Prove natural number statements by assuming P(k) for all k less than n.
npx skills add https://github.com/0bserver07/bourbaki --skill strong-induction
Please help me install this Agent Skill. Skill: strong-induction Source: https://github.com/0bserver07/bourbaki/tree/main/src/skills/strong-induction Command: npx skills add https://github.com/0bserver07/bourbaki --skill strong-induction
Proves statements about natural numbers using strong induction to establish P(n) from P(k) for all k < n.
Prove a target property P(n) for natural numbers by assuming P(k) holds for all k < n and deriving P(n).
High-intent search queries and answers about installing and using this skill.
Strong induction is needed when the inductive step relies on all smaller cases rather than just the immediate predecessor, such as in recurrence relations and well-ordering arguments over natural numbers.
A strong induction proof requires a clear base case, a strong inductive hypothesis assuming the property holds for all k < n, and a constructive derivation of the target property P(n) from that hypothesis.
Yes, the skill provides formalization hints and templates for encoding strong induction proofs in Lean, guiding the setup of base cases and strong hypotheses for natural number theorems.
To prove recurrence relations with strong induction, establish the base case and then derive the recurrence step by applying the inductive hypothesis across all preceding values less than n.
Yes, strong induction applies directly to well-ordering arguments on natural numbers, allowing proofs to proceed by assuming the property holds for all smaller values to establish the current case.
Standard induction fails when the step requires multiple prior cases because it only assumes the immediate predecessor; strong induction resolves this by assuming the property for all k < n.
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