feat: add Equiv.prodSubtypeFstEquivSubtypeProd (#12802)

See [Zulip](https://leanprover.zulipchat.com/#narrow/stream/217875-Is-there-code-for-X.3F/topic/A.20basic.20equivalence/near/437968727)



Co-authored-by: Xavier Roblot <[email protected]>

Mathlib/Logic/Equiv/Basic.lean

@@ -1380,6 +1380,14 @@ def subtypeProdEquivProd {p : α → Prop} {q : β → Prop} :
   right_inv := fun ⟨⟨_, _⟩, ⟨_, _⟩⟩ => rfl
 #align equiv.subtype_prod_equiv_prod Equiv.subtypeProdEquivProd
 
+/-- A subtype of a `Prod` that depends only on the first component is equivalent to the
+corresponding subtype of the first type times the second type. -/
+def prodSubtypeFstEquivSubtypeProd {p : α → Prop} : {s : α × β // p s.1} ≃ {a // p a} × β where
+  toFun x := ⟨⟨x.1.1, x.2⟩, x.1.2⟩
+  invFun x := ⟨⟨x.1.1, x.2⟩, x.1.2⟩
+  left_inv _ := rfl
+  right_inv _ := rfl
+
 /-- A subtype of a `Prod` is equivalent to a sigma type whose fibers are subtypes. -/
 def subtypeProdEquivSigmaSubtype (p : α → β → Prop) :
     { x : α × β // p x.1 x.2 } ≃ Σa, { b : β // p a b } where