formal-methods

name	formal-methods
description	Verify proofs, check theorem correctness, and solve satisfiability problems using Lean 4, Coq, and Z3 SMT solver. Use when the user asks to prove theorems, verify mathematical proofs, check logical satisfiability, or work with proof assistants.
_source	Canonical source at /skills/formal-methods/SKILL.md

formal-methods

Formal verification tools for the academic workspace. Type-check Lean 4 proofs, verify Coq theories, and solve SMT satisfiability problems with Z3.

Process

1. Check availability — Use prover_status to see which provers are installed
2. Write proof — Draft your Lean/Coq code or SMT formula
3. Verify — Use lean_check, coq_check, or z3_solve to verify
4. Iterate — Fix errors based on output and re-check

Tools

• lean_check — Type-check Lean 4 code. Params: code (required), filename
• coq_check — Check a Coq proof. Params: code (required), filename
• coq_compile — Compile Coq to .vo object file. Params: code (required), filename
• z3_solve — Solve SMT-LIB2 formula. Params: formula (required)
• prover_status — Check available provers and versions. No params.

Example:

{ "code": "theorem add_comm (a b : Nat) : a + b = b + a := Nat.add_comm a b" }

See canonical skill for full tool documentation and parameter details.