fix: FunInd: support structural recursion on reflexive types #4327
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types like
```
inductive Many (α : Type u) where
| none : Many α
| more : α → (Unit → Many α) → Many α
```
have a `.brecOn` only supports motives producing `Type u`, but not `Sort
u`, but our induction principles produce `Prop`. So the previous
implementation of functional induction would fail for functions that
structurally recurse over such types.
We recognize this case now and, rather hazardously, replace `.brecOn`
with `.binductionOn` (and thus `.below ` with `.ibelow` and `PProd` with
`And`). This assumes that these definitions are highly analogous.
This also improves the error message when realizing a reserved name
fails with an exception, by prepending
```
Failed to realize constant {id}:
```
to the error message.
Fixes #4320
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types like
have a
.brecOnonly supports motives producingType u, but notSort u, but our induction principles produceProp. So the previousimplementation of functional induction would fail for functions that
structurally recurse over such types.
We recognize this case now and, rather hazardously, replace
.brecOnwith
.binductionOn(and thus.belowwith.ibelowandPProdwithAnd). This assumes that these definitions are highly analogous.This also improves the error message when realizing a reserved name
fails with an exception, by prepending
to the error message.
Fixes #4320