Guide Lean 4 proofs involving Option and Except monads with tactical advice.
npx skills add https://github.com/kim-em/lean-zip --skill lean-monad-proofs
Please help me install this Agent Skill. Skill: lean-monad-proofs Source: https://github.com/kim-em/lean-zip/tree/main/.claude/skills/lean-monad-proofs Command: npx skills add https://github.com/kim-em/lean-zip --skill lean-monad-proofs
This Skill provides expert guidance and tactical advice for navigating complex proof patterns in Lean 4, specifically when dealing with monads like Option and Except.
for/while loops in specifications and prove properties about them, including the critical distinction between pure functions and partial definitions.Except.bind or Option.pure, consult this Skill for the precise tactic sequence or lemma to apply.Use the lean-monad-proofs skill to understand how to correctly use Except.mapError in simp sets.
High-intent search queries and answers about installing and using this skill.
Proving properties of Lean 4 Option and Except monads requires advanced tactical guidance for unfolding do-notation, handling bind operations, and resolving constructor inequalities. This provides precise tactic sequences for these specific monadic proof scenarios.
nomatch failures in Lean 4 monad proofs occur when the tactic cannot resolve contradictory constructor states. You can fix this by applying specific case analysis tactics like `cases hrd : expr` to explicitly expose the contradiction.
Handling forIn loop invariants in the Id monad involves proving properties across loop iterations while distinguishing between pure function definitions and partial definitions. This ensures specifications hold correctly throughout the loop execution.
Using Except.mapError in Lean 4 simp sets requires careful tactical placement to simplify error handling during proofs. Correctly adding it to simp sets allows automated rewriting of error-mapping operations in Except monads.
This Lean 4 tactical guidance addresses loop invariants by explicitly distinguishing between pure functions and partial definitions. It provides specific solutions to prove specifications correctly depending on whether the definition is pure or partial.
Resolving constructor inequalities when proving Lean 4 monad properties involves using targeted case analysis and specific tactical sequences. This Skill offers solutions for navigating these structural inequalities during Option and Except bind operations.
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