Firstorder clean-ups after class

60083ed1 · Adam Chlipala · e8b7e237 · 60083ed1
Commit 60083ed1 authored Nov 04, 2008 by Adam Chlipala
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Showing with 6 additions and 16 deletions

Firstorder.v src/Firstorder.v +6 -16

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--- a/src/Firstorder.v
+++ b/src/Firstorder.v
@@ -102,13 +102,7 @@ Module Concrete.
      eapply weaken_hasType'; eauto.
  Qed.
-  Theorem weaken_hasType_closed : forall e t,
+  Hint Resolve weaken_hasType.
-    nil |-e e : t
-    -> forall G, G |-e e : t.
-    intros; rewrite (app_nil_end G); apply weaken_hasType; auto.
-  Qed.
-  Hint Resolve weaken_hasType_closed.
  Section subst.
    Variable x : var.
@@ -243,7 +237,8 @@ Module Concrete.
  Inductive step : exp -> exp -> Prop :=
  | Beta : forall x e1 e2,
-    App (Abs x e1) e2 ==> [x ~> e2] e1
+    val e2
+    -> App (Abs x e1) e2 ==> [x ~> e2] e1
  | Cong1 : forall e1 e2 e1',
    e1 ==> e1'
    -> App e1 e2 ==> App e1' e2
@@ -367,13 +362,7 @@ Module DeBruijn.
      eapply weaken_hasType'; eauto.
  Qed.
-  Theorem weaken_hasType_closed : forall e t,
+  Hint Resolve weaken_hasType.
-    nil |-e e : t
-    -> forall G, G |-e e : t.
-    intros; rewrite (app_nil_end G); apply weaken_hasType; auto.
-  Qed.
-  Hint Resolve weaken_hasType_closed.
  Section subst.
    Variable e1 : exp.
@@ -465,7 +454,8 @@ Module DeBruijn.
  Inductive step : exp -> exp -> Prop :=
  | Beta : forall e1 e2,
-    App (Abs e1) e2 ==> [O ~> e2] e1
+    val e2
+    -> App (Abs e1) e2 ==> [O ~> e2] e1
  | Cong1 : forall e1 e2 e1',
    e1 ==> e1'
    -> App e1 e2 ==> App e1' e2