Change notation to remain compatible with multiple Coq versions

ConcurrentSeparationLogic.v

@@ -1219,7 +1219,7 @@ Transparent heq himp lift star exis ptsto.
 
 (* Guarded predicates *)
 Definition guarded (P : Prop) (p : hprop) : hprop :=
-  fun h => IF P then p h else emp%sep h.
+  fun h => IFF P then p h else emp%sep h.
 
 Infix "===>" := guarded : sep_scope.
 

ConcurrentSeparationLogic_template.v

@@ -1127,7 +1127,7 @@ Qed.
 Transparent heq himp lift star exis ptsto.
 
 Definition guarded (P : Prop) (p : hprop) : hprop :=
-  fun h => IF P then p h else emp%sep h.
+  fun h => IFF P then p h else emp%sep h.
 
 Infix "===>" := guarded : sep_scope.
 

FrapWithoutSets.v

@@ -458,4 +458,4 @@ Arguments N.add: simpl never.
 Definition IF_then_else (p q1 q2 : Prop) :=
   (p /\ q1) \/ (~p /\ q2).
   
-Notation "'IF' p 'then' q1 'else' q2" := (IF_then_else p q1 q2) (at level 95).
+Notation "'IFF' p 'then' q1 'else' q2" := (IF_then_else p q1 q2) (at level 95).

RuleInduction.v

@@ -586,7 +586,7 @@ Module PropositionalWithImplication.
   Lemma interp_valid'' : forall p hyps,
       (forall x, In x (varsOf p) -> hyps (Var x) \/ hyps (Not (Var x)))
       -> (forall x, hyps (Var x) -> ~hyps (Not (Var x)))
-      -> IF interp (fun x => hyps (Var x)) p
+      -> IFF interp (fun x => hyps (Var x)) p
          then valid hyps p
          else valid hyps (Not p).
   Proof.
@@ -612,18 +612,18 @@ Module PropositionalWithImplication.
     excluded_middle (interp (fun x => hyps (Var x)) p2).
     left; propositional.
     apply ValidAndIntro.
-    assert (IF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
+    assert (IFF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
     apply IHp1; propositional.
     apply H.
     apply in_or_app; propositional.
     unfold IF_then_else in H3; propositional.
-    assert (IF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
+    assert (IFF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
     apply IHp2; propositional.
     apply H.
     apply in_or_app; propositional.
     unfold IF_then_else in H3; propositional.
     right; propositional.
-    assert (IF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
+    assert (IFF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
     apply IHp2; propositional.
     apply H.
     apply in_or_app; propositional.
@@ -637,7 +637,7 @@ Module PropositionalWithImplication.
     apply ValidHyp.
     propositional.
     right; propositional.
-    assert (IF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
+    assert (IFF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
     apply IHp1; propositional.
     apply H.
     apply in_or_app; propositional.
@@ -654,7 +654,7 @@ Module PropositionalWithImplication.
     excluded_middle (interp (fun x => hyps (Var x)) p1).
     left; propositional.
     apply ValidOrIntro1.
-    assert (IF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
+    assert (IFF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
     apply IHp1; propositional.
     apply H.
     apply in_or_app; propositional.
@@ -662,7 +662,7 @@ Module PropositionalWithImplication.
     excluded_middle (interp (fun x => hyps (Var x)) p2).
     left; propositional.
     apply ValidOrIntro2.
-    assert (IF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
+    assert (IFF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
     apply IHp2; propositional.
     apply H.
     apply in_or_app; propositional.
@@ -672,7 +672,7 @@ Module PropositionalWithImplication.
     apply ValidOrElim with p1 p2.
     apply ValidHyp.
     propositional.
-    assert (IF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
+    assert (IFF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
     apply IHp1; propositional.
     apply H.
     apply in_or_app; propositional.
@@ -683,7 +683,7 @@ Module PropositionalWithImplication.
     propositional.
     apply ValidHyp.
     propositional.
-    assert (IF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
+    assert (IFF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
     apply IHp2; propositional.
     apply H.
     apply in_or_app; propositional.
@@ -699,7 +699,7 @@ Module PropositionalWithImplication.
     excluded_middle (interp (fun x => hyps (Var x)) p2).
     left; propositional.
     apply ValidImplyIntro.
-    assert (IF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
+    assert (IFF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
     apply IHp2; propositional.
     apply H.
     apply in_or_app; propositional.
@@ -709,12 +709,12 @@ Module PropositionalWithImplication.
     propositional.
     right; propositional.
     apply ValidImplyIntro.
-    assert (IF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
+    assert (IFF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
     apply IHp1; propositional.
     apply H.
     apply in_or_app; propositional.
     unfold IF_then_else in H3; propositional.
-    assert (IF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
+    assert (IFF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
     apply IHp2; propositional.
     apply H.
     apply in_or_app; propositional.
@@ -731,7 +731,7 @@ Module PropositionalWithImplication.
     propositional.
     left; propositional.
     apply ValidImplyIntro.
-    assert (IF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
+    assert (IFF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
     apply IHp1; propositional.
     apply H.
     apply in_or_app; propositional.
@@ -759,7 +759,7 @@ Module PropositionalWithImplication.
     induct leftToDo; simplify.
 
     rewrite app_nil_r in H.
-    assert (IF interp (fun x : var => hyps (Var x)) p then valid hyps p else valid hyps (Not p)).
+    assert (IFF interp (fun x : var => hyps (Var x)) p then valid hyps p else valid hyps (Not p)).
     apply interp_valid''; first_order.
     unfold IF_then_else in H4; propositional.
     exfalso.

