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Update Mathlib/Data/Setoid/Basic.lean
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Co-authored-by: Johan Commelin <[email protected]>
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jsm28 and jcommelin authored Oct 9, 2024
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Expand Up @@ -121,6 +121,7 @@ lemma piSetoid_apply {ι : Sort*} {α : ι → Sort*} {r : ∀ i, Setoid (α i)}

/-- A bijection between the product of two quotients and the quotient by the product of the
equivalence relations. -/
@[simps]
def prodQuotientEquiv (r : Setoid α) (s : Setoid β) :
Quotient r × Quotient s ≃ Quotient (r.prod s) where
toFun := fun (x, y) ↦ Quotient.map₂' Prod.mk (fun _ _ hx _ _ hy ↦ ⟨hx, hy⟩) x y
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