prove-plus-comm

To prove addition commutativity for natural numbers in Coq, apply a structured inductive proof pattern, using lemmas like plus_n_O and plus_n_Sm to rewrite the base and inductive step goals.

Your Coq natural-number arithmetic proof may fail if the inductive step is not properly rewritten; use the plus_n_Sm lemma to simplify successor expressions and align the goal with your induction hypothesis.

The best way to debug incomplete Coq proofs involving natural-number arithmetic is to follow a structured inductive proof strategy, checking if standard lemmas like plus_n_O and plus_n_Sm apply to your current goal.

You need to use the plus_n_O and plus_n_Sm lemmas in Coq when rewriting natural-number arithmetic goals during inductive proofs, specifically to simplify expressions involving zero and the successor of natural numbers.

Yes, you can apply the structured inductive proof pattern to other natural-number arithmetic lemmas in Coq, provided the proof relies on standard arithmetic lemmas and follows similar base and inductive step structures.

No external libraries are required; this approach assumes a standard Coq development environment and relies on applying built-in natural-number arithmetic lemmas to establish your inductive proofs.