Else the `case` will now allow introducing all necessary variables.
Induction principles with `let` in the types of the cases will be more
common with #3432.
This implementation no longer reduces the type as it goes, but really
only counts
manifest foralls and lets. I find this more sensible and predictable: If
you have
```
theorem induction₂_symm {P : EReal → EReal → Prop} (symm : Symmetric P) …
```
then previously, writing
```
case symm =>
```
would actually bring a fresh `x` and `y` and variable `h : P x y` into
scope and produce a
goal of `P y x`, because `Symmetric P` happens to be
```
def Symmetric := ∀ ⦃x y⦄, x ≺ y → y ≺ x
```
After this change, after `case symm =>` will leave `Symmetric P` as the
goal.
This gives more control to the author of the induction hypothesis about
the actual
goal of the cases. This shows up in mathlib in two places; fixes in
https://github.com/leanprover-community/mathlib4/pull/11023.
I consider these improvements.
fa058ed228