diff --git a/CHANGELOG.md b/CHANGELOG.md
index 6583178012847822c8a86b0a4de62a50ec0a4bb9..386bf52984814aefad468ccebafc323e602cfba6 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -161,6 +161,8 @@ Changes in Coq:
   `s/◯!/◯F/g; s/●!/●F/g;`.
 * Lemma `prop_ext` works in both directions; its default direction is the
   opposite of what it used to be.
+* Make direction of `f_op` rewrite lemmas more consistent: Flip `pair_op`,
+  `Cinl_op`, `Cinr_op`, `cmra_morphism_op`.
 * Rename `C` suffixes into `O` since we no longer use COFEs but OFEs. Also
   rename `ofe_fun` into `discrete_fun` and the corresponding notation `-c>` into
   `-d>`. The renaming can be automatically done using the following script (on
diff --git a/tests/one_shot_once.v b/tests/one_shot_once.v
index ad8ea81479c2ff18ddf1133a436351174dd8dac9..9bc49a9ebe542569575c99b86f36967bdb4524b6 100644
--- a/tests/one_shot_once.v
+++ b/tests/one_shot_once.v
@@ -40,7 +40,7 @@ Definition one_shot_inv (γ : gname) (l : loc) : iProp Σ :=
 Lemma pending_split γ q :
   own γ (Pending q) ⊣⊢ own γ (Pending (q/2)) ∗ own γ (Pending (q/2)).
 Proof.
-  rewrite /Pending. rewrite -own_op Cinl_op. rewrite frac_op' Qp_div_2 //.
+  rewrite /Pending. rewrite -own_op -Cinl_op. rewrite frac_op' Qp_div_2 //.
 Qed.
 
 Lemma pending_shoot γ n :
diff --git a/theories/algebra/auth.v b/theories/algebra/auth.v
index 6466762915684d38c6a625777abb32f528a1d4b6..b2dad6a874ec382cffc2f47c45072e909fd4f7d9 100644
--- a/theories/algebra/auth.v
+++ b/theories/algebra/auth.v
@@ -299,11 +299,11 @@ Proof. by rewrite auth_both_frac_op. Qed.
 Lemma auth_auth_frac_op p q a : ●{p + q} a ≡ ●{p} a ⋅ ●{q} a.
 Proof.
   intros; split; simpl; last by rewrite left_id.
-  by rewrite -Some_op pair_op agree_idemp.
+  by rewrite -Some_op -pair_op agree_idemp.
 Qed.
 Lemma auth_auth_frac_op_invN n p a q b : ✓{n} (●{p} a ⋅ ●{q} b) → a ≡{n}≡ b.
 Proof.
-  rewrite /op /auth_op /= left_id -Some_op pair_op auth_validN_eq /=.
+  rewrite /op /auth_op /= left_id -Some_op -pair_op auth_validN_eq /=.
   intros (?&?& Eq &?&?). apply to_agree_injN, agree_op_invN. by rewrite Eq.
 Qed.
 Lemma auth_auth_frac_op_inv p a q b : ✓ (●{p} a ⋅ ●{q} b) → a ≡ b.
@@ -388,7 +388,7 @@ Lemma auth_local_update (a b0 b1 a' b0' b1': A) :
 Proof.
   rewrite !local_update_unital=> Hup ? ? n /=.
     move=> [[[qc ac]|] bc] /auth_both_validN [Le Val] [] /=.
-  - move => Ha. exfalso. move : Ha. rewrite right_id -Some_op pair_op.
+  - move => Ha. exfalso. move : Ha. rewrite right_id -Some_op -pair_op.
     move => /Some_dist_inj [/=]. rewrite frac_op' => Eq _.
     apply (Qp_not_plus_q_ge_1 qc). by rewrite -Eq.
   - move => _. rewrite !left_id=> ?.
@@ -442,8 +442,7 @@ Proof.
     naive_solver eauto using cmra_morphism_monotoneN, cmra_morphism_validN.
   - intros [??]. apply Some_proper; rewrite /auth_map /=.
     by f_equiv; rewrite /= cmra_morphism_core.
-  - intros [[[??]|]?] [[[??]|]?]; try apply Auth_proper=>//=; try by rewrite cmra_morphism_op.
-    by rewrite -Some_op pair_op cmra_morphism_op.
+  - intros [[[??]|]?] [[[??]|]?]; try apply Auth_proper=>//=; by rewrite cmra_morphism_op.
 Qed.
 Definition authO_map {A B} (f : A -n> B) : authO A -n> authO B :=
   OfeMor (auth_map f).
diff --git a/theories/algebra/cmra.v b/theories/algebra/cmra.v
index 54f32f720a24ae8bb6df8fb08a9e5f7103af706d..f96b8c5b075604419f5524da6fb4b79c70b78c17 100644
--- a/theories/algebra/cmra.v
+++ b/theories/algebra/cmra.v
@@ -252,7 +252,7 @@ Class CmraMorphism {A B : cmraT} (f : A → B) := {
   cmra_morphism_ne :> NonExpansive f;
   cmra_morphism_validN n x : ✓{n} x → ✓{n} f x;
   cmra_morphism_pcore x : pcore (f x) ≡ f <$> pcore x;
-  cmra_morphism_op x y : f x ⋅ f y ≡ f (x ⋅ y)
+  cmra_morphism_op x y : f (x ⋅ y) ≡ f x ⋅ f y
 }.
 Arguments cmra_morphism_validN {_ _} _ {_} _ _ _.
 Arguments cmra_morphism_pcore {_ _} _ {_} _.
@@ -1136,7 +1136,7 @@ Section prod.
   Qed.
   Canonical Structure prodR := CmraT (prod A B) prod_cmra_mixin.
 
