Metamath Proof Explorer


Theorem cdlemkuvN

Description: Part of proof of Lemma K of Crawley p. 118. Value of the sigma_1 (p) function U . (Contributed by NM, 2-Jul-2013) (New usage is discouraged.)

Ref Expression
Hypotheses cdlemk1.b B = Base K
cdlemk1.l ˙ = K
cdlemk1.j ˙ = join K
cdlemk1.m ˙ = meet K
cdlemk1.a A = Atoms K
cdlemk1.h H = LHyp K
cdlemk1.t T = LTrn K W
cdlemk1.r R = trL K W
cdlemk1.s S = f T ι i T | i P = P ˙ R f ˙ N P ˙ R f F -1
cdlemk1.o O = S D
cdlemk1.u U = e T ι j T | j P = P ˙ R e ˙ O P ˙ R e D -1
Assertion cdlemkuvN G T U G = ι j T | j P = P ˙ R G ˙ O P ˙ R G D -1

Proof

Step Hyp Ref Expression
1 cdlemk1.b B = Base K
2 cdlemk1.l ˙ = K
3 cdlemk1.j ˙ = join K
4 cdlemk1.m ˙ = meet K
5 cdlemk1.a A = Atoms K
6 cdlemk1.h H = LHyp K
7 cdlemk1.t T = LTrn K W
8 cdlemk1.r R = trL K W
9 cdlemk1.s S = f T ι i T | i P = P ˙ R f ˙ N P ˙ R f F -1
10 cdlemk1.o O = S D
11 cdlemk1.u U = e T ι j T | j P = P ˙ R e ˙ O P ˙ R e D -1
12 1 2 3 5 6 7 8 4 11 cdlemksv G T U G = ι j T | j P = P ˙ R G ˙ O P ˙ R G D -1