QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  womaa Unicode version
Theorem womaa 222
Description: Weak OM-like absorption law for ortholattices.
Assertion
Ref Expression
womaa (a' v (a ^ (a' v (a ^ b)))) = (a' v (a ^ b))
Proof of Theorem womaa
StepHypRef Expression
1 leo 158 . . 3 a' =< (a' v (a ^ b))
2 lear 161 . . 3 (a ^ (a' v (a ^ b))) =< (a' v (a ^ b))
31, 2lel2or 170 . 2 (a' v (a ^ (a' v (a ^ b)))) =< (a' v (a ^ b))
4 leo 158 . . 3 a' =< (a' v (a ^ (a' v (a ^ b))))
5 lea 160 . . . . 5 (a ^ b) =< a
6 leor 159 . . . . 5 (a ^ b) =< (a' v (a ^ b))
75, 6ler2an 173 . . . 4 (a ^ b) =< (a ^ (a' v (a ^ b)))
8 leor 159 . . . 4 (a ^ (a' v (a ^ b))) =< (a' v (a ^ (a' v (a ^ b))))
97, 8letr 137 . . 3 (a ^ b) =< (a' v (a ^ (a' v (a ^ b))))
104, 9lel2or 170 . 2 (a' v (a ^ b)) =< (a' v (a ^ (a' v (a ^ b))))
113, 10lebi 145 1 (a' v (a ^ (a' v (a ^ b)))) = (a' v (a ^ b))
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-le1 130  df-le2 131
This theorem is referenced by:  nom13  310  lem3.3.7i3e1  1066
  Copyright terms: Public domain W3C validator