399 crrei 15360 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15285 remimd 15366 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15452 absval2d 15616 absval2i 15566 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15309 cjaddd 15388 cjaddi 15356 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15310 cjmuld 15389 cjmuli 15357 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15308 cjcjd 15367 cjcji 15339 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15307 cjreb 15291 cjrebd 15370 cjrebi 15342 cjred 15394 rere 15290 rereb 15288 rerebd 15369 rerebi 15341 rered 15392 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15316 addcjd 15380 addcji 15351 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15406 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15447 abscjd 15621 abscji 15570 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15457 abs00d 15617 abs00i 15567 absne0d 15618 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15490 releabsd 15622 releabsi 15571 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15462 absmuld 15625 absmuli 15573 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15450 sqabsaddi 15574 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15499 abstrid 15627 abstrii 15577 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14206 exp0 14209 expp1 14212 expp1d 14291 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 27008 cxpaddd 27046 expadd 14248 expaddd 14292 expaddz 14250 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 27017 cxpmuld 27066 expmul 14251 expmuld 14293 expmulz 14252 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 27014 mulcxpd 27057 mulexp 14245 mulexpd 14305 mulexpz 14246 |
| [Gleason] p. 140 | Exercise 1 | znnen 16381 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13642 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15800 rlimadd 15811 rlimdiv 15814 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15802 rlimsub 15812 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15801 rlimmul 15813 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15805 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15751 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15772 climcj 15773 climim 15775 climre 15774 rlimabs 15777 rlimcj 15778 rlimim 15780 rlimre 15779 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11349 df-xr 11348 ltxr 13245 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15639 limsupval 15642 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15838 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15847 caucvgb 15848 caucvgbf 46575 caucvgr 15844 climcau 15839 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15984 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 16053 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15504 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13969 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21673 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24663 xmet0 24662 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24679 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24670 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24672 mstri 24789 xmettri 24671 xmstri 24788 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24702 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23968 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25632 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24860 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 25186 addcn2 15762 mulcn 25188 mulcn2 15764 subcn 25187 subcn2 15763 |
| [Gleason] p. 295 | Remark | bcval3 14451 bcval4 14452 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14466 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14449 df-bc 14448 |
| [Gleason] p. 296 | Remark | bcn0 14455 bcnn 14457 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 16000 |
| [Gleason] p. 308 | Equation 2 | ef0 16258 |
| [Gleason] p. 308 | Equation 3 | efcj 16259 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16265 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16270 |
| [Gleason] p. 310 | Equation 14 | sinadd 16333 |
| [Gleason] p. 310 | Equation 15 | cosadd 16334 |
| [Gleason] p. 311 | Equation 17 | sincossq 16345 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16350 sinbnd 16349 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14361 sqeqori 14359 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16239 |
| [Godowski] p. 730 | Equation SF | goeqi 32876 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 32271 |
| [Golan] p. 1 | Remark | srgisid 20436 |
| [Golan] p. 1 | Definition | df-srg 20414 |
| [Golan] p. 149 | Definition | df-slmd 33805 |
| [Gonshor] p. 7 | Definition | df-cuts 28147 |
| [Gonshor] p. 9 | Theorem 2.5 | lesrec 28186 lesrecd 28187 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 28307 cofcut1d 28308 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 28309 cofcut2d 28310 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 28311 cofcutr1d 28312 cofcutr2d 28313 |
| [Gonshor] p. 13 | Definition | df-adds 28347 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 28363 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 28389 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28517 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28537 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28845 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28847 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28846 |
| [Gonshor] p. 39 | Theorem 4.4(b) | elreno2 28882 |
| [Gonshor] p. 95 | Theorem 6.1 | addbday 28405 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36999 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17757 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17759 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 49361 df-cllaw 49359 df-comlaw 49360 |
| [Hall] p. 2 | Section 1.2 | df-clintop 49373 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 49394 |
| [Halmos] p. 28 | Partition ` ` | df-parts 39876 dfmembpart2 39881 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32668 riesz2 32669 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 32544 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32776 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32788 elpjidm 32787 pjnmopi 32751 |
| [Halmos] p. 44 | Remark | pjinormi 32290 pjinormii 32279 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32792 pjrn 32310 pjrni 32305 pjvec 32299 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 32330 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32757 hmopidmpji 32755 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32794 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32783 pjocvec 32300 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32772 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32775 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32778 pjssdif2i 32777 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 32458 |
| [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 1827 |
| [Hatcher] p. 25 | Definition | df-phtpc 25314 df-phtpy 25293 |
| [Hatcher] p. 26 | Definition | df-pco 25327 df-pi1 25330 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 25317 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 25372 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22806 df-dmatalt 49586 |
| [Helfgott] p. 2 | Theorem | tgoldbach 48991 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 48976 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 48988 bgoldbtbnd 48983 bgoldbtbnd 48983 tgblthelfgott 48989 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 35314 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 35315 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 35329 hgt750lemb 35328 hgt750leme 35330 hgt750lemf 35325 hgt750lemg 35326 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 48985 tgoldbachgt 35335 tgoldbachgtALTV 48986 tgoldbachgtd 35334 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 35316 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 31096 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 19156 grpoideu 31112 mndideu 18935 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 19186 grpoinveu 31122 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 19217 grpo2inv 31134 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 19229 grpoinvop 31136 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 19251 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1800 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1801 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1803 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 33023 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 33036 cdj3i 33044 cdj3lem1 33037 cdjreui 33035 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 33034 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 43094 |
| [Holland95] p. 14 | Line 15 | hgmapvs 43024 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 43046 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 43047 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 43044 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 43050 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 42969 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 43064 |
| [Holland95] p. 204 | Definition of involution | df-srng 21098 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 40636 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 42661 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 42614 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 41066 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 42510 poml4N 41086 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 42601 pexmidALTN 41111 pexmidN 41102 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 42666 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 40257 ldualset 40258 |
| [Holland95] p. 222 | Item 1 | df-lines 40634 df-pointsN 40635 |
| [Holland95] p. 222 | Item 2 | df-polarityN 41036 |
| [Holland95] p. 223 | Remark | ispsubcl2N 41080 omllaw4 40379 pol1N 41043 polcon3N 41050 |
| [Holland95] p. 223 | Definition | df-psubclN 41068 |
| [Holland95] p. 223 | Equation for polarity | polval2N 41039 |
| [Holmes] p. 40 | Definition | df-xrn 39388 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31687 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32785 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 32566 eigre 32438 eigrei 32437 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 32567 eigorth 32441 eigorthi 32440 |
| [Hughes] p. 137 | Remark (ii) | eigposi 32439 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30911 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30907 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30908 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30909 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30927 frgrregorufr0 30926 frgrregorufrg 30928 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30934 frrusgrord 30943 frrusgrord0 30942 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30680 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30917 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30920 frgrwopreg2 30921 frgrwopregasn 30918 frgrwopregbsn 30919 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30923 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30937 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30940 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30678 numclwlk1 30973 numclwlk1lem1 30971 numclwlk1lem2 30972 numclwwlk1 30963 numclwwlk8 30994 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30914 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 30359 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30949 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30975 numclwwlkovh0 30974 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30983 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 30570 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30987 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30990 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30993 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 31005 natded 31005 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 31005 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 31005 natded 31005 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 31005 |
| [Jech] p. 4 | Definition of class | cv 1568 cvjust 2754 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10665 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10663 alephmul 10664 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10662 infmap2 10296 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9823 |
| [Jech] p. 72 | Equation 9.3 | df-scott 9930 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9885 rankval4b 9881 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9955 |
| [Jech] p. 78 | Note | opthprc 5714 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 43998 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 44086 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 44087 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 44010 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 44014 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 44015 rmyp1 44016 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 44017 rmym1 44018 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 44008 rmx1 44009 rmxluc 44019 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 44012 rmy1 44013 rmyluc 44020 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 44022 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 44023 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 44043 jm2.17b 44044 jm2.17c 44045 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 44076 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 44080 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 44071 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 44046 jm2.24nn 44042 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 44085 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 44091 rmygeid 44047 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 44103 |
| [Juillerat] p. 11 | Section *5 | etransc 47369 etransclem47 47367 etransclem48 47368 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 47364 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 47366 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 47352 |
