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Let ( L, ≤ ) be a lattice, x, y, z ∈ L

I am unable to understand why ( x ∧ z ) ∧ ( y ∧ z ) = z ∧ ( y ∧ x ) is mentioned as fact in Y.N. Singh's "Mathematical Foundation of Computer Science" - Pg 157

Could I prove this somehow, or is it an axiom?

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    Both sides equal the infimum of the set $\{x,y,z\}$.2010-11-22

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