Sum.elim_map should be simp

Prerequisites

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• 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

Sum.elim_map isn’t @[simp] but arguably could and should be?

Context

This came up in a debugging session during office hours, where a in a somewhat complicated proof I spotted Sum.elim … (Sum.map …), and maybe if simp simplified that right away (as was the expectation of the user) it might have saved us.

The similarity to List.map_map indicates that it’s not unreasonable.

Versions

7dc1ceb8d4312850b39cef9e751e0a3b651946e3

Impact

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Start with the Sum.elim_map declaration linked from Init/Data/Sum/Lemmas.html and inspect nearby simplification lemmas. Try a minimal Lean example using simp, then verify that the requested attribute produces the expected simplification without unwanted behavior.