Construct direct proofs in Lean 4 by applying definitions and inference rules.
npx skills add https://github.com/bneb/perqed --skill direct-proof-bneb
Please help me install this Agent Skill. Skill: direct_proof Source: https://github.com/bneb/perqed/tree/main/.agents/skills/direct_proof Command: npx skills add https://github.com/bneb/perqed --skill direct-proof-bneb
Direct proof guides learners and practitioners to derive conclusions from hypotheses without resorting to case splits or contradiction, streamlining formal reasoning in Lean.
Prove a simple implication by assuming the antecedent and applying established lemmas to derive the consequent.
High-intent search queries and answers about installing and using this skill.
A direct proof in Lean 4 assumes the antecedent with intro and systematically applies definitions, lemmas, and inference rules via apply or exact to forward-reason toward the consequent without contradiction.
Handling existential goals in Lean 4 mathlib4 requires providing an explicit witness, then systematically applying definitions and basic tactics like apply or exact to close the remaining proof leaves.
Yes, calc blocks provide a structured proof environment for forward reasoning in Lean 4, allowing you to systematically chain definitions and lemmas to derive a conclusion from hypotheses.
No, universal statements in Lean 4 are handled by introducing variables with intro, whereas existential goals require explicit witnesses to construct the derivation and close the proof.
Direct proofs stall in Lean 4 when the structured proof environment lacks proper forward reasoning; systematically applying definitions and lemmas via intro, apply, exact, and calc resolves remaining proof leaves.
Avoid direct proofs in Lean 4 when the derivation cannot be constructed by purely forward reasoning from hypotheses, requiring case splits or contradiction tactics to close the goal instead.
fmhallProvide Lean 4 tactics for simplifying proofs with simp only failures.
fmhallOptimize Lean 4 proofs involving monads and do-notation.
bnebDerive proofs by contradiction in Lean 4 using by_contra and absurd.
dzackgarzaFormalize and verify mathematical problems using ITPs and SMT solvers.
