lean-fuel-induction

To prove fuel independence in Lean 4, you structure your induction to show that a recursive function's output remains consistent regardless of its fuel parameter. This Skill provides proof patterns to handle recursive calls efficiently.

You establish loop invariants in Lean 4 by threading invariants through monadic operations during stateful recursion. This Skill guides you through techniques to maintain and prove these invariants across recursive calls.

Avoiding `forIn` on `Range` in Lean 4 prevents complex proof obligations and compilation limits. This Skill addresses these challenges by offering structured proof patterns for fuel-based recursion instead.

You optimize Lean 4 proof compilation by managing `maxRecDepth` and `maxHeartbeats` parameters. This Skill provides advice on reducing these limits to achieve faster compilation and more robust termination proofs.

Fuel-based recursion proofs in Lean 4 are techniques for verifying functions that depend on a fuel parameter for termination. You need them when proving properties about recursive functions that consume fuel to guarantee termination.