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This skill provides a structured methodology for completing incomplete Coq proofs involving arithmetic properties of natural numbers, such as commutativity and associativity. It guides users through inductive proof structures, goal state analysis, and the correct application of standard library lemmas like plus_n_O and plus_n_Sm. Whether you are debugging complex proof states or filling in unfinished theorems, this skill ensures best practices for rewrite directions and tactic selection to achieve successful formal verification.
