Derive proofs by contradiction in Lean 4 using by_contra and absurd.
npx skills add https://github.com/bneb/perqed --skill proof-by-contradiction
Please help me install this Agent Skill. Skill: proof_by_contradiction Source: https://github.com/bneb/perqed/tree/main/.agents/skills/proof_by_contradiction Command: npx skills add https://github.com/bneb/perqed --skill proof-by-contradiction
Proof by contradiction provides a structured method to prove statements by assuming the negation and deriving False, letting you conclude the original assertion holds. In Lean 4, this approach supports both constructive and non-constructive arguments and helps formalize classical reasoning when explicit witnesses are unavailable.
Start a Lean proof by assuming the negation of the goal with by_contra and derive a contradiction to conclude the goal.
High-intent search queries and answers about installing and using this skill.
Proof by contradiction in Lean 4 uses the by_contra tactic to assume the negation of a goal, then derives False to conclude the original assertion. You typically combine push_neg and absurd to simplify and close the contradiction.
Proof by contradiction is needed for mathematical results requiring non-constructive arguments, such as irrationality proofs and non-existence claims, where explicit witnesses are unavailable and classical reasoning is permitted.
Start a Lean proof with by_contra to introduce a negated goal, apply push_neg to simplify the assumption, and use absurd to derive a contradiction, establishing the original statement.
Deriving proofs by contradiction in Lean 4 requires a Lean 4 environment with Mathlib and familiarity with classical reasoning tactics like by_contra, push_neg, and absurd to extract contradictions.
Proof by contradiction in Lean 4 supports both constructive and non-constructive arguments, helping formalize classical reasoning in mathematical libraries when explicit witnesses cannot be constructed directly.
The by_contra tactic introduces a negated goal but requires deriving False to succeed. If the contradiction is not explicit, use push_neg to simplify assumptions and absurd to close the logical gap.
kim-emProvide Lean 4 tactic replacements for environments without Mathlib.
sandraschiGuide students in constructing rigorous mathematical proofs with LaTeX-friendly notation.
fmhallProvide Lean 4 tactics for simplifying proofs with simp only failures.
bnebProve existence statements with concrete witnesses in Lean 4.
