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chore(set/function): remove reducible on eq_on (#8738)
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This backs out #8736, and instead removes the unnecessary `@[reducible]`. 

This leaves the `simp` lemma available if anyone wants it (although it is not currently used in mathlib3), but should still resolve the problem that @dselsam's experimental `simp` in the binport of mathlib3 was excessively enthusiastic about using this lemma.
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semorrison committed Aug 18, 2021
1 parent 02b90ab commit a47d49d
Showing 1 changed file with 2 additions and 2 deletions.
4 changes: 2 additions & 2 deletions src/data/set/function.lean
Expand Up @@ -70,10 +70,10 @@ variables {s s₁ s₂ : set α} {t t₁ t₂ : set β} {p : set γ} {f f₁ f

/-- Two functions `f₁ f₂ : α → β` are equal on `s`
if `f₁ x = f₂ x` for all `x ∈ a`. -/
@[reducible] def eq_on (f₁ f₂ : α → β) (s : set α) : Prop :=
def eq_on (f₁ f₂ : α → β) (s : set α) : Prop :=
∀ ⦃x⦄, x ∈ s → f₁ x = f₂ x

lemma eq_on_empty (f₁ f₂ : α → β) : eq_on f₁ f₂ ∅ := λ x, false.elim
@[simp] lemma eq_on_empty (f₁ f₂ : α → β) : eq_on f₁ f₂ ∅ := λ x, false.elim

@[symm] lemma eq_on.symm (h : eq_on f₁ f₂ s) : eq_on f₂ f₁ s :=
λ x hx, (h hx).symm
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