RuleInduction_template.v

@@ -433,7 +433,7 @@ Fixpoint varsOf (p : prop) : list var :=
 Lemma interp_valid'' : forall p hyps,
     (forall x, In x (varsOf p) -> hyps (Var x) \/ hyps (Not (Var x)))
     -> (forall x, hyps (Var x) -> ~hyps (Not (Var x)))
-    -> IF interp (fun x => hyps (Var x)) p
+    -> IFF interp (fun x => hyps (Var x)) p
        then valid hyps p
        else valid hyps (Not p).
 Proof.
@@ -459,18 +459,18 @@ Proof.
   excluded_middle (interp (fun x => hyps (Var x)) p2).
   left; propositional.
   apply ValidAndIntro.
-  assert (IF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
+  assert (IFF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
   apply IHp1; propositional.
   apply H.
   apply in_or_app; propositional.
   unfold IF_then_else in H3; propositional.
-  assert (IF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
+  assert (IFF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
   apply IHp2; propositional.
   apply H.
   apply in_or_app; propositional.
   unfold IF_then_else in H3; propositional.
   right; propositional.
-  assert (IF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
+  assert (IFF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
   apply IHp2; propositional.
   apply H.
   apply in_or_app; propositional.
@@ -484,7 +484,7 @@ Proof.
   apply ValidHyp.
   propositional.
   right; propositional.
-  assert (IF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
+  assert (IFF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
   apply IHp1; propositional.
   apply H.
   apply in_or_app; propositional.
@@ -501,7 +501,7 @@ Proof.
   excluded_middle (interp (fun x => hyps (Var x)) p1).
   left; propositional.
   apply ValidOrIntro1.
-  assert (IF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
+  assert (IFF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
   apply IHp1; propositional.
   apply H.
   apply in_or_app; propositional.
@@ -509,7 +509,7 @@ Proof.
   excluded_middle (interp (fun x => hyps (Var x)) p2).
   left; propositional.
   apply ValidOrIntro2.
-  assert (IF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
+  assert (IFF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
   apply IHp2; propositional.
   apply H.
   apply in_or_app; propositional.
@@ -519,7 +519,7 @@ Proof.
   apply ValidOrElim with p1 p2.
   apply ValidHyp.
   propositional.
-  assert (IF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
+  assert (IFF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
   apply IHp1; propositional.
   apply H.
   apply in_or_app; propositional.
@@ -530,7 +530,7 @@ Proof.
   propositional.
   apply ValidHyp.
   propositional.
-  assert (IF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
+  assert (IFF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
   apply IHp2; propositional.
   apply H.
   apply in_or_app; propositional.
@@ -546,7 +546,7 @@ Proof.
   excluded_middle (interp (fun x => hyps (Var x)) p2).
   left; propositional.
   apply ValidImplyIntro.
-  assert (IF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
+  assert (IFF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
   apply IHp2; propositional.
   apply H.
   apply in_or_app; propositional.
@@ -556,12 +556,12 @@ Proof.
   propositional.
   right; propositional.
   apply ValidImplyIntro.
-  assert (IF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
+  assert (IFF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
   apply IHp1; propositional.
   apply H.
   apply in_or_app; propositional.
   unfold IF_then_else in H3; propositional.
-  assert (IF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
+  assert (IFF interp (fun x : var => hyps (Var x)) p2 then valid hyps p2 else valid hyps (Not p2)).
   apply IHp2; propositional.
   apply H.
   apply in_or_app; propositional.
@@ -578,7 +578,7 @@ Proof.
   propositional.
   left; propositional.
   apply ValidImplyIntro.
-  assert (IF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
+  assert (IFF interp (fun x : var => hyps (Var x)) p1 then valid hyps p1 else valid hyps (Not p1)).
   apply IHp1; propositional.
   apply H.
   apply in_or_app; propositional.
@@ -606,7 +606,7 @@ Proof.
   induct leftToDo; simplify.
 
   rewrite app_nil_r in H.
-  assert (IF interp (fun x : var => hyps (Var x)) p then valid hyps p else valid hyps (Not p)).
+  assert (IFF interp (fun x : var => hyps (Var x)) p then valid hyps p else valid hyps (Not p)).
   apply interp_valid''; first_order.
   unfold IF_then_else in H4; propositional.
   exfalso.