Construct explicit δ(ε) or N witnesses for Lean 4 / mathlib4 limit proofs.
npx skills add https://github.com/bneb/perqed --skill epsilon-delta-bounding
Please help me install this Agent Skill. Skill: epsilon_delta_bounding Source: https://github.com/bneb/perqed/tree/main/.agents/skills/epsilon_delta_bounding Command: npx skills add https://github.com/bneb/perqed --skill epsilon-delta-bounding
The epsilon-delta method formalizes the intuitive notion of "closeness" in analysis. To prove lim_{x→a} f(x) = L, one must exhibit δ(ε) > 0 such that 0 < |x - a| < δ → |f(x) - L| < ε. The same structure extends to sequences, uniform continuity, and convergence in metric spaces.
Provide a Lean 4 goal for a limit or convergence and request an explicit δ(ε) witness to complete the proof.
High-intent search queries and answers about installing and using this skill.
To construct an explicit delta witness for epsilon-delta proofs in Lean 4, you provide a specific δ(ε) bound and apply tactics like norm_num, positivity, and linarith to close algebraic inequalities and certify limits.
Yes, you can use mathlib4 to formalize sequence convergence by constructing explicit N witnesses, applying Lean 4 tactics to close arithmetic bounds and verify that sequence terms satisfy convergence criteria.
The best way to prove limits in Lean 4 using the epsilon-delta method is to exhibit δ(ε) > 0 such that 0 < |x - a| < δ implies |f(x) - L| < ε, leveraging tactics like gcongr to automate closing algebraic inequalities.
Yes, formalizing continuity proofs with explicit bounds requires Lean 4 tooling and mathlib4 imports to construct δ(ε) witnesses that guarantee |f(x) - L| < ε across metric space contexts.
Your epsilon-delta proof may fail in Lean 4 if the explicit δ(ε) bounds are insufficient to close algebraic inequalities, requiring tactics like linarith or positivity to automatically verify that |f(x) - L| < ε holds.
Yes, the epsilon-delta bounding approach extends to uniform continuity and convergence in metric spaces by constructing explicit δ(ε) or N witnesses within Lean 4 and mathlib4 to certify the bounds.
bnebConstruct direct proofs in Lean 4 by applying definitions and inference rules.
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scooter-lacroixFormalize mathematical statements and generate machine-verified proofs using Lean 4.
