`pp.analyze` should imply `pp.proofs`

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

MWE:

/--
error: unsolved goals
α : Prop
P : α → Prop
a : α
⊢ P ⋯
-/
#guard_msgs in
set_option pp.analyze true in
example (α : Prop) (P : α → Prop) (a : α) : P (id a) := by {}

/--
error: unsolved goals
α : Prop
P : α → Prop
a : α
⊢ P (id a)
-/
#guard_msgs in
set_option pp.analyze true in
set_option pp.proofs true in
example (α : Prop) (P : α → Prop) (a : α) : P (id a) := by {}

Expected behavior: Both versions output ... ⊢ P (id a).

Context

I hit this bug in aesop?, where I use pp.analyze to output tactic scripts that can be read back by Lean.

Versions

"4.15.0-nightly-2024-11-25"

Impact

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Start by running the two #guard_msgs examples from the issue against the reported or current Lean nightly and compare the pp.analyze output with and without pp.proofs. Trace the pretty-printing option handling implicated by the MWE; done means both versions preserve P (id a) rather than shortening it to P ⋯.