Lean 4 fork for HoTT-compatible kernel extensions (Path types, transport, HITs). Maintained against upstream leanprover/lean4.
3857603dbb
This PR changes the definition of `Nat.div` and `Nat.mod` to use a structurally recursive, fuel-based implementation rather than well-founded recursion. This leads to more predicable reduction behavior in the kernel. `Nat.div` and `Nat.mod` are somewhat special because the kernel has native reduction for them when applied to literals. But sometimes this does not kick in, and the kernel has to unfold `Nat.div`/`Nat.mod` (e.g. in `lazy_delta_reduction` when there are open terms around). In these cases we want a well-behaved definition. We really do not want to reduce proofs in the kernel, which we want to prevent anyways well-founded recursion (to be prevented by #5182). Hence we avoid well-founded recursion here, and use a (somewhat standard) translation to a fuel-based definition. (If this idiom is needed more often we could even support it in Lean with `termination_by +fuel <measure>` rather easily.) |
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