feat: LawfulBEq instances for Array and Vector (leanprover#6922)

This PR adds `LawfulBEq` instances for `Array` and `Vector`.

(Note this replaces a contribution of @mehbark to Batteries for the
LawfulBEq instance for Vector, which was dropped during the release
process due to conflicts. Thanks for that contribution!)

Author: kim-em

Diff for: src/Init/Data/Array/DecidableEq.lean

@@ -108,3 +108,13 @@ namespace List
   simp [beq_eq_decide, Array.beq_eq_decide]
 
 end List
+
+namespace Array
+
+instance [BEq α] [LawfulBEq α] : LawfulBEq (Array α) where
+  rfl := by simp [BEq.beq, isEqv_self_beq]
+  eq_of_beq := by
+    rintro ⟨a⟩ ⟨b⟩ h
+    simpa using h
+
+end Array

Diff for: src/Init/Data/Vector/DecidableEq.lean

@@ -49,10 +49,20 @@ theorem beq_eq_decide [BEq α] (a b : Vector α n) :
     (a == b) = decide (∀ (i : Nat) (h' : i < n), a[i] == b[i]) := by
   simp [BEq.beq, isEqv_eq_decide]
 
+@[simp] theorem beq_mk [BEq α] (a b : Array α) (ha : a.size = n) (hb : b.size = n) :
+    (mk a ha == mk b hb) = (a == b) := by
+  simp [BEq.beq]
+
 @[simp] theorem beq_toArray [BEq α] (a b : Vector α n) : (a.toArray == b.toArray) = (a == b) := by
   simp [beq_eq_decide, Array.beq_eq_decide]
 
 @[simp] theorem beq_toList [BEq α] (a b : Vector α n) : (a.toList == b.toList) = (a == b) := by
   simp [beq_eq_decide, List.beq_eq_decide]
 
+instance [BEq α] [LawfulBEq α] : LawfulBEq (Vector α n) where
+  rfl := by simp [BEq.beq, isEqv_self_beq]
+  eq_of_beq := by
+    rintro ⟨a, rfl⟩ ⟨b, h⟩ h'
+    simpa using h'
+
 end Vector

Diff for: src/Init/Data/Vector/Lemmas.lean

@@ -1289,12 +1289,9 @@ theorem mem_setIfInBounds (v : Vector α n) (i : Nat) (hi : i < n) (a : α) :
     · intro h
       constructor
       · rintro ⟨a, ha⟩ ⟨b, hb⟩ h
-        simp at h
-        obtain ⟨hs, hi⟩ := Array.isEqv_iff_rel.mp h
-        ext i h
-        · simpa using hi _ (by omega)
+        simp_all
       · rintro ⟨a, ha⟩
-        simpa using Array.isEqv_self_beq ..
+        simp
 
 /-! ### isEqv -/