Two is a Locale

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Theorem

Let $\struct{\mathbf 2, \vee, \wedge, \neg, \preceq}$ denote (Boolean lattice) two.

Then:

$\struct{\mathbf 2, \vee, \wedge, \preceq}$ is a locale.

Proof

Follows immediately from:

• Two is Boolean Lattice
• Finite Boolean Lattice is a Locale

$\blacksquare$