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

If ${\displaystyle x\leq y}$ then ${\displaystyle y=x\cup (y\cap x^{\perp })}$

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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