refactor: FunInd overhaul #4789
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This refactoring PR changes the structure of the
FunIndmodule, with the main purpose to make it easier to support mutual structural recursion.In particular the recursive calls are now longer recognized by their terms (simple for well-founded recursion,
.app oldIH [arg, proof], but tedious for structural recursion and even more so for mutual structural recursion), but the type after replacingoldIHwithnewIH, where the type will be simply and plainlymkAppN motive args).We also no longer try to guess whether we deal with well-founded or structural recursion but instead rely on the
EqnInfoenvironment extensions. The previous code tried to handle both variants, but they differ too much, so having separate top-level functions is easier.This also fuses the
foldCallsandcollectIHstraversals and introduces a suitable monad for collecting the inductive hypotheses.