Prove natural number properties using weak and strong induction in Lean 4.
npx skills add https://github.com/bneb/perqed --skill mathematical-induction
Please help me install this Agent Skill. Skill: mathematical_induction Source: https://github.com/bneb/perqed/tree/main/.agents/skills/mathematical_induction Command: npx skills add https://github.com/bneb/perqed --skill mathematical-induction
Proves properties of natural numbers using induction, enabling rigorous formal reasoning in mathematics and computer science.
Prove a property P(n) for all natural numbers by establishing a base case and an inductive step in Lean 4.
High-intent search queries and answers about installing and using this skill.
Mathematical induction in Lean 4 proves statements for all natural numbers by encoding a base case and an inductive step. This template-driven approach establishes that if the property holds for a base value and propagates from n to n+1, it holds universally.
Weak induction assumes only the immediate predecessor case to prove the inductive step, while strong induction allows assuming the statement holds for all smaller natural numbers. Strong induction primitives in Lean 4 help express complex proofs where weak induction is insufficient.
Yes, structural induction applies to custom data types in Lean 4. Instead of natural numbers, it proves properties by analyzing the recursive structure of a data type, handling base constructors and recursive constructors to verify formal properties.
Yes, a Lean 4 environment is required to execute mathematical induction proofs. The Skill provides templates and guides practical proof scripting using Lean 4 tactics specifically designed for educational and research contexts in formal verification.
Use strong induction for algorithm correctness proofs when the proof for the n-th case depends on multiple smaller cases rather than just the immediate predecessor. This approach allows assuming all smaller natural numbers to establish complex formal properties.
0bserver07Automate induction proofs for natural numbers with Lean 4 verification.
xaionaroProve algorithm correctness in Lean 4 before implementing in the target language.
scooter-lacroixSolve proof theory problems using direct proof, contradiction, cases, and induction.
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