lean-wf-recursion

To prove properties of well-founded recursive functions in Lean 4, use specific proof strategies like unfolding the functions and applying custom induction principles such as `f.induct` to manage termination measures.

Migrating from fuel-based recursion to well-founded recursion in Lean 4 involves following a structured checklist to convert older functions, ensuring a more robust termination definition and simplifying subsequent property proofs.

The `simp` tactic loops infinitely when unfolding well-founded recursion in Lean 4 if the simplification engine repeatedly triggers the recursive definition, requiring specific proof patterns to break the cycle and control the unfolding.

Defining a termination measure for a recursive function in Lean 4 requires specifying a decreasing metric that the well-founded recursion mechanism can verify, ensuring the function structurally reduces its input on each recursive call.

Handling dependent `if` guards in well-founded recursion proofs requires careful management of the guard conditions during simplification to avoid breaking the termination measure assumptions and failing the proof.

You should use `f.induct` instead of standard structural induction in Lean 4 when proving properties of well-founded recursive functions, as it directly mirrors the function's specific recursive structure and termination logic.