Convert implications to their contrapositive in Lean 4 proofs.
npx skills add https://github.com/bneb/perqed --skill proof-by-contraposition
Please help me install this Agent Skill. Skill: proof_by_contraposition Source: https://github.com/bneb/perqed/tree/main/.agents/skills/proof_by_contraposition Command: npx skills add https://github.com/bneb/perqed --skill proof-by-contraposition
Contraposition-based proofs in Lean 4: convert implications to their contrapositive to obtain a more concrete hypothesis and complete the proof.
Apply contraposition in Lean 4 to convert P → Q into ¬Q → ¬P and complete the proof from the negated premise.
High-intent search queries and answers about installing and using this skill.
Use the contrapose or contrapose! tactic in Lean 4 to convert an implication P → Q into its contrapositive ¬Q → ¬P, allowing you to prove the goal from the negated conclusion instead of the original premise.
Use contraposition in Lean 4 when the negated conclusion provides a stronger, more concrete hypothesis. It is particularly effective for simplifying proofs involving inequalities, divisibility, and graph connectivity arguments.
The contrapose tactic converts an implication P → Q into its contrapositive ¬Q → ¬P, while push_neg pushes negations inward to simplify logical expressions. They are often used together to transform and normalize goals before applying standard tactics.
Yes, the contrapose tactic works for inequalities and divisibility proofs in Lean 4. Contraposition is specifically useful in these domains because negating the conclusion often produces a more concrete and directly applicable mathematical assumption.
Contraposition tactics may fail if the logical structure resists automatic negation or requires manual normalization. Apply push_neg after contrapose to push negations inward and resolve nested definitions that prevent the tactic from completing the proof.
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