| [Juillerat] p. 13 | Proof | etransclem35 47355 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 47358 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 47344 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 47361 |
| [Juillerat] p. 14 | Proof | etransclem23 47343 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1999 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2044 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2049 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2039 cbvaliw 2038 wl-cbvmotv 38521 wl-motae 38523 wl-moteq 38522 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 2018 spimw 2002 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2065 spw 2066 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 32119 chabs1i 32121 chabs2 32120 chabs2i 32122 chjass 32136 chjassi 32089 latabs1 18650 latabs2 18651 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32941 ela 32942 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32886 cvrval2 40407 |
| [Kalmbach] p. 16 | Definition | df-ol 40311 df-oml 40312 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 32187 cmbri 32193 cmtvalN 40344 df-cm 32186 df-cmtN 40310 |
| [Kalmbach] p. 22 | Remark | omllaw5N 40380 pjoml5 32216 pjoml5i 32191 |
| [Kalmbach] p. 22 | Definition | pjoml2 32214 pjoml2i 32188 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 32217 cmcmi 32195 cmcmii 32200 cmtcomN 40382 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 40378 omlsi 32007 pjoml 32039 pjomli 32038 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 40377 |
| [Kalmbach] p. 23 | Remark | cmbr2i 32199 cmcm3 32218 cmcm3i 32197 cmcm3ii 32202 cmcm4i 32198 cmt3N 40384 cmt4N 40385 cmtbr2N 40386 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 32211 cmbr3i 32203 cmtbr3N 40387 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 32221 fh1i 32224 fh2 32222 fh2i 32225 omlfh1N 40391 |
| [Kalmbach] p. 65 | Remark | chjatom 32960 chslej 32101 chsleji 32061 shslej 31983 shsleji 31973 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 32098 chocini 32057 chsupcl 31943 chsupval2 32013 h0elch 31858 helch 31846 hsupval2 32012 ocin 31899 ococss 31896 shococss 31897 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31915 |
| [Kalmbach] p. 66 | Remark | df-pjh 31998 pjssmi 32768 pjssmii 32284 |
| [Kalmbach] p. 67 | Lemma 3 | osum 32248 osumi 32245 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32803 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 33003 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32913 |
| [Kalmbach] p. 140 | Remark | hatomic 32963 hatomici 32962 hatomistici 32965 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 40452 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32984 lsatexch 40176 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32958 cvlcvr1 40472 cvr1 40543 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32977 cvexchi 32972 cvrexch 40553 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32967 hlrelat 40535 hlrelat5N 40534 lrelat 40147 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21420 lsmsatcv 40143 spansncv 32256 spansncvi 32255 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 40162 spansncv2 32896 |
| [Kalmbach] p. 266 | Definition | df-st 32814 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 32452 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10732 fpwwe2 10729 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10733 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10740 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10735 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10737 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10750 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10754 gchxpidm 10755 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10766 gchhar 10765 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10294 unxpwdom 9584 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10756 |
| [Kreyszig] p. 3 | Property M1 | metcl 24652 xmetcl 24651 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24659 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24892 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 12035 muleqadd 11961 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24758 |
| [Kreyszig] p. 19 | Remark | mopntopon 24759 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24818 mopnm 24764 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24816 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24821 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24862 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23577 lmmbr 25580 lmmbr2 25581 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23699 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25635 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25598 iscmet2 25616 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25638 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23781 metelcls 25627 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25628 metcld2 25629 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25421 lmodvneg1 21181 nvinv 31242 vcm 31179 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25417 lmod0vs 21171 slmd0vs 33828 vc0 31177 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 21172 slmdvs0 33829 vcz 31178 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 31294 ngpmet 24923 nrmmetd 24894 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 31289 imsdval2 31290 ncvspds 25483 ngpds 24924 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24909 nvnd 31291 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24938 nmge0 24937 nvge0 31276 nvz 31272 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24944 nvabs 31275 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 31404 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 31348 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 31410 blocni 31408 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 31409 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25526 ipeq0 21945 ipz 31322 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25538 pythi 31453 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 31457 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25560 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 16026 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25758 minveco 31487 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 31353 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25651 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 31476 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32726 leopg 32725 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32744 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 31521 |
| [Kulpa] p. 547 | Theorem | poimir 38647 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 38646 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 38645 |
| [Kulpa] p. 548 | Theorem | broucube 38648 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 38640 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 38641 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2412 axnul 5258 |
| [Kunen] p. 11 | Axiom 3 | axnul 5258 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 5241 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8859 mapvalg 8857 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10601 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7952 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9769 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9815 r1elssi 9814 |
| [Kunen] p. 107 | Exercise 4 | rankop 9873 rankopb 9867 rankuni 9880 rankxplim 9897 rankxpsuc 9900 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 46020 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 46028 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 46027 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 46029 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 46034 rexabso 46035 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 46041 n0abso 46042 ssabso 46040 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 46043 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 46053 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 46048 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 46051 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 46052 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 46047 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 46059 wfaxpr 46064 wfaxreg 46066 wfaxrep 46060 wfaxsep 46061 wfaxun 46065 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 46050 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 46063 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 46059 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 46058 omelaxinf2 46055 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 46068 wfaxinf2 46067 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 46081 permaxext 46071 permaxinf2 46079 permaxnul 46074 permaxpow 46075 permaxpr 46076 permaxrep 46072 permaxsep 46073 permaxun 46077 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 46069 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 46080 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4963 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 34340 |
| [Lang] p. | Definition | df-rn 5661 |
| [Lang] p. 3 | Statement | lidrideqd 18851 mndbn0 18941 |
| [Lang] p. 3 | Definition | df-mnd 18925 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18877 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 19038 |
| [Lang] p. 5 | Equation | gsumreidx 20132 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 49355 |
| [Lang] p. 6 | Example | nn0mnd 49352 |
| [Lang] p. 6 | Equation | gsumxp2 20195 |
| [Lang] p. 6 | Statement | cycsubm 19418 |
| [Lang] p. 6 | Definition | mulgnn0gsum 19291 |
| [Lang] p. 6 | Observation | mndlsmidm 19885 |
| [Lang] p. 7 | Definition | dfgrp2e 19175 |
| [Lang] p. 30 | Definition | df-tocyc 33711 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33756 |
| [Lang] p. 32 | Property (b) | cyc3conja 33761 cycpmconjv 33746 |
| [Lang] p. 53 | Definition | df-cat 17843 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18273 cat1lem 18272 |
| [Lang] p. 54 | Definition | df-iso 17925 |
| [Lang] p. 57 | Definition | df-inito 18160 df-termo 18161 |
| [Lang] p. 58 | Example | irinitoringc 21786 |
| [Lang] p. 58 | Statement | initoeu1 18187 termoeu1 18194 |
| [Lang] p. 62 | Definition | df-func 18034 |
| [Lang] p. 65 | Definition | df-nat 18122 |
| [Lang] p. 83 | Definition of "ring with unit" | dfring2 20518 |
| [Lang] p. 91 | Note | df-ringc 20899 |
| [Lang] p. 92 | Statement | mxidlprm 34038 |
| [Lang] p. 92 | Definition | isprmidlc 21629 |
| [Lang] p. 128 | Remark | dsmmlmod 22052 |
| [Lang] p. 129 | Proof | lincscm 49618 lincscmcl 49620 lincsum 49617 lincsumcl 49619 |
| [Lang] p. 129 | Statement | lincolss 49622 |
| [Lang] p. 129 | Observation | dsmmfi 22045 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 34302 qusdimsum 34303 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 34283 |
| [Lang] p. 147 | Definition | snlindsntor 49659 |
| [Lang] p. 504 | Statement | mat1 22763 matring 22759 |
| [Lang] p. 504 | Definition | df-mamu 22707 |
| [Lang] p. 505 | Statement | mamuass 22718 mamutpos 22774 matassa 22760 mattposvs 22771 tposmap 22773 |
| [Lang] p. 513 | Definition | mdet1 22917 mdetf 22911 |
| [Lang] p. 513 | Theorem 4.4 | cramer 23010 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22903 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22927 |
| [Lang] p. 515 | Definition | df-minmar1 22951 smadiadetr 22991 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22926 mdetralt 22924 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22939 |
| [Lang] p. 518 | Definition | df-madu 22950 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22961 madurid 22960 matinv 22993 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 23209 |
| [Lang], p. 190 | Chapter 6 | vieta 34255 |
| [Lang], p. 224 | Proposition 1.1 | extdgfialg 34369 finextalg 34373 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 34338 fedgmul 34306 |
| [Lang], p. 225 | Proposition 1.4 | algextdeg 34400 |
| [Lang], p. 561 | Remark | chpmatply1 23151 |
| [Lang], p. 561 | Definition | df-chpmat 23146 |
| [Lang2] p. 3 | Notations | df-ind 12322 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 45394 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 45389 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 45395 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5258 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2739 wl-df.clab 38506 |
| [Levy] p. 59 | Definition | df-ttrcl 9710 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9756 |
| [Levy] p. 338 | Axiom | df-clel 2835 df-cleq 2752 wl-df.cleq 38507 |
| [Levy] p. 338 | Axiom. See also comments under ~ df-clab , ~ df-cleq , and ~ eqabb . Alternate characterizations | wl-df.clel 38510 |
| [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 38510 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2835 df-cleq 2752 wl-df.cleq 38507 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2739 wl-df.clab 38506 |
| [Levy] p. 358 | Axiom | df-clab 2739 wl-df.clab 38506 |
| [Levy58] p. 2 | Definition I | isfin1-3 10465 |
| [Levy58] p. 2 | Definition II | df-fin2 10365 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10364 |
| [Levy58] p. 2 | Definition III | df-fin3 10367 |
| [Levy58] p. 3 | Definition V | df-fin5 10368 |
| [Levy58] p. 3 | Definition IV | df-fin4 10366 |
| [Levy58] p. 4 | Definition VI | df-fin6 10369 |
| [Levy58] p. 4 | Definition VII | df-fin7 10370 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10494 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 28044 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 28055 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 28087 nosupbnd1 28072 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 28089 nosupbnd2 28074 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 28093 noetasuplem4 28094 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 28090 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1800 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1801 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1803 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 33011 |
