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proof-by-contradiction - Proof by Contradiction: Mathematical Proof Technique

Proves mathematical statements by assuming the negation and deriving a contradiction

Tags

Updated: 2026-02-14
mathematicsprooflogictheorem-provinglean

Capabilities

Negate mathematical statementsDerive logical consequencesIdentify contradiction patternsFormalize proofs in Lean

Typical Inputs

Mathematical statementLean theorem proverProof assumptions

Typical Outputs

Formalized proofProof documentationLean code file

What this skill does

  • Negate mathematical statements
  • Derive logical consequences
  • Identify contradiction patterns
  • Formalize proofs in Lean
  • Verify proof correctness

Inputs

  • Mathematical statement
  • Lean theorem prover
  • Proof assumptions

Outputs

  • Formalized proof
  • Proof documentation
  • Lean code file

Requirements

  • Lean theorem prover environment
  • Mathematical statement to prove

Source

  • Spec: SKILL.md

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