split fails for non-propositional goals

[JLimperg]

Prerequisites

Please put an X between the brackets as you perform the following steps:

• Check that your issue is not already filed:
  https://github.com/leanprover/lean4/issues
• Reduce the issue to a minimal, self-contained, reproducible test case.
  Avoid dependencies to Mathlib or Batteries.
• Test your test case against the latest nightly release, for example on
  https://live.lean-lang.org/#project=lean-nightly
  (You can also use the settings there to switch to “Lean nightly”)

Description

The current implementation of split splits on p ∨ ¬p, where p is the condition of an ite. This fails if the goal is non-propositional since Or.elim can only eliminate into Prop. MWE:

example {A B : Type} {p : Prop} [Decidable p] (h : if p then A else B) :
    Sum A B := by
  split at h
  /-
  tactic 'cases' failed, nested error:
  tactic 'induction' failed, recursor 'Or.casesOn' can only eliminate into Prop
  AB: Type
  p: Prop
  inst✝: Decidable p
  h: if p then A else B
  hByCases✝: p ∨ ¬p
  ⊢ A ⊕ B
  -/

Versions

"4.9.0-nightly-2024-05-31"

Additional Information

I believe the implementation strategy suggested in #2414 would also fix this issue.

Impact

Add 👍 to issues you consider important. If others are impacted by this issue, please ask them to add 👍 to it.