| [Maeda] p. 168 | Lemma 5 | mdsym 33015 mdsymi 33014 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 33009 mdsymlem6 33011 mdsymlem7 33012 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 33013 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32916 ssdmd2 32917 ssmd1 32914 ssmd2 32915 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32912 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32884 df-md 32883 mdbr 32897 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32934 mdslj1i 32922 mdslj2i 32923 mdslle1i 32920 mdslle2i 32921 mdslmd1i 32932 mdslmd2i 32933 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32924 mdsl2bi 32926 mdsl2i 32925 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32938 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32935 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32936 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32913 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32918 mdsl3 32919 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32937 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 33032 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 40454 hlrelat1 40533 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 40172 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32939 cvmdi 32927 cvnbtwn4 32892 cvrnbtwn4 40412 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32940 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 40473 cvp 32978 cvrp 40549 lcvp 40173 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 33002 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 33001 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 40466 hlexch4N 40525 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 33004 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 40576 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 40882 atpsubN 40886 df-pointsN 40635 pointpsubN 40884 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 40637 pmap11 40895 pmaple 40894 pmapsub 40901 pmapval 40890 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 40898 pmap1N 40900 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 40903 pmapglb2N 40904 pmapglb2xN 40905 pmapglbx 40902 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 40985 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 40610 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 40929 paddclN 40975 paddidm 40974 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 40611 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 40971 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 40610 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 40611 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19890 lsmmod2 19891 lssats 40145 shatomici 32961 shatomistici 32964 shmodi 31993 shmodsi 31992 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32903 mdsymlem7 33012 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 32192 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 32096 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 33018 |
| [Margaris] p. 40 | Rule C | exlimiv 1962 |
| [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 1812 df-or 862 dfbi2 480 |
| [Margaris] p. 51 | Theorem 1 | idALT 24 |
| [Margaris] p. 56 | Theorem 3 | conventions 31002 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 45973 |
| [Margaris] p. 60 | Theorem 8 | jcn 163 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 45974 |
| [Margaris] p. 79 | Rule C | exinst01 45684 exinst11 45685 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 2008 19.2g 2224 r19.2z 4454 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2238 rr19.3v 3620 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2195 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1858 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1813 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2217 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2241 19.9h 2319 exlimd 2254 exlimdh 2323 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2198 excomim 2199 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2357 |
| [Margaris] p. 90 | Section 19 | conventions-labels 31003 conventions-labels 31003 conventions-labels 31003 conventions-labels 31003 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1859 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 45438 albi 1850 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2261 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2262 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 45440 exbi 1879 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2265 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 45437 2alimdv 1950 alimd 2248 alimdh 1849 alimdv 1948 ax-4 1841 ralimdaa 3263 ralimdv 3176 ralimdva 3174 ralimdvva 3209 sbcimdv 3806 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2243 19.21h 2320 19.21t 2242 19.21vv 45436 alrimd 2251 alrimdd 2250 alrimdh 1895 alrimdv 1961 alrimi 2249 alrimih 1856 alrimiv 1959 alrimivv 1960 bj-alrimdh 37569 hbralrimi 3152 r19.21be 3255 r19.21bi 3254 ralrimd 3267 ralrimdv 3160 ralrimdva 3162 ralrimdvv 3206 ralrimdvva 3217 ralrimi 3260 ralrimia 3261 ralrimiv 3153 ralrimiva 3154 ralrimivv 3203 ralrimivva 3205 ralrimivvva 3208 ralrimivw 3158 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 45439 2eximdv 1951 bj-exim 37584 exim 1866 eximd 2252 eximdh 1896 eximdv 1949 rexim 3103 reximd2a 3272 reximdai 3264 reximdd 46239 reximddv 3178 reximddv2 3221 reximddv3 3179 reximdv 3177 reximdv2 3172 reximdva 3175 reximdvai 3173 reximdvva 3210 reximi2 3095 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2247 19.23bi 2227 19.23h 2321 19.23t 2246 exlimdv 1965 exlimdvv 1966 exlimexi 45583 exlimiv 1962 exlimivv 1964 rexlimd3 46235 rexlimdv 3161 rexlimdv3a 3167 rexlimdva 3163 rexlimdva2 3165 rexlimdvaa 3164 rexlimdvv 3218 rexlimdvva 3219 rexlimdvvva 3220 rexlimdvw 3168 rexlimiv 3156 rexlimiva 3155 rexlimivv 3204 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 2023 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1912 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1902 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2263 r19.27z 4465 r19.27zv 4466 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2264 19.28vv 45446 r19.28z 4457 r19.28zf 46250 r19.28zv 4461 rr19.28v 3621 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1905 r19.29d2r 3149 r19.29imd 3127 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1913 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2270 19.31vv 45444 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2269 r19.32 48244 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 45442 19.33 1916 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 2024 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1909 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2266 19.36vv 45443 r19.36zv 4467 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2268 19.37vv 45445 r19.37zv 4462 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1871 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 2022 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1919 19.40 1918 r19.40 3128 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2271 19.41rg 45609 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2272 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1914 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2273 r19.44zv 4464 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2274 r19.45zv 4463 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2635 |
| [Mayet] p. 370 | Remark | jpi 32873 largei 32870 stri 32860 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32815 ishst 32817 |
| [Mayet3] p. 10 | Theorem | hstrbi 32869 hstri 32868 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 32331 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 32332 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32881 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31935 chsupcl 31943 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32963 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32957 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32984 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 41116 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18662 latj32 18660 latjass 18658 |
| [Megill] p. 444 | Axiom C5 | ax-5 1942 ax5ALT 40040 |
| [Megill] p. 444 | Section 7 | conventions 31002 |
| [Megill] p. 445 | Lemma L12 | aecom-o 40034 ax-c11n 40021 axc11n 2455 |
| [Megill] p. 446 | Lemma L17 | equtrr 2054 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 40029 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 40061 hbnae 2461 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2510 sbid 2290 sbidd-misc 50888 sbidd 50887 |
| [Megill] p. 448 | Remark 9.6 | axc14 2492 |
| [Megill] p. 448 | Scheme C4' | ax-c4 40017 |
| [Megill] p. 448 | Scheme C5' | ax-c5 40016 sp 2219 |
| [Megill] p. 448 | Scheme C6' | ax-11 2193 |
| [Megill] p. 448 | Scheme C7' | ax-c7 40018 |
| [Megill] p. 448 | Scheme C8' | ax-7 2040 |
| [Megill] p. 448 | Scheme C9' | ax-c9 40023 |
| [Megill] p. 448 | Scheme C10' | ax-6 1999 ax-c10 40019 |
| [Megill] p. 448 | Scheme C11' | ax-c11 40020 |
| [Megill] p. 448 | Scheme C12' | ax-8 2146 |
| [Megill] p. 448 | Scheme C13' | ax-9 2154 |
| [Megill] p. 448 | Scheme C14' | ax-c14 40024 |
| [Megill] p. 448 | Scheme C15' | ax-c15 40022 |
| [Megill] p. 448 | Scheme C16' | ax-c16 40025 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 40037 dral1 2468 dral2-o 40063 dral2 2467 drex1 2470 drex2 2471 drsb1 2524 drsb2 2300 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2208 sbequ 2119 sbid2v 2538 |
| [Megill] p. 450 | Example in Appendix | hba1-o 40030 hba1 2326 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 48038 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 24 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3825 rspsbca 3826 stdpc4 2104 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 40017 ra4 3832 stdpc5 2244 |
| [Mendelson] p. 81 | Rule C | exlimiv 1962 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2060 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2285 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3737 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5486 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4347 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4348 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4222 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4279 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4223 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4077 |
| [Mendelson] p. 231 | Definition of union | dfun3 4221 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5418 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4863 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5541 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4574 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5542 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4890 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5803 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6271 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7789 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6368 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8605 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9160 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 9081 xpsneng 9082 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9088 xpcomeng 9089 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9091 |
| [Mendelson] p. 255 | Definition | brsdom 9002 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9084 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8852 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 9066 mapsnend 9065 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9166 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9165 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8911 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 9069 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9085 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10258 djucomen 10257 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10262 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10256 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8540 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8567 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10644 |
| [Mendelson] p. 281 | Definition | df-r1 9769 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9822 |
| [Mendelson] p. 287 | Axiom system MK | ru 3737 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30861 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30896 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30898 vdgn1frgrv3 30899 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30900 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30893 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30886 2pthfrgrrn 30884 2pthfrgrrn2 30885 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31855 |
| [Monk1] p. 22 | Remark | conventions 31002 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 31002 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4135 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5758 ssrelf 33252 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5759 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5167 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6264 coi2 6265 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5901 rn0 5907 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 5862 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5668 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5910 rnxp 6161 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5749 xp0 5750 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6074 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6071 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7926 imaexg 7925 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6197 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7075 funfvop 7049 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6939 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6950 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6586 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7258 dff13f 7259 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7225 funrnex 7966 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7251 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6228 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4923 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 8018 df-1st 8001 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 8019 df-2nd 8002 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9869 ranksnb 9838 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9870 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9871 rankunb 9865 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9851 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9769 r1val2 9850 |
