This PR introduces stricter inference for the `@[defeq]` attribute and a
companion `@[backward_defeq]` attribute that preserves the pre-PR
behavior
as an opt-in.
### What changed
* `@[defeq]` is now inferred only when the equation holds at
`.instances` transparency (the transparency `dsimp` operates at).
* `@[backward_defeq]` is the old set: every theorem whose `rfl` proof
the legacy inference would have accepted is tagged `@[backward_defeq]`,
so `defeq ⊆ backward_defeq` holds by construction.
* The option `backward.defeqAttrib.useBackward` (default `false`) makes
`dsimp` also use `@[backward_defeq]` theorems, restoring the pre-PR
behavior for a specific proof or file.
* The option is eqn-affecting: its value at the point of a function's
definition is recorded so that the equation lemmas later generated for
that function use the same value, regardless of the ambient option at
the use site.
### Mathlib adaption
A companion adaption branch (`lean-pr-testing-backward-defeq-attrib` on
mathlib4) builds cleanly against this PR and passes `lake test` without
warnings. Most adaption changes are scoped
`set_option backward.defeqAttrib.useBackward true in` additions on the
failing declarations; a small number of files needed proof-level edits
where the stored form of a `dsimp%`/`@[reassoc]`/`@[elementwise]`
/`@[simps]`/`@[to_app]`-generated lemma had drifted under the stricter
regime.
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Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
ac9a1cb415