Natural Number m is Less than n implies n is not Greater than Successor of n/Proof using Naturally Ordered Semigroup

Theorem

Let $\N$ be the natural numbers.

Let $m, n \in \N$.

Then:

$m < n \implies m + 1 \le n$

Proof

Let $\N$ be considered as the naturally ordered semigroup:

$\struct {\N, +, \le}$

The result follows from Sum with One is Immediate Successor in Naturally Ordered Semigroup.