Clean up names in prelude/option.

algebra/cmra_big_op.v

@@ -64,7 +64,7 @@ Proof.
   { by intros m2; rewrite (symmetry_iff (≡)) map_equiv_empty; intros ->. }
   intros m2 Hm2; rewrite big_opM_insert //.
   rewrite (IH (delete i m2)); last by rewrite -Hm2 delete_insert.
-  destruct (map_equiv_lookup (<[i:=x]> m1) m2 i x)
+  destruct (map_equiv_lookup_l (<[i:=x]> m1) m2 i x)
     as (y&?&Hxy); auto using lookup_insert.
   rewrite Hxy -big_opM_insert; last auto using lookup_delete.
   by rewrite insert_delete.

prelude/fin_maps.v

@@ -173,11 +173,9 @@ Section setoid.
     split; [intros Hm; apply map_eq; intros i|by intros ->].
     by rewrite lookup_empty, <-equiv_None, Hm, lookup_empty.
   Qed.
-  Lemma map_equiv_lookup (m1 m2 : M A) i x :
+  Lemma map_equiv_lookup_l (m1 m2 : M A) i x :
     m1 ≡ m2 → m1 !! i = Some x → ∃ y, m2 !! i = Some y ∧ x ≡ y.
-  Proof.
-    intros Hm ?. destruct (equiv_Some (m1 !! i) (m2 !! i) x) as (y&?&?); eauto.
-  Qed.
+  Proof. generalize (equiv_Some_inv_l (m1 !! i) (m2 !! i) x); naive_solver. Qed.
 End setoid.
 
 (** ** General properties *)