chore: lower List/Array/Vector.mem_map simp priority (#6815)

This PR lowers the simp priority of `List/Array/Vector.mem_map`, as
downstream in Mathlib many lemmas currently need their priority raised
to fire before this.

src/Init/Data/Array/Lemmas.lean

@@ -1091,7 +1091,9 @@ theorem map_id'' {f : α → α} (h : ∀ x, f x = x) (l : Array α) : map f l =
 
 theorem map_singleton (f : α → β) (a : α) : map f #[a] = #[f a] := rfl
 
-@[simp] theorem mem_map {f : α → β} {l : Array α} : b ∈ l.map f ↔ ∃ a, a ∈ l ∧ f a = b := by
+-- We use a lower priority here as there are more specific lemmas in downstream libraries
+-- which should be able to fire first.
+@[simp 500] theorem mem_map {f : α → β} {l : Array α} : b ∈ l.map f ↔ ∃ a, a ∈ l ∧ f a = b := by
   simp only [mem_def, toList_map, List.mem_map]
 
 theorem exists_of_mem_map (h : b ∈ map f l) : ∃ a, a ∈ l ∧ f a = b := mem_map.1 h

src/Init/Data/List/Lemmas.lean

@@ -1046,7 +1046,9 @@ theorem map_id'' {f : α → α} (h : ∀ x, f x = x) (l : List α) : map f l =
 
 theorem map_singleton (f : α → β) (a : α) : map f [a] = [f a] := rfl
 
-@[simp] theorem mem_map {f : α → β} : ∀ {l : List α}, b ∈ l.map f ↔ ∃ a, a ∈ l ∧ f a = b
+-- We use a lower priority here as there are more specific lemmas in downstream libraries
+-- which should be able to fire first.
+@[simp 500] theorem mem_map {f : α → β} : ∀ {l : List α}, b ∈ l.map f ↔ ∃ a, a ∈ l ∧ f a = b
   | [] => by simp
   | _ :: l => by simp [mem_map (l := l), eq_comm (a := b)]
 

src/Init/Data/Vector/Lemmas.lean

@@ -1188,7 +1188,9 @@ theorem map_id'' {f : α → α} (h : ∀ x, f x = x) (l : Vector α n) : map f
 
 theorem map_singleton (f : α → β) (a : α) : map f #v[a] = #v[f a] := rfl
 
-@[simp] theorem mem_map {f : α → β} {l : Vector α n} : b ∈ l.map f ↔ ∃ a, a ∈ l ∧ f a = b := by
+-- We use a lower priority here as there are more specific lemmas in downstream libraries
+-- which should be able to fire first.
+@[simp 500] theorem mem_map {f : α → β} {l : Vector α n} : b ∈ l.map f ↔ ∃ a, a ∈ l ∧ f a = b := by
   cases l
   simp