Prove existence statements with concrete witnesses in Lean 4.
npx skills add https://github.com/bneb/perqed --skill explicit-construction
Please help me install this Agent Skill. Skill: explicit_construction Source: https://github.com/bneb/perqed/tree/main/.agents/skills/explicit_construction Command: npx skills add https://github.com/bneb/perqed --skill explicit-construction
Explicit construction provides concrete witnesses for existential statements, enabling direct verification rather than relying on non-constructive arguments.
exact, refine, and decide to discharge goals.Provide a concrete witness and verify its property inside a Lean 4 proof.
High-intent search queries and answers about installing and using this skill.
To prove an existence statement in Lean 4, provide a specific witness object and use tactics like exact or refine to verify that the object satisfies the required property. This direct construction avoids non-constructive arguments.
Constructive proof in Lean 4 requires presenting a concrete object alongside a proof of its property. You need an explicit witness when formalizing existence statements for tasks like Ramsey-type proofs or bijection constructions.
Use the refine tactic to structure a proof goal around a concrete witness, then apply exact to discharge remaining goals by providing the specific proof term that verifies the witness satisfies the property.
Yes, you can verify Ramsey-type proofs in Lean 4 by embedding concrete witnesses into Lean terms. This approach satisfies formal verification requirements by constructively proving the existence of the required structures.
The decide tactic works alongside exact and refine to discharge goals in constructive existence proofs. It evaluates concrete witnesses to verify their properties, satisfying Lean 4 proof script requirements for formal verification tasks.
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