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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > cdlemkuvN | Structured version Visualization version GIF version |
Description: Part of proof of Lemma K of [Crawley] p. 118. Value of the sigma1 (p) function π. (Contributed by NM, 2-Jul-2013.) (New usage is discouraged.) |
Ref | Expression |
---|---|
cdlemk1.b | β’ π΅ = (BaseβπΎ) |
cdlemk1.l | β’ β€ = (leβπΎ) |
cdlemk1.j | β’ β¨ = (joinβπΎ) |
cdlemk1.m | β’ β§ = (meetβπΎ) |
cdlemk1.a | β’ π΄ = (AtomsβπΎ) |
cdlemk1.h | β’ π» = (LHypβπΎ) |
cdlemk1.t | β’ π = ((LTrnβπΎ)βπ) |
cdlemk1.r | β’ π = ((trLβπΎ)βπ) |
cdlemk1.s | β’ π = (π β π β¦ (β©π β π (πβπ) = ((π β¨ (π βπ)) β§ ((πβπ) β¨ (π β(π β β‘πΉ)))))) |
cdlemk1.o | β’ π = (πβπ·) |
cdlemk1.u | β’ π = (π β π β¦ (β©π β π (πβπ) = ((π β¨ (π βπ)) β§ ((πβπ) β¨ (π β(π β β‘π·)))))) |
Ref | Expression |
---|---|
cdlemkuvN | β’ (πΊ β π β (πβπΊ) = (β©π β π (πβπ) = ((π β¨ (π βπΊ)) β§ ((πβπ) β¨ (π β(πΊ β β‘π·)))))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdlemk1.b | . 2 β’ π΅ = (BaseβπΎ) | |
2 | cdlemk1.l | . 2 β’ β€ = (leβπΎ) | |
3 | cdlemk1.j | . 2 β’ β¨ = (joinβπΎ) | |
4 | cdlemk1.a | . 2 β’ π΄ = (AtomsβπΎ) | |
5 | cdlemk1.h | . 2 β’ π» = (LHypβπΎ) | |
6 | cdlemk1.t | . 2 β’ π = ((LTrnβπΎ)βπ) | |
7 | cdlemk1.r | . 2 β’ π = ((trLβπΎ)βπ) | |
8 | cdlemk1.m | . 2 β’ β§ = (meetβπΎ) | |
9 | cdlemk1.u | . 2 β’ π = (π β π β¦ (β©π β π (πβπ) = ((π β¨ (π βπ)) β§ ((πβπ) β¨ (π β(π β β‘π·)))))) | |
10 | 1, 2, 3, 4, 5, 6, 7, 8, 9 | cdlemksv 39353 | 1 β’ (πΊ β π β (πβπΊ) = (β©π β π (πβπ) = ((π β¨ (π βπΊ)) β§ ((πβπ) β¨ (π β(πΊ β β‘π·)))))) |
Colors of variables: wff setvar class |
Syntax hints: β wi 4 = wceq 1542 β wcel 2107 β¦ cmpt 5189 β‘ccnv 5633 β ccom 5638 βcfv 6497 β©crio 7313 (class class class)co 7358 Basecbs 17088 lecple 17145 joincjn 18205 meetcmee 18206 Atomscatm 37771 LHypclh 38493 LTrncltrn 38610 trLctrl 38667 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 ax-sep 5257 ax-nul 5264 ax-pr 5385 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ne 2941 df-ral 3062 df-rex 3071 df-rab 3407 df-v 3446 df-dif 3914 df-un 3916 df-in 3918 df-ss 3928 df-nul 4284 df-if 4488 df-sn 4588 df-pr 4590 df-op 4594 df-uni 4867 df-br 5107 df-opab 5169 df-mpt 5190 df-id 5532 df-xp 5640 df-rel 5641 df-cnv 5642 df-co 5643 df-dm 5644 df-iota 6449 df-fun 6499 df-fv 6505 df-riota 7314 df-ov 7361 |
This theorem is referenced by: (None) |
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