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[Merged by Bors] - feat(Logic/Embedding): add a lemma #10096

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[Merged by Bors] - feat(Logic/Embedding): add a lemma #10096

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6 changes: 6 additions & 0 deletions Mathlib/Logic/Embedding/Basic.lean
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Expand Up @@ -210,11 +210,17 @@ def setValue {α β} (f : α ↪ β) (a : α) (b : β) [∀ a', Decidable (a' =
· exact h ⟩
#align function.embedding.set_value Function.Embedding.setValue

@[simp]
theorem setValue_eq {α β} (f : α ↪ β) (a : α) (b : β) [∀ a', Decidable (a' = a)]
[∀ a', Decidable (f a' = b)] : setValue f a b a = b := by
simp [setValue]
#align function.embedding.set_value_eq Function.Embedding.setValue_eq

@[simp]
theorem setValue_eq_iff {α β} (f : α ↪ β) {a a' : α} {b : β} [∀ a', Decidable (a' = a)]
[∀ a', Decidable (f a' = b)] : setValue f a b a' = b ↔ a' = a :=
(setValue f a b).injective.eq_iff' <| setValue_eq ..

/-- Embedding into `Option α` using `some`. -/
@[simps (config := .asFn)]
protected def some {α} : α ↪ Option α :=
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