Report r11631 from 8.2 and handle non-dependent goals better in

[dependent induction].


git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11881 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 29 insertions, 25 deletions

diff --git a/test-suite/success/dependentind.v b/test-suite/success/dependentind.v
index 488b057f3..3ab7682d9 100644
--- a/test-suite/success/dependentind.v
+++ b/test-suite/success/dependentind.v
@@ -40,7 +40,7 @@ Delimit Scope context_scope with ctx.
 
 Arguments Scope snoc [context_scope].
 
-Notation " Γ ,, τ " := (snoc Γ τ) (at level 25, t at next level, left associativity).
+Notation " Γ , τ " := (snoc Γ τ) (at level 25, τ at next level, left associativity) : context_scope.
 
 Fixpoint conc (Δ Γ : ctx) : ctx :=
   match Δ with
@@ -48,60 +48,64 @@ Fixpoint conc (Δ Γ : ctx) : ctx :=
     | snoc Δ' x => snoc (conc Δ' Γ) x
   end.
 
-Notation " Γ ;; Δ " := (conc Δ Γ) (at level 25, left associativity) : context_scope.
+Notation " Γ  ; Δ " := (conc Δ Γ) (at level 25, left associativity) : context_scope.
+
+Reserved Notation " Γ ⊢ τ " (at level 30, no associativity). 
 
 Inductive term : ctx -> type -> Type :=
-| ax : forall Γ τ, term (snoc Γ τ) τ
-| weak : forall Γ τ, term Γ τ -> forall τ', term (Γ ,, τ') τ
-| abs : forall Γ τ τ', term (snoc Γ τ) τ' -> term Γ (τ --> τ')
-| app : forall Γ τ τ', term Γ (τ --> τ') -> term Γ τ -> term Γ τ'.
+| ax : `(Γ, τ ⊢ τ)
+| weak : `{Γ ⊢ τ -> Γ, τ' ⊢ τ}
+| abs : `{Γ, τ ⊢ τ' -> Γ ⊢ τ --> τ'}
+| app : `{Γ ⊢ τ --> τ' -> Γ ⊢ τ -> Γ ⊢ τ'}
+
+where " Γ ⊢ τ " := (term Γ τ) : type_scope.
 
 Hint Constructors term : lambda.
 
 Open Local Scope context_scope.
 
-Notation " Γ |-- τ " := (term Γ τ) (at level 0) : type_scope.
+Ltac eqns := subst ; reverse ; simplify_dep_elim ; simplify_IH_hyps.
 
-Lemma weakening : forall Γ Δ τ, term (Γ ;; Δ) τ -> 
-  forall τ', term (Γ ,, τ' ;; Δ) τ.
-Proof with simpl in * ; reverse ; simplify_dep_elim ; simplify_IH_hyps ; eauto with lambda.
+Lemma weakening : forall Γ Δ τ, Γ ; Δ ⊢ τ -> 
+  forall τ', Γ , τ' ; Δ ⊢ τ.
+Proof with simpl in * ; eqns ; eauto with lambda.
   intros Γ Δ τ H.
 
   dependent induction H.
 
-  destruct Δ...
+  destruct Δ as [|Δ τ']...
 
-  destruct Δ...
+  destruct Δ as [|Δ τ'']...
 
-  destruct Δ...
-    apply abs...
-    
-    specialize (IHterm (Δ,, t,, τ)%ctx Γ0)...
+  destruct Δ as [|Δ τ'']...
+    apply abs.
 
-  intro.
-  apply app with τ...
+    specialize (IHterm (Δ, τ'', τ) Γ0)...
+
+  intro. eapply app...
 Qed.
 
-Lemma exchange : forall Γ Δ α β τ, term (Γ,, α,, β ;; Δ) τ -> term (Γ,, β,, α ;; Δ) τ.
-Proof with simpl in * ; subst ; reverse ; simplify_dep_elim ; simplify_IH_hyps ; auto.
+Lemma exchange : forall Γ Δ α β τ, term (Γ, α, β ; Δ) τ -> term (Γ, β, α ; Δ) τ.
+Proof with simpl in * ; eqns ; eauto.
   intros until 1.
+
   dependent induction H.
 
-  destruct Δ...
+  destruct Δ ; eqns.
     apply weak ; apply ax.
 
     apply ax.
 
   destruct Δ...
-    pose (weakening Γ0 (empty,, α))...
+    pose (weakening Γ0 (empty, α))...
 
     apply weak...
 
   apply abs... 
-  specialize (IHterm (Δ ,, τ))...
+    specialize (IHterm (Δ, τ))...
 
-  eapply app with τ...
-Save.
+  eapply app...
+Defined.
 
 (** Example by Andrew Kenedy, uses simplification of the first component of dependent pairs. *)