| [Monk1] p. 117 | Lemma | zorn2 10585 zorn2g 10582 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 10068 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10646 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 10063 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1841 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2040 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2212 ax-c15 40022 ax12v2 2214 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 40017 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2193 |
| [Monk2] p. 109 | Lemma 15 | equvini 2484 equvinv 2061 eqvinop 5455 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1942 ax5ALT 40040 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2177 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2193 |
| [Monk2] p. 114 | Lemma 21 | sp 2219 |
| [Monk2] p. 114 | Lemma 22 | axc4 2351 hba1-o 40030 hba1 2326 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2189 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2209 nfra2 3361 nfra2w 3298 |
| [Moore] p. 53 | Part I | df-mre 17757 |
| [Munkres] p. 77 | Example 2 | distop 23314 indistop 23321 indistopon 23320 |
| [Munkres] p. 77 | Example 3 | fctop 23323 fctop2 23324 |
| [Munkres] p. 77 | Example 4 | cctop 23325 |
| [Munkres] p. 78 | Definition of basis | df-bases 23265 isbasis3g 23268 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17615 tgval2 23275 |
| [Munkres] p. 79 | Remark | tgcl 23288 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 23282 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 23306 tgss3 23305 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 23307 basgen2 23308 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 38348 topdifinfeq 38349 topdifinffin 38347 topdifinfindis 38345 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23479 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 23357 topcld 23354 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 23358 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 23360 |
| [Munkres] p. 94 | Definition of closure | clsval 23356 |
| [Munkres] p. 94 | Definition of interior | ntrval 23355 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 23394 elcls 23392 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 23402 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23467 neindisj 23436 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23469 |
| [Munkres] p. 97 | Definition of limit point | islp2 23464 lpval 23458 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23634 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23546 iscn 23554 iscn2 23557 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23599 cncnp2 23600 cncnpi 23597 df-cnp 23547 iscnp 23556 iscnp2 23558 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24863 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25633 |
| [Nathanson] p. 123 | Remark | reprgt 35293 reprinfz1 35294 reprlt 35291 |
| [Nathanson] p. 123 | Definition | df-repr 35281 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 35313 |
| [Nathanson] p. 123 | Proposition | breprexp 35305 breprexpnat 35306 itgexpif 35278 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32707 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 48984 |
| [Pfenning] p. 17 | Definition XM | natded 31005 |
| [Pfenning] p. 17 | Definition NNC | natded 31005 notnotrd 134 |
| [Pfenning] p. 17 | Definition ` `C | natded 31005 |
| [Pfenning] p. 18 | Rule" | natded 31005 |
| [Pfenning] p. 18 | Definition /\I | natded 31005 |
| [Pfenning] p. 18 | Definition ` `E | natded 31005 natded 31005 natded 31005 natded 31005 natded 31005 |
| [Pfenning] p. 18 | Definition ` `I | natded 31005 natded 31005 natded 31005 natded 31005 natded 31005 |
| [Pfenning] p. 18 | Definition ` `EL | natded 31005 |
| [Pfenning] p. 18 | Definition ` `ER | natded 31005 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 31005 |
| [Pfenning] p. 18 | Definition ` `IR | natded 31005 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 31005 |
| [Pfenning] p. 127 | Definition =E | natded 31005 |
| [Pfenning] p. 127 | Definition =I | natded 31005 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25524 df-dip 31304 dip0l 31321 ip0l 21943 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25565 ipval 31306 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 31317 ipcj 21941 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25527 dipdir 31445 ipdir 21946 ipdiri 31433 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 31313 nmsq 25516 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 31428 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 31430 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 31431 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25533 dipass 31448 ipass 21952 ipassi 31444 |
| [Prugovecki] p. 186 | Definition of bra | braval 32547 df-bra 32453 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 32454 kbval 32557 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32985 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 41021 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32999 atcvat4i 33000 cvrat3 40575 cvrat4 40576 lsatcvat3 40185 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32885 cvrval 40402 df-cv 32882 df-lcv 40152 lspsncv0 21425 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 41033 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 41034 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2739 rabid 3432 rabidd 46246 wl-df.clab 38506 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2312 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2752 wl-df.cleq 38507 |
| [Quine] p. 19 | Definition 2.9 | conventions 31002 df-v 3452 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2899 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2896 abid2f 2952 |
| [Quine] p. 37 | Paragraph 1 | mirimanoff 36530 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2309 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2121 sbalex 2278 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2835 wl-df.clel 38510 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2760 eqid1 31069 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2767 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3739 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3740 dfsbcq2 3741 |
| [Quine] p. 43 | Theorem 6.8 | vex 3454 |
| [Quine] p. 43 | Theorem 6.9 | isset 3464 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3545 spcgv 3550 spcimgf 3513 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3751 spsbcd 3752 |
| [Quine] p. 44 | Theorem 6.12 | elex 3471 |
| [Quine] p. 44 | Theorem 6.13 | elab 3632 elabg 3629 elabgf 3627 |
| [Quine] p. 44 | Theorem 6.14 | noel 4283 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4677 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4586 df-sn 4584 |
| [Quine] p. 49 | Theorem 7.4 | snss 4744 snssg 4743 |
| [Quine] p. 49 | Theorem 7.5 | prss 4780 prssg 4779 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4722 prid1g 4720 prid2 4723 prid2g 4721 snid 4622 snidg 4620 |
| [Quine] p. 51 | Theorem 7.12 | snex 5396 |
| [Quine] p. 51 | Theorem 7.13 | prex 5395 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4885 unisnALT 45984 unisng 4884 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4889 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4898 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4895 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6508 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 48232 dfiota2 6495 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 48241 iotaval 6512 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6518 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6514 |
| [Quine] p. 58 | Definition 9.1 | df-op 4590 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5498 opabidw 5497 opelopab 5516 opelopaba 5509 opelopabaf 5518 opelopabf 5519 opelopabg 5512 opelopabga 5506 opelopabgf 5514 oprabid 7452 oprabidw 7451 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5656 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5658 |
| [Quine] p. 64 | Definition 9.15 | df-id 5545 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6605 |
| [Quine] p. 65 | Theorem 10.4 | funi 6572 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6593 funsng 6591 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6540 |
| [Quine] p. 65 | Definition 10.2 | args 6089 dffv4 6882 |
| [Quine] p. 68 | Definition 10.11 | conventions 31002 df-fv 6546 fv2 6880 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14417 nn0opth2i 14416 nn0opthi 14415 omopthi 8671 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8419 |
| [Quine] p. 232 | Equation i | carddom 10639 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6627 funimaexg 6626 |
| [Quine] p. 331 | Axiom system NF | ru 3737 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31687 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 31304 polid 31762 polid2i 31760 polidi 31761 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 31416 |
| [ReedSimon] p. 195 | Remark | lnophm 32622 lnophmi 32621 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32735 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32737 leopmuli 32736 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32740 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 32455 leoppos 32729 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32739 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32728 |
| [Ribenboim] p. 181 | Remark | nprmdvdsfacm1 48785 |
| [Ribenboim], p. 181 | Statement | ppivalnn 48793 |
| [Roman] p. 4 | Definition | df-dmat 22806 df-dmatalt 49586 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20376 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20462 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 49673 |
| [Roman] p. 112 | Note | isldepslvec2 49673 ldepsnlinc 49696 zlmodzxznm 49685 |
| [Roman] p. 112 | Example | zlmodzxzequa 49684 zlmodzxzequap 49687 zlmodzxzldep 49692 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 23209 |
| [Rosenlicht] p. 80 | Theorem | heicant 38649 |
| [Rosser] p. 281 | Definition | df-op 4590 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 35317 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 35318 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 49554 pmtr3ncom 19690 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19686 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19629 cayleyth 19630 |
| [Rudin] p. 164 | Equation 27 | efcan 16263 |
| [Rudin] p. 164 | Equation 30 | efzval 16271 |
| [Rudin] p. 167 | Equation 48 | absefi 16365 |
| [Russell1905] p. 482 | Example of "the father | dfalseu2 51008 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 200 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1803 |
| [Sanford] p. 39 | Rule 4 | mptxor 1801 |
| [Sanford] p. 40 | Rule 1 | mptnan 1800 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6108 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6111 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6107 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6105 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17757 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17758 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17758 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17760 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10216 |
| [Schechter] p. 141 | Definition (MC) | dfac11 44140 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10525 axdc3 10533 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20464 isrngo 38907 |
| [Schechter] p. 276 | Remark 11.6.e | span0 32145 |
| [Schechter] p. 276 | Definition of span | df-span 31912 spanval 31936 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 23312 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6387 onelond 37023 onelord 44329 ordelon 6386 ordelord 6384 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 44330 sucidg 6446 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6418 onsuc 7824 ord0 6417 ordsuci 7822 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 44331 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5215 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 44111 elon2 6373 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6368 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5553 epelg 5551 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9595 epirron 44332 ordirr 6380 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 44334 oneptr 44333 ontr1 6410 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6406 oneptri 44335 ordtri3or 6395 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8510 ord0eln0 6419 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6432 onsucss 44344 trsucss 6453 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7829 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6459 ordnbtwn 6458 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 44346 ordnexbtwnsuc 44345 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10480 onsucf1lem 44347 onsucf1o 44350 onsucf1olem 44348 onsucrn 44349 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 44351 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7856 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 44340 ordne0gt0 44339 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 44342 limnsuc 44343 onsucelab 44341 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9645 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7871 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9648 ordom 7887 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9649 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8650 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7794 ssorduni 7793 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8540 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9652 limom 7893 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8477 df1o2 8484 