The operations and have the following consistency properties. For every x; y in a lattice
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1. x ∨ y ≿ x ≿ x ∧ y
2. x ≿ y =⇒ x ∨ y = x and x ∧ y = y
3. x ∨ x ∧ y = x = x ∧(x ∨ y)
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