Running `simp?` output produces different goal than `simp`

Prerequisites

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• Reduce the issue to a minimal, self-contained, reproducible test case.
  Avoid dependencies to Mathlib or Batteries.
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Description

 /-- info: "4.10.0-rc1" -/
#guard_msgs in
#eval Lean.versionString

/--
info: Try this: simp only [exists_prop, exists_and_left, exists_eq_right_right]
---
warning: declaration uses 'sorry'
---
info: [Meta.Tactic.simp.rewrite] exists_prop:1000, ∃ x_1, a = x ==> 1 < a ∧ a = x
[Meta.Tactic.simp.rewrite] exists_and_left:1000, ∃ x_1, 1 < a ∧ a = x ==> 1 < a ∧ ∃ x_1, a = x
[Meta.Tactic.simp.rewrite] exists_prop:1000, ∃ x_1, a = x ==> 0 < a ∧ a = x
[Meta.Tactic.simp.rewrite] exists_eq_right_right:1000, ∃ a, 1 < a ∧ 0 < a ∧ a = x ==> 1 < x ∧ 0 < x
-/
#guard_msgs in
set_option trace.Meta.Tactic.simp.rewrite true in
example (x : Nat) : ∃ (a : Nat) (_ : 0 < a) (_ : 1 < a), a = x := by
  simp?
  show 1 < x ∧ 0 < x
  sorry

example (x : Nat) : ∃ (a : Nat) (_ : 0 < a) (_ : 1 < a), a = x := by
  simp only [exists_prop, exists_and_left, exists_eq_right_right]
  show 0 < x ∧ 1 < x
  sorry

Context

Originally reported on Zulip.

Steps to Reproduce

Paste the above code into a Lean editor.

Expected behavior: The goal is the same.

Actual behavior: The goal is different.

Versions

This particular repro works on 4.7.0+ (where the simp lemmas were introduced), but there may be a simpler reproduction that uses pre-4.7.0 simp lemmas.

Impact

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Start by running the self-contained reproduction from the issue in a Lean nightly environment and compare the goals after simp? and the explicit simp only invocation. Investigate the simp? tactic output and the simplifier rewrite trace; done means both forms produce the same goal for this example and the reproduced test passes.