proof_by_contradiction

What problem does it solve?

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.

Core Features & Use Cases

• Tactic guidance: use by_contra to introduce a negated goal, push_neg to simplify it, and absurd to close the contradiction.
• Education & verification: ideal for teaching reductio ad absurdum, and for proving irrationality or non-existence results within Lean 4.
• Applicability in formal proofs: supports classical reasoning in mathematical libraries where existence or equality cannot be constructed directly.

Quick Start

Start a Lean proof by assuming the negation of the goal with by_contra and derive a contradiction to conclude the goal.