prove-plus-comm

To prove addition commutativity in Coq, apply induction on natural numbers and rewrite goals using standard lemmas like plus_n_O and plus_n_Sm. This skill guides you through the step-by-step process to complete such arithmetic proofs correctly.

Coq arithmetic proofs often fail during induction due to common pitfalls like wrong rewrite direction, missing imports, or incorrect induction variables. This skill analyzes your proof structure and helps apply appropriate lemmas to resolve these issues.

Yes, you need to import the Arith library to prove natural number addition lemmas in Coq. This skill requires the Arith library to access standard lemmas like plus_n_O and plus_n_Sm needed for finishing commutativity and associativity proofs.

The standard Coq lemmas used to prove natural number addition commutativity are plus_n_O and plus_n_Sm. This skill relies on these specific lemmas to correctly rewrite goals when formalizing arithmetic properties involving induction.

Yes, you can use this approach to prove associativity and related arithmetic lemmas in Coq. The skill is designed to complete incomplete proofs concerning natural number addition properties, guiding you through the necessary induction steps and lemma applications.