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8525 oa0suclim 44353 oalim 8541 oasuc 8533 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8526 om0suclim 44354 omlim 8542 omsuc 8535 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8531 oe0m1 8530 oe0suclim 44355 oelim 8543 oesuc 8536 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 44307 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 44357 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 44358 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 44359 limexissupab 44361 limiun 44360 limuni 6425 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8547 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8551 om1om1r 44362 om1r 8552 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8544 oaomoecl 44356 oecl 8546 omcl 8545 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 44309 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8553 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8554 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 44363 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 44364 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8621 nnamecl 44365 nnecl 8623 nnmcl 8622 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 44366 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8561 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8562 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8569 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 44368 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 44369 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 44371 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8568 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 44375 omword1 8582 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 44374 oaordnrex 44373 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 44370 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 44376 omword2 8583 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 44377 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 44378 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 44379 omordi 8575 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8577 omord2com 44380 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 44381 df-2o 8478 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 44384 oewordi 8601 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 44385 oeworde 8603 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 44386 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 44387 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 44383 omnord1ex 44382 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 44388 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 44390 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 44394 oenord1ex 44393 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 44395 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8570 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 44389 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8588 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8589 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 44397 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8607 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 44398 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 44399 cantnfub2 44400 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 44403 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 29493 axtgcgrrflx 28925 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 29494 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 29495 axtgcgrid 28926 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28911 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 29506 axtgsegcon 28927 df-trkgcb 28913 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 29517 axtg5seg 28928 df-trkgcb 28913 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 29518 axtgbtwnid 28929 df-trkgb 28912 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 29520 axtgpasch 28930 df-trkgb 28912 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 29539 df-trkg2d 35337 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28933 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28934 df-trkg2d 35337 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 29542 axtgeucl 28935 df-trkge 28914 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 29555 axtgcont 28932 axtgcont1 28931 df-trkgb 28912 |
| [Schwabhauser] p. 24 | Theorem A10 | prlngmo 29433 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 36827 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 36829 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 36832 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 36836 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 36837 tgcgrcomimp 28940 tgcgrcoml 28942 tgcgrcomr 28941 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 36842 tgcgrtriv 28947 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 36846 tg5segofs 35348 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 35345 df-ofs 36823 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 36848 tgcgrextend 28948 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 36850 tgsegconeq 28949 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36862 btwntriv2 36852 tgbtwntriv2 28951 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 36853 tgbtwncom 28952 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36856 tgbtwntriv1 28955 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36857 tgbtwnswapid 28956 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36863 btwnintr 36859 tgbtwnexch2 28960 tgbtwnintr 28957 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36865 btwnexch3 36860 tgbtwnexch 28962 tgbtwnexch3 28958 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36864 tgbtwnouttr 28961 tgbtwnouttr2 28959 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 29538 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36867 tgbtwndiff 28970 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28963 trisegint 36868 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36884 tgifscgr 28972 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 29022 colrot1 29023 colrot2 29024 lncom 29091 lnrot1 29092 lnrot2 29093 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36880 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36885 tgcgrsub 28973 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36895 tgcgrxfr 28982 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28981 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36881 df-cgrg 28975 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28975 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36896 tgbtwnxfr 28994 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36902 colinearperm2 36904 colinearperm3 36903 colinearperm4 36905 colinearperm5 36906 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28997 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36879 tgellng 29017 tglng 29010 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36907 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36915 lnxfr 29030 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36916 lnext 29031 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36920 tgfscgr 29032 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36921 lncgr 29033 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36882 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36923 lnid 29034 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36924 tgidinside 29035 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36941 tgbtwnconn1 29039 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36942 tgbtwnconn2 29040 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36943 tgbtwnconn3 29041 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36949 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36947 legov 29049 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 29050 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 29063 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36950 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36952 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36954 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36955 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36956 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36953 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36958 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 29051 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 29053 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 29054 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 29055 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 29056 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36965 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36966 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36961 df-outsideof 36960 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36962 ishlg 29069 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 29074 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 29076 outsideofrflx 36967 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 29070 hlcomd 29071 outsideofcom 36968 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 29077 outsideoftr 36969 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreq 29086 hlcgreu 29085 outsideofeu 36971 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36978 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36979 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36972 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36987 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36988 tglineelsb2 29101 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36990 linerflx1 36989 linerflx2 36991 tglinecom 29104 tglinerflx1 29102 tglinerflx2 29103 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36993 tglinethru 29105 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36977 tglng 29010 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 29058 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36996 tglinethrueu 29108 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36997 tglineineq 29112 tglineinsn 29113 tglineinteq 29115 tglineintmo 29111 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 29119 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 29120 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 29121 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 29139 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 29135 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 29127 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 29126 ismir 29132 mirbtwn 29131 mircgr 29130 mirfv 29129 mirval 29128 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 29137 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 29138 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 29139 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 29142 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 29143 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 29148 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 29145 mirbtwni 29144 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 29146 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 29158 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 29162 symquadmid 29305 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 29159 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 29160 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 29161 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 29164 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 29165 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 29174 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 29170 israg 29173 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 29175 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 29176 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 29178 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 29179 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 29180 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 29181 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 29182 ragncol 29185 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 29183 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 29189 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 29193 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 29190 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 29172 isperp 29188 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 29191 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 29198 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 29207 colperpexlem2 29208 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 29210 colperpexlem3 29209 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 29215 midex 29214 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 29212 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 29221 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 29216 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 29225 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 29228 opphllem6 29229 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 29231 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28930 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 29234 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 29242 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 29237 hpgbr 29239 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 29244 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 29243 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 29245 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 29246 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 29247 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 29248 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 29249 |
| [Schwabhauser] p. 74 | Lemma 9.22 | lnincplng 29263 |
| [Schwabhauser] p. 74 | Theorem 9.21 | plngcp 29265 |
| [Schwabhauser] p. 74 | Theorem 9.24 | plngrot 29269 |
| [Schwabhauser] p. 74 | Definition 9.20 | df-plng 29253 elplng 29259 |
| [Schwabhauser] p. 75 | Theorem 9.25 | lnssplng 29271 lnssplng1 29272 |
