Orthomodular lattice

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An orthomodular lattice is an orthocomplemented lattice L that satisfies the following condition for all x, y \in L:

If x \leq y then y = x \cup (y \cap x^\perp)

Lattices of this form are of crucial importance for the study of quantum logic, since they are part of the axiomisation of the Hilbert space formulation of quantum mechanics.

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