Identity Mapping is Semilattice Homomorphism

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Theorem

Let $S = \struct{A, \circ}$ be a semilattice.

Let $\operatorname{id}_A$ denote the identity mapping on $A$.

Then:

$\operatorname{id}_A$ is a semilattice homomorphism of $S$ to $S$

Proof

Follows immediately from Identity Mapping is Automorphism.

$\blacksquare$