Min Operation is Idempotent

Theorem
The min operation operation is idempotent:


 * $\map \min {x, x} = x$

Proof
Follows immediately from the definition of min operation:


 * $\map \min {a, b} = \begin {cases} a & : a \le b \\ b & : b \le a \end {cases}$

Setting $x = a = b$ returns the result.

Also see

 * Max Operation is Idempotent