| [Schwabhauser] p. 76 | Theorem 9.26 | plng3p 29276 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 29290 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 29280 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 29294 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 29295 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 29296 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 29297 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 29298 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 29301 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 29303 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 29281 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 29304 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 29308 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 29309 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 29310 lnperpexs 29311 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 29312 trgcopyeu 29314 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 29339 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 29317 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 29326 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 29324 cgrahl2 29325 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 29327 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 29328 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 29330 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 29331 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 29335 cgrahl 29336 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 29340 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 29341 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 29342 acopyeu 29343 |
| [Schwabhauser] p. 98 | Theorem 11.16 | ragcgra 29344 |
| [Schwabhauser] p. 98 | Theorem 11.17 | cgrarag 29345 |
| [Schwabhauser] p. 98 | Theorem 11.18 | ragsupplcgra 29346 |
| [Schwabhauser] p. 99 | Theorem 11.19 | ragraghl 29347 |
| [Schwabhauser] p. 99 | Theorem 11.20 | perpeq 29349 |
| [Schwabhauser] p. 99 | Theorem 11.22 | tgaaddcpbl 29353 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 29361 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 29365 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 29358 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 29373 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 29366 isleag 29367 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 29401 tgsas1 29400 tgsas2 29402 tgsas3 29403 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 29405 tgasa1 29404 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 29406 tgsss2 29407 tgsss3 29408 |
| [Schwabhauser] p. 121 | Definition 12.2 | df-prlng 29416 |
| [Schwabhauser] p. 122 | Theorem 12.4 | prlngref 29419 |
| [Schwabhauser] p. 122 | Theorem 12.5 | prlngsym 29420 |
| [Schwabhauser] p. 122 | Theorem 12.6 | prlnghpg 29425 |
| [Schwabhauser] p. 122 | Theorem 12.7 | dfprlng2 29426 dfprlng3 29427 |
| [Schwabhauser] p. 122 | Theorem 12.9 | perpprlng 29429 |
| [Schwabhauser] p. 122 | Theorem 12.10 | prlngex 29430 |
| [Schwabhauser] p. 123 | Theorem 12.11 | prlngmo 29433 prlngmo2 29435 |
| [Schwabhauser] p. 124 | Theorem 12.13 | prlngeu 29434 |
| [Schwabhauser] p. 124 | Theorem 12.14 | prlngpln4 29437 |
| [Schwabhauser] p. 124 | Theorem 12.15 | prlngplngtr 29438 |
| [Schwabhauser] p. 125 | Theorem 12.16 | prlnginn0 29439 |
| [Schwabhauser] p. 125 | Theorem 12.17 | prlngmid2 29440 |
| [Schwabhauser] p. 126 | Theorem 12.18 | symquadprlng 29441 |
| [Schwabhauser] p. 126 | Theorem 12.19 | prlngsymquad 29443 prlngsymquadopp 29444 |
| [Schwabhauser] p. 126 | Theorem 12.20 | quadcgrprlng 29445 |
| [Schwabhauser] p. 126 | Theorem 12.21 | tgaltai 29446 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27599 dchrsum 27597 dchrsum2 27596 sumdchr 27600 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27601 sum2dchr 27602 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 20283 ablfacrp2 20284 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27544 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27545 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27552 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27810 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27813 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27867 vmalogdivsum2 27866 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27857 dirith2 27856 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27855 rpvmasum 27854 rpvmasum2 27840 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27815 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27853 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27820 dchrisumlem1 27817 dchrisumlem2 27818 dchrisumlem3 27819 dchrisumlema 27816 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27823 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27852 dchrmusumlem 27850 dchrvmasumlem 27851 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27822 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27824 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27848 dchrisum0re 27841 dchrisumn0 27849 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27834 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27838 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27839 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27894 pntrsumbnd2 27895 pntrsumo1 27893 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27858 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27860 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27862 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27865 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27870 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27871 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27876 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27878 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27879 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27887 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27888 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27885 selberg3lem2 27886 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27889 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27883 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27896 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27897 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27898 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27912 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27924 pntlemb 27925 pntlemc 27923 pntlemd 27922 pntlemg 27926 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27924 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27916 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27921 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27924 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27937 pntleml 27939 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 34418 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 34405 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 34437 constrinvcl 34448 constrmulcl 34446 constrnegcl 34438 constrsqrtcl 34454 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 34424 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 34434 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 34456 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 34466 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4251 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4355 dif0 4326 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4446 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4428 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4242 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4243 |
| [Stoll] p. 20 | Remark | invdif 4224 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4592 |
| [Stoll] p. 43 | Definition | uniiun 5016 |
| [Stoll] p. 44 | Definition | intiin 5017 |
| [Stoll] p. 45 | Definition | df-iin 4953 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4952 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 407 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4251 |
| [Strang] p. 242 | Section 6.3 | expgrowth 45395 |
| [Suppes] p. 22 | Theorem 2 | eq0 4296 eq0f 4293 |
| [Suppes] p. 22 | Theorem 4 | eqss 3923 eqssd 3925 eqssi 3924 |
| [Suppes] p. 23 | Theorem 5 | ss0 4351 ss0b 4350 |
| [Suppes] p. 23 | Theorem 6 | sstr 3916 sstrALT2 45893 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4030 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4032 |
| [Suppes] p. 23 | Theorem 9 | psstr 4035 |
| [Suppes] p. 23 | Theorem 10 | pssss 4025 |
| [Suppes] p. 25 | Theorem 12 | elin 4093 elun 4152 |
| [Suppes] p. 26 | Theorem 15 | inidm 4123 |
| [Suppes] p. 26 | Theorem 16 | in0 4344 |
| [Suppes] p. 27 | Theorem 23 | unidm 4156 |
| [Suppes] p. 27 | Theorem 24 | un0 4343 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4176 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4184 |
| [Suppes] p. 27 | Theorem 27 | unss 4188 |
| [Suppes] p. 27 | Theorem 28 | indir 4231 |
| [Suppes] p. 27 | Theorem 29 | undir 4232 |
| [Suppes] p. 28 | Theorem 32 | difid 4324 |
| [Suppes] p. 29 | Theorem 33 | difin 4217 |
| [Suppes] p. 29 | Theorem 34 | indif 4225 |
| [Suppes] p. 29 | Theorem 35 | undif1 4429 |
| [Suppes] p. 29 | Theorem 36 | difun2 4436 |
| [Suppes] p. 29 | Theorem 37 | difin0 4427 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4425 |
| [Suppes] p. 29 | Theorem 39 | difundi 4235 |
| [Suppes] p. 29 | Theorem 40 | difindi 4237 |
| [Suppes] p. 30 | Theorem 41 | nalset 5267 |
| [Suppes] p. 39 | Theorem 61 | uniss 4874 |
| [Suppes] p. 39 | Theorem 65 | uniop 5487 |
| [Suppes] p. 41 | Theorem 70 | intsn 4943 |
| [Suppes] p. 42 | Theorem 71 | intpr 4941 intprg 4940 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5439 |
| [Suppes] p. 42 | Theorem 78 | intun 4939 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4989 dfiun2g 4987 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4990 |
| [Suppes] p. 47 | Theorem 86 | elpw 4560 elpw2 5295 elpw2g 5294 elpwg 4559 elpwgdedVD 45975 |
| [Suppes] p. 47 | Theorem 87 | pwid 4579 |
| [Suppes] p. 47 | Theorem 89 | pw0 4772 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4773 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5665 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5809 xpindir 5810 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5719 xpundir 5720 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9592 |
| [Suppes] p. 58 | Theorem 2 | relss 5757 |
| [Suppes] p. 59 | Theorem 4 | eldm 5881 eldm2 5882 eldm2g 5880 eldmg 5879 |
| [Suppes] p. 59 | Definition 3 | df-dm 5660 |
| [Suppes] p. 60 | Theorem 6 | dmin 5892 |
| [Suppes] p. 60 | Theorem 8 | rnun 6135 |
| [Suppes] p. 60 | Theorem 9 | rnin 6136 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5869 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5859 brcnvg 5856 |
| [Suppes] p. 62 | Equation 5 | elcnv 5853 elcnv2 5854 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6099 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6134 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6132 |
| [Suppes] p. 63 | Definition | dftrrels2 39667 |
| [Suppes] p. 63 | Theorem 20 | co02 6262 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5956 |
| [Suppes] p. 63 | Definition 7 | df-co 5659 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5866 |
| [Suppes] p. 64 | Theorem 27 | coass 6267 |
| [Suppes] p. 65 | Theorem 31 | resundi 5983 |
| [Suppes] p. 65 | Theorem 34 | elima 6060 elima2 6061 elima3 6062 elimag 6059 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6140 |
| [Suppes] p. 66 | Theorem 40 | dminss 6142 |
| [Suppes] p. 66 | Theorem 41 | imainss 6143 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6146 |
| [Suppes] p. 81 | Definition 34 | dfec2 8721 |
| [Suppes] p. 82 | Theorem 72 | elec 8765 elecALTV 39279 elecg 8763 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 39703 erth 8773 erth2 8774 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 39706 erdisj 8776 |
| [Suppes] p. 83 | Definition 35, | df-parts 39876 dfmembpart2 39881 |
| [Suppes] p. 89 | Theorem 96 | map0b 8912 |
| [Suppes] p. 89 | Theorem 97 | map0 8916 map0g 8913 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8917 mapsnd 8915 |
| [Suppes] p. 89 | Theorem 99 | mapss 8918 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 10148 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 10147 |
| [Suppes] p. 92 | Theorem 1 | enref 9013 enrefg 9012 |
| [Suppes] p. 92 | Theorem 2 | ensym 9031 ensymb 9030 ensymi 9032 |
| [Suppes] p. 92 | Theorem 3 | entr 9034 |
| [Suppes] p. 92 | Theorem 4 | unen 9074 |
| [Suppes] p. 94 | Theorem 15 | endom 9007 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 9028 |
| [Suppes] p. 94 | Theorem 17 | domtr 9035 |
| [Suppes] p. 95 | Theorem 18 | sbth 9117 |
| [Suppes] p. 97 | Theorem 23 | canth2 9150 canth2g 9151 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9121 df-sdom 8977 dfsdom2 9120 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9134 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9123 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9122 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9132 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 9010 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9135 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9130 |
| [Suppes] p. 98 | Exercise 4 | fundmen 9060 fundmeng 9061 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9095 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9131 |
| [Suppes] p. 104 | Theorem 37 | fofi 9306 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9311 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9311 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10636 |
| [Suppes] p. 130 | Definition 3 | df-tr 5212 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7794 |
| [Suppes] p. 134 | Definition 6 | df-suc 6368 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7912 finds 7908 finds1 7911 finds2 7910 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9654 isfinite2 9291 isfiniteg 9293 unbnn 9289 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 11004 df-ltpq 10996 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7874 tfinds 7871 tfinds2 7875 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8560 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8562 |
| [Suppes] p. 211 | Theorem 25 | oaass 8570 |
| [Suppes] p. 225 | Definition 8 | iscard2 10058 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10648 |