-  Lemma pair_op (a a' : A) (b b' : B) : (a, b) â‹… (a', b') = (a â‹… a', b â‹… b').
+  Lemma pair_op (a a' : A) (b b' : B) : (a â‹… a', b â‹… b') = (a, b) â‹… (a', b').
   Proof. done. Qed.
   Lemma pair_valid (a : A) (b : B) : ✓ (a, b) ↔ ✓ a ∧ ✓ b.
   Proof. done. Qed.
@@ -1193,7 +1193,7 @@ Section prod_unit.
   Canonical Structure prodUR := UcmraT (prod A B) prod_ucmra_mixin.
 
   Lemma pair_split (x : A) (y : B) : (x, y) ≡ (x, ε) ⋅ (ε, y).
-  Proof. by rewrite pair_op left_id right_id. Qed.
+  Proof. by rewrite -pair_op left_id right_id. Qed.
 
   Lemma pair_split_L `{!LeibnizEquiv A, !LeibnizEquiv B} (x : A) (y : B) :
     (x, y) = (x, ε) ⋅ (ε, y).
@@ -1214,7 +1214,7 @@ Proof.
     assert (Hg := cmra_morphism_pcore g (x.2)).
     destruct (pcore (g (x.2))), (pcore (x.2)); inversion_clear Hg=>//=.
     by setoid_subst.
-  - intros. by rewrite /prod_map /= -!cmra_morphism_op.
+  - intros. by rewrite /prod_map /= !cmra_morphism_op.
 Qed.
 
 Program Definition prodRF (F1 F2 : rFunctor) : rFunctor := {|
@@ -1475,7 +1475,7 @@ Proof.
   split; first apply _.
   - intros n [a|] ?; rewrite /cmra_validN //=. by apply (cmra_morphism_validN f).
   - move=> [a|] //. by apply Some_proper, cmra_morphism_pcore.
-  - move=> [a|] [b|] //=. by rewrite -(cmra_morphism_op f).
+  - move=> [a|] [b|] //=. by rewrite (cmra_morphism_op f).
 Qed.
 
 Program Definition optionRF (F : rFunctor) : rFunctor := {|
diff --git a/theories/algebra/csum.v b/theories/algebra/csum.v
index a16994265b4a70b12ee14caa787045e360313f25..f41f2d81d43a0b562349341dcc0c954d75bbeb5d 100644
--- a/theories/algebra/csum.v
+++ b/theories/algebra/csum.v
@@ -172,9 +172,9 @@ Instance csum_op : Op (csum A B) := λ x y,
   | _, _ => CsumBot
   end.
 
