ac9a1cb415
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. --------- Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
45 lines
864 B
Text
45 lines
864 B
Text
def Nat.isZero (x : Nat) : Bool :=
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match x with
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| 0 => true
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| _+1 => false
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axiom P : Bool → Prop
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axiom P_false : P false
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/--
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trace: x : Nat
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⊢ P (1 + x).isZero
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-/
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#guard_msgs in
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example (x : Nat) : P (1 + id x.succ.pred).isZero := by
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dsimp
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trace_state
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simp [Nat.succ_add]
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dsimp [Nat.isZero]
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apply P_false
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example (x : Nat) : P (id x.succ.succ).isZero := by
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dsimp [Nat.isZero]
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apply P_false
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/--
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trace: x : Nat
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⊢ P false
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-/
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#guard_msgs in
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set_option backward.defeqAttrib.useBackward true in
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example (x : Nat) : P (id x.succ.succ).isZero := by
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dsimp [Nat.isZero.eq_2]
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trace_state
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apply P_false
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example (x : Nat) : P (id x.succ.succ).isZero := by
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dsimp!
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apply P_false
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@[simp] theorem isZero_succ (x : Nat) : (x + 1).isZero = false :=
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rfl
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theorem ex1 (x : Nat) : P (id x.succ.succ.pred).isZero := by
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dsimp
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apply P_false
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