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Theorem dp23 1195
 Description: Part of theorem from Alan Day and Doug Pickering, "A note on the Arguesian lattice identity," Studia Sci. Math. Hungar. 19:303-305 (1982). (2)=>(3)
Hypotheses
Ref Expression
dp23.1 c0 = ((a1a2) ∩ (b1b2))
dp23.2 c1 = ((a0a2) ∩ (b0b2))
dp23.3 c2 = ((a0a1) ∩ (b0b1))
dp23.4 p = (((a0b0) ∩ (a1b1)) ∩ (a2b2))
Assertion
Ref Expression
dp23 p ≤ (a0 ∪ (b0 ∩ (b1 ∪ (c2 ∩ (c0c1)))))

Proof of Theorem dp23
StepHypRef Expression
1 dp23.1 . . 3 c0 = ((a1a2) ∩ (b1b2))
2 dp23.2 . . 3 c1 = ((a0a2) ∩ (b0b2))
3 dp23.3 . . 3 c2 = ((a0a1) ∩ (b0b1))
4 dp23.4 . . 3 p = (((a0b0) ∩ (a1b1)) ∩ (a2b2))
51, 2, 3, 4dp32 1194 . 2 p ≤ ((a0 ∩ (a1 ∪ (c2 ∩ (c0c1)))) ∪ (b0 ∩ (b1 ∪ (c2 ∩ (c0c1)))))
6 lea 160 . . 3 (a0 ∩ (a1 ∪ (c2 ∩ (c0c1)))) ≤ a0
76leror 152 . 2 ((a0 ∩ (a1 ∪ (c2 ∩ (c0c1)))) ∪ (b0 ∩ (b1 ∪ (c2 ∩ (c0c1))))) ≤ (a0 ∪ (b0 ∩ (b1 ∪ (c2 ∩ (c0c1)))))
85, 7letr 137 1 p ≤ (a0 ∪ (b0 ∩ (b1 ∪ (c2 ∩ (c0c1)))))
 Colors of variables: term Syntax hints:   = wb 1   ≤ wle 2   ∪ wo 6   ∩ wa 7 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-ml 1120  ax-arg 1151 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: (None)
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