| [Suppes] p. 228 | Theorem 59 | harcard 10060 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 10146 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6415 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7807 onminsb 7808 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10658 |
| [Suppes] p. 229 | Theorem 65 | alephcard 10150 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 10157 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 10151 |
| [Suppes] p. 229 | Definition 12 | df-aleph 10022 |
| [Suppes] p. 242 | Theorem 6 | weth 10574 |
| [Suppes] p. 242 | Theorem 8 | entric 10642 |
| [Suppes] p. 242 | Theorem 9 | carden 10636 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 36536 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 36540 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2732 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2752 wl-df.cleq 38507 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2835 wl-df.clel 38510 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2754 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2780 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7424 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3737 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5382 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4608 elpr2 4610 elpr2g 4609 elprg 4606 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4598 elsn2 4625 elsn2g 4624 elsng 4597 velsn 4599 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5435 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4593 sneqr 4799 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4604 dfsn2 4596 dfsn2ALT 4605 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7758 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5444 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5431 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5415 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7761 unexg 7760 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4651 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4867 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 4091 df-un 4151 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4883 uniprg 4882 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5338 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4649 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6435 elsucg 6433 sstr2 3915 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4157 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4106 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4170 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4124 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4229 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4230 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 4014 df-ss 3896 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4558 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4185 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 4094 sseqin2 4120 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3930 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4133 inss2 4134 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 3972 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4877 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5416 sspwimp 45976 sspwimpALT 45983 sspwimpALT2 45986 sspwimpcf 45978 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5423 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5231 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3413 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5260 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 4047 |
| [TakeutiZaring] p. 20 | Definition 5.14 | bj-dfnul2 37515 dfnul2 4281 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4324 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4299 n0f 4295 neq0 4298 neq0f 4294 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9591 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9734 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9749 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3452 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5273 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4349 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5281 ssexg 5280 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5276 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9603 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9595 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4313 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4071 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4245 undif3VD 45940 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4072 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4079 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3077 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3087 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7767 xpexg 7764 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5657 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6611 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6789 fun11 6614 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6551 svrelfun 6612 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5868 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5870 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5662 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5663 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5659 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6185 dfrel2 6180 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5666 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5788 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5795 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5808 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 5995 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5975 opelresi 5977 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 6002 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5991 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 5996 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6582 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6103 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6580 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6791 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2634 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 31002 df-fv 6546 fv3 6903 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7937 cnvexg 7936 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7921 dmexg 7913 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7922 rnexg 7914 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 45512 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7932 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6898 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 48320 tz6.12-1-afv2 48387 tz6.12-1 6908 tz6.12-afv 48319 tz6.12-afv2 48386 tz6.12 6909 tz6.12c-afv2 48388 tz6.12c 6907 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 48383 tz6.12-2 6872 tz6.12i-afv2 48389 tz6.12i 6911 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6541 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6542 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6544 wfo 6536 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6543 wf1 6535 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6545 wf1o 6537 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 7029 eqfnfv2 7030 eqfnfv2f 7033 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6983 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7223 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7221 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6627 funimaexg 6626 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5103 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5559 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5611 dffr3 6096 eliniseg 6091 iniseg 6094 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5550 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5627 fr3nr 7786 frirr 5626 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5603 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7788 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5614 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5636 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6350 tz6.26i 6351 wefrc 5644 wereu2 5647 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6352 wfii 6353 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6547 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7337 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7338 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7344 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7345 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7346 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7350 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7357 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7359 |
| [TakeutiZaring] p. 35 | Notation | wtr 5211 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 45513 tz7.2 5633 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5216 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6375 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6383 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6384 ordelordALT 45596 ordelordALTVD 45925 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6390 ordelssne 6389 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6388 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6393 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7796 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7797 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6366 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6395 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 45608 ordon 7791 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7792 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7864 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6411 ontr2d 37024 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5213 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7806 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7842 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6469 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6468 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7793 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4898 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6368 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6445 sucidg 6446 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7824 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6459 ordnbtwn 6458 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7839 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6367 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7892 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7897 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7852 ordelsuc 7831 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7833 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7862 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7879 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7900 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7901 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7902 |
| [TakeutiZaring] p. 43 | Remark | omon 7889 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9637 omex 9645 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7887 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7907 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7904 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7905 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7882 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4921 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5230 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4922 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5304 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7809 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6414 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4907 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9662 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7804 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8384 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8406 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8407 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8408 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8415 tz7.44-2 8416 tz7.44-3 8417 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8376 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8371 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8355 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8456 tz7.49c 8457 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8454 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8453 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8455 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2680 |
| [TakeutiZaring] p. 54 | Definition 7.55 | df-lexo 35921 |
| [TakeutiZaring] p. 54 | Definition 7.57 | df-r0 35922 |
| [TakeutiZaring] p. 54 | Proposition 7.58 | r0weseon 35932 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 10091 lexoweon 35930 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 10092 |
| [TakeutiZaring] p. 55 | Definition 7.59 | df-j0 35923 j0iso 35936 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8541 oasuc 8533 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7872 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8544 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8525 oa0r 8547 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8545 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8557 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8629 nnaordi 8628 oaord 8556 oaordi 8555 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5007 uniss2 4901 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8559 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8564 oawordex 8566 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8621 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8658 |
