Existence of Non-Empty Finite Infima in Meet Semilattice

Theorem
Let $\left({S, \preceq}\right)$ be a meet semilattice.

Let $A$ be a non-empty finite subset of $S$.

Then $A$ admits a infimum in $\left({S, \preceq}\right)$.

Proof
This follows by mutatis mutandis of the proof of Existence of Non-Empty Finite Suprema in Join Semilattice.