From c801fc3376a65eee82f7d202b8598d0acacc257f Mon Sep 17 00:00:00 2001
From: jihgfee <jihgfee@gmail.com>
Date: Sat, 18 Apr 2020 12:31:58 +0200
Subject: [PATCH] Nits

---
 theories/channel/proto.v        |  8 ++++----
 theories/logrel/session_types.v |  2 +-
 theories/logrel/subtyping.v     | 10 +++++-----
 3 files changed, 10 insertions(+), 10 deletions(-)

diff --git a/theories/channel/proto.v b/theories/channel/proto.v
index d5b2335..64ebbed 100644
--- a/theories/channel/proto.v
+++ b/theories/channel/proto.v
@@ -152,7 +152,7 @@ Program Definition iProto_map_cont {Σ V}
   λne p2, (∃ p1, pc (Next p1) ∗ p2 ≡ Next (rec p1))%I.
 Next Obligation. solve_proper. Qed.
 
-Program Definition iProto_map_app_aux {Σ V} 
+Program Definition iProto_map_app_aux {Σ V}
     (f : action → action) (p2 : iProto Σ V)
     (rec : iProto Σ V -n> iProto Σ V) : iProto Σ V -n> iProto Σ V := λne p1,
   match proto_unfold p1 return _ with
@@ -579,7 +579,7 @@ Section proto.
     { by iDestruct (proto_message_end_equivI with "Heq") as %[]. }
     iDestruct "H" as (a1 a2 pc1 pc2') "(Hp1 & Hp2 & H)".
     iDestruct (proto_message_equivI with "Hp2") as (<-) "{Hp2} #Hpc".
-    iExists _, _; iSplit; [done|]. destruct a1. 
+    iExists _, _; iSplit; [done|]. destruct a1.
     - iIntros (v p2'). by iRewrite ("Hpc" $! v (Next p2')).
     - iIntros (v1 v2 p1' p2'). by iRewrite ("Hpc" $! v2 (Next p2')).
   Qed.
@@ -800,14 +800,14 @@ Section proto.
   Lemma iProto_le_dual_l p1 p2 :
     iProto_le (iProto_dual p2) p1 -∗ iProto_le (iProto_dual p1) p2.
   Proof.
-    iIntros "H". iEval (rewrite -(iProto_dual_involutive p2)).
+    iIntros "H". iEval (rewrite -(involutive iProto_dual p2)).
     by iApply iProto_le_dual.
   Qed.
 
   Lemma iProto_le_dual_r p1 p2 :
     iProto_le p2 (iProto_dual p1) -∗ iProto_le p1 (iProto_dual p2).
   Proof.
-    iIntros "H". iEval (rewrite -(iProto_dual_involutive p1)).
+    iIntros "H". iEval (rewrite -(involutive iProto_dual p1)).
     by iApply iProto_le_dual.
   Qed.
 
diff --git a/theories/logrel/session_types.v b/theories/logrel/session_types.v
index a9a15d6..d08389f 100644
--- a/theories/logrel/session_types.v
+++ b/theories/logrel/session_types.v
@@ -106,7 +106,7 @@ Section Propers.
   Global Instance lsty_app_proper : Proper ((≡) ==> (≡) ==> (≡)) (@lsty_app Σ).
   Proof. apply ne_proper_2, _. Qed.
   Global Instance lsty_app_assoc : Assoc (≡) (@lsty_app Σ).
-  Proof. intros S1 S2 S3. rewrite /lsty_app. by rewrite iProto_app_assoc. Qed.
+  Proof. intros S1 S2 S3. rewrite /lsty_app. by rewrite assoc. Qed.
   Global Instance lsty_app_end_l : LeftId (≡) lsty_end (@lsty_app Σ).
   Proof. intros [S]. rewrite /lsty_app. by rewrite left_id. Qed.
   Global Instance lsty_app_end_r : RightId (≡) lsty_end (@lsty_app Σ).
diff --git a/theories/logrel/subtyping.v b/theories/logrel/subtyping.v
index 11e4b5d..f315b96 100644
--- a/theories/logrel/subtyping.v
+++ b/theories/logrel/subtyping.v
@@ -100,7 +100,7 @@ Section subtype.
   Qed.
 
   Lemma lty_le_exist_elim C B :
-    ⊢ (C B) <: (∃ A, C A).
+    ⊢ C B <: ∃ A, C A.
   Proof. iIntros "!>" (v) "Hle". by iExists B. Qed.
 
   Lemma lty_le_rec_1 (C : lty Σ → lty Σ) `{!Contractive C} :
@@ -293,12 +293,12 @@ Section subtype.
   Proof. iIntros "#H1 #H2 !>". by iApply iProto_le_app. Qed.
 
   Lemma lsty_le_app_assoc_l S1 S2 S3 :
-    ⊢ (S1 <++> (S2 <++> S3)) <s: ((S1 <++> S2) <++> S3).
-  Proof. rewrite lsty_app_assoc. iApply lsty_le_refl. Qed.
+    ⊢ S1 <++> (S2 <++> S3) <s: (S1 <++> S2) <++> S3.
+  Proof. rewrite assoc. iApply lsty_le_refl. Qed.
 
   Lemma lsty_le_app_assoc_r S1 S2 S3 :
-    ⊢ ((S1 <++> S2) <++> S3) <s: (S1 <++> (S2 <++> S3)).
-  Proof. rewrite lsty_app_assoc. iApply lsty_le_refl. Qed.
+    ⊢ (S1 <++> S2) <++> S3 <s: S1 <++> (S2 <++> S3).
+  Proof. rewrite assoc. iApply lsty_le_refl. Qed.
 
   Lemma lsty_le_app_id_l_l S :
     ⊢ (END <++> S) <s: S.
-- 
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