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