feat: backward.isDefEq.respectTransparency#12179
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This PR leverages the fact that expressions are type correct in `grind` and the conclusion of extensionality theorems is of the form `?a = ?b`. This PR is relevant for #12179 because it enables us to use a weaker `isDefEq` that does not bump the transparency level when processing implicit arguments.
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This PR leverages the fact that expressions are type correct in `grind` and the conclusion of extensionality theorems is of the form `?a = ?b`. This PR is relevant for #12179 because it enables us to use a weaker `isDefEq` that does not bump the transparency level when processing implicit arguments.
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It is needed for some bitvector problems. Example:
```
theorem msb_extractLsb' {start len : Nat} {x : BitVec w} :
(extractLsb' start len x).msb =
(decide (0 < len) &&
(decide (start + len ≤ w) &&
x.getMsbD (w - (start + len)))) := by
simp [BitVec.msb]
```
After the simplifier we get
```
w start len : Nat
x : BitVec w
⊢ (decide (0 < len) && (decide (start + len ≤ w) && x.getMsbD (w - (start + len)))) =
(decide (0 < len) && (decide (start + len ≤ w) && x.getMsbD (w - (start + len))))
```
The implicit terms are off because a `_ - 0` term occurring in an
implicit argument.
unification hint
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This PR implements preparatory work for #12179. It implements a new feature in `isDefEq` to ensure it does not increase the transparency level to `.default` when checking definitionally equality of implicit arguments. This transparency level bump was introduced in Lean 3, but it is not a performance issue and is affecting Mathlib. This PR adds the new feature, but it is disabled by default.
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