Theorem womaan 215

Description: Weak OM-like absorption law for ortholattices.

Assertion

Ref	Expression
womaan	(a v (a_|_ ^ (a v (a_|_ ^ b)))) = (a v (a_|_ ^ b))

Proof of Theorem womaan

Step	Hyp	Ref	Expression
1		leo 150	. . 3 a =< (a v (a_|_ ^ b))
2		lear 153	. . 3 (a_|_ ^ (a v (a_|_ ^ b))) =< (a v (a_|_ ^ b))
3	1, 2	lel2or 162	. 2 (a v (a_|_ ^ (a v (a_|_ ^ b)))) =< (a v (a_|_ ^ b))
4		leo 150	. . 3 a =< (a v (a_|_ ^ (a v (a_|_ ^ b))))
5		lea 152	. . . . 5 (a_|_ ^ b) =< a_|_
6		leor 151	. . . . 5 (a_|_ ^ b) =< (a v (a_|_ ^ b))
7	5, 6	ler2an 165	. . . 4 (a_|_ ^ b) =< (a_|_ ^ (a v (a_|_ ^ b)))
8		leor 151	. . . 4 (a_|_ ^ (a v (a_|_ ^ b))) =< (a v (a_|_ ^ (a v (a_|_ ^ b))))
9	7, 8	letr 129	. . 3 (a_|_ ^ b) =< (a v (a_|_ ^ (a v (a_|_ ^ b))))
10	4, 9	lel2or 162	. 2 (a v (a_|_ ^ b)) =< (a v (a_|_ ^ (a v (a_|_ ^ b))))
11	3, 10	lebi 137	1 (a v (a_|_ ^ (a v (a_|_ ^ b)))) = (a v (a_|_ ^ b))

Syntax hints:   = wb 1  _|_wn 4   v wo 6   ^ wa 7

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-a 39  df-t 40  df-f 41  df-le1 122  df-le2 123

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