| [TakeutiZaring] p. 60 | Remark | oancom 9653 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8569 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8626 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8561 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8528 omlim 8542 omsuc 8535 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8526 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8623 nnmcl 8622 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8642 nnmordi 8641 omord 8577 omordi 8575 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8578 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8646 omwordri 8581 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8548 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8551 om1r 8552 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8584 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8586 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8587 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8588 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8589 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8618 oe0 8531 oelim 8543 oesuc 8536 onesuc 8539 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8529 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8596 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8597 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8530 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8554 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8598 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8604 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8602 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8603 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8607 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8609 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9730 tz9.1 9731 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9769 r10 9776 r1lim 9780 r1limg 9779 r1suc 9778 r1sucg 9777 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9788 r1ord2 9789 r1ordg 9786 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9798 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9825 tz9.13 9799 tz9.13g 9800 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9770 rankval 9826 rankvalb 9806 rankvalg 9827 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9852 rankelb 9834 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9868 rankval3 9854 rankval3b 9837 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9840 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9804 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9847 rankr1c 9831 rankr1g 9845 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9848 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9864 rankssb 9863 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9856 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9855 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10554 dfac3 10201 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 10110 numth 10551 numth2 10550 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10631 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10632 cardid2 10035 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 10042 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10636 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 10041 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 10026 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 10047 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 10039 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9170 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 9046 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9175 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9099 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 10045 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10178 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9222 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9230 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10179 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9227 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10168 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 10146 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 10054 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10295 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9315 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8978 isfi 9003 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9231 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10614 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9092 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10606 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10265 unxpdom 9251 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 10056 cardsdomelir 10055 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9253 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 10094 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8850 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10647 infxpidm2 10097 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10286 infxp 10293 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9104 pw2f1o 9102 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9163 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10566 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10561 ac6s5 10570 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10628 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10629 uniimadomf 10630 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10353 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10348 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10332 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10329 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10336 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10343 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10352 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10668 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10330 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10355 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10177 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10176 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10188 alephfp2 10189 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10785 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10192 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10655 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10669 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10670 |
| [TakeutiZaring] p. 143 | Definition 14.1(1) | df-cnv2 35901 |
| [TakeutiZaring] p. 143 | Definition 14.1(2) | df-cnv3 35902 |
| [TakeutiZaring] p. 144 | Definition 14.2 | df-gdlop1 35903 df-gdlop2 35904 df-gdlop3 35905 df-gdlop4 35906 df-gdlop5 35907 df-gdlop6 35908 df-gdlop7 35909 df-gdlop8 35910 df-gdlopc 35911 |
| [TakeutiZaring] p. 154 | Proposition 15.1(1) | maxssj0 35938 |
| [TakeutiZaring] p. 154 | Proposition 15.1(2) | j0ltaleph 35940 |
| [TakeutiZaring] p. 155 | Definition 15.2 | df-j 35924 |
| [TakeutiZaring] p. 156 | Definition 15.7 | df-k1 35925 df-k2 35926 df-k3 35927 |
| [TakeutiZaring] p. 158 | Definition 15.13 | df-fnl 35928 |
| [TakeutiZaring] p. 158 | Definition 15.15 | df-l 35929 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 40016 |
| [Tarski] p. 67 | Scheme B5 | sp 2219 |
| [Tarski] p. 68 | Lemma 6 | avril1 31065 equid 2044 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2049 |
| [Tarski] p. 70 | Lemma 14 | spim 2416 spime 2418 spimew 2003 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2212 ax-c15 40022 ax12i 1998 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2121 |
| [Tarski] p. 75 | Axiom B7 | ax6v 2000 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1942 ax5ALT 40040 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2040 ax-8 2146 ax-9 2154 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28927 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28928 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28930 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28930 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28931 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16412 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 38653 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 38655 |
| [Weierstrass] p. 272 | Definition | df-mdet 22901 mdetuni 22938 |
| [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 38444 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 44876 imim2 59 wl-luk-imim2 38439 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 48165 imim1 84 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 910 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2687 syl 18 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 916 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 23 wl-luk-id 38442 |
| [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 45985 wl-luk-notnotr 38443 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 147 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 44906 axfrege28 44905 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 38436 |
| [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 31003 pm2.27 43 wl-luk-pm2.27 38434 |
| [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 39379 |
| [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 37566 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 45418 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 45419 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1902 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 45420 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 45421 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 45422 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1925 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 45423 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 45424 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 45425 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 45426 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 45427 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 45429 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 45430 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 45431 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 45428 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2126 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 45434 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 45435 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2106 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2196 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1861 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1862 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 45436 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 45437 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 45438 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 45439 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 45441 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 45440 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1919 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 45443 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 45444 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 45442 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1860 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 45445 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 45446 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1878 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 45447 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2375 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1892 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 45452 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 45448 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 45449 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 45450 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 45451 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 45456 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 45453 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 45454 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 45455 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 45457 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2594 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 45467 pm13.13b 45468 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 45469 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3036 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3037 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3619 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 45475 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 45476 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 45470 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 45611 pm13.193 45471 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 45472 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 45473 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 45474 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 45481 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 45480 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 45479 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3800 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 45482 pm14.122b 45483 pm14.122c 45484 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 45485 pm14.123b 45486 pm14.123c 45487 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 45489 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 45488 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 45490 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6519 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 45491 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6520 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 45492 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 45494 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2658 eupickbi 2661 sbaniota 45495 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 45493 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2609 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 45496 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 31002 df-fv 6546 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 10083 pm54.43lem 10082 |
| [Young] p. 141 | Definition of operator ordering | leop2 32727 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32733 idleop 32734 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 43911 |
| [vandenDries] p. 43 | Theorem 62 | pellex 43918 pellexlem1 43912 |