-Lemma Cinl_op a a' : Cinl a â‹… Cinl a' = Cinl (a â‹… a').
+Lemma Cinl_op a a' : Cinl (a â‹… a') = Cinl a â‹… Cinl a'.
 Proof. done. Qed.
-Lemma Cinr_op b b' : Cinr b â‹… Cinr b' = Cinr (b â‹… b').
+Lemma Cinr_op b b' : Cinr (b â‹… b') = Cinr b â‹… Cinr b'.
 Proof. done. Qed.
 
 Lemma csum_included x y :
@@ -367,7 +367,7 @@ Proof.
   split; try apply _.
   - intros n [a|b|]; simpl; auto using cmra_morphism_validN.
   - move=> [a|b|]=>//=; rewrite cmra_morphism_pcore; by destruct pcore.
-  - intros [xa|ya|] [xb|yb|]=>//=; by rewrite -cmra_morphism_op.
+  - intros [xa|ya|] [xb|yb|]=>//=; by rewrite cmra_morphism_op.
 Qed.
 
 Program Definition csumRF (Fa Fb : rFunctor) : rFunctor := {|
diff --git a/theories/algebra/ufrac_auth.v b/theories/algebra/ufrac_auth.v
index d7c1e89ea1dd0df7d3d293983010aa7c0900a796..cec6d972f60f3a69d8193fd0d096cd44f625eae7 100644
--- a/theories/algebra/ufrac_auth.v
+++ b/theories/algebra/ufrac_auth.v
@@ -137,7 +137,7 @@ Section ufrac_auth.
     intros n m; simpl; intros [Hvalid1 Hvalid2] Heq.
     split.
     - split; by apply cmra_valid_validN.
-    - rewrite -pair_op Some_op Heq comm.
+    - rewrite pair_op Some_op Heq comm.
       destruct m; simpl; [rewrite left_id | rewrite right_id]; done.
   Qed.
 End ufrac_auth.
diff --git a/theories/base_logic/lib/gen_heap.v b/theories/base_logic/lib/gen_heap.v
index 309940e3b067c6766ff234dafb0645acde1cbb82..18ba74aba4a86a656a88a0e3250a9646b7a2f436 100644
--- a/theories/base_logic/lib/gen_heap.v
+++ b/theories/base_logic/lib/gen_heap.v
@@ -190,7 +190,7 @@ Section gen_heap.
   Global Instance mapsto_fractional l v : Fractional (λ q, l ↦{q} v)%I.
   Proof.
     intros p q. by rewrite mapsto_eq /mapsto_def -own_op -auth_frag_op
-      op_singleton pair_op agree_idemp.
+      op_singleton -pair_op agree_idemp.
   Qed.
   Global Instance mapsto_as_fractional l q v :
     AsFractional (l ↦{q} v) (λ q, l ↦{q} v)%I q.
@@ -200,7 +200,7 @@ Section gen_heap.
   Proof.
     apply wand_intro_r.
     rewrite mapsto_eq /mapsto_def -own_op -auth_frag_op own_valid discrete_valid.
-    f_equiv. rewrite auth_frag_valid op_singleton singleton_valid pair_op.
+    f_equiv. rewrite auth_frag_valid op_singleton singleton_valid -pair_op.
     by intros [_ ?%agree_op_invL'].
   Qed.
 
diff --git a/theories/base_logic/lib/na_invariants.v b/theories/base_logic/lib/na_invariants.v
index c92594bf03bd69529cc77263d2a513d64c3fe8ef..680d3429535dcc2d90ea6cebd8bc22bef8117a30 100644
--- a/theories/base_logic/lib/na_invariants.v
+++ b/theories/base_logic/lib/na_invariants.v
@@ -63,7 +63,7 @@ Section proofs.
   Lemma na_own_union p E1 E2 :
     E1 ## E2 → na_own p (E1 ∪ E2) ⊣⊢ na_own p E1 ∗ na_own p E2.
   Proof.
-    intros ?. by rewrite /na_own -own_op pair_op left_id coPset_disj_union.
+    intros ?. by rewrite /na_own -own_op -pair_op left_id coPset_disj_union.
   Qed.
 
   Lemma na_own_acc E2 E1 tid :