some more changes and corrections

[helm.git] / helm / coq-contribs / LAMBDA-TYPES / csub0_props.v

diff --git a/helm/coq-contribs/LAMBDA-TYPES/csub0_props.v b/helm/coq-contribs/LAMBDA-TYPES/csub0_props.v
new file mode 100644 (file)
index 0000000..04c4edd
--- /dev/null
+++ b/helm/coq-contribs/LAMBDA-TYPES/csub0_props.v
@@ -0,0 +1,67 @@
+(*#* #stop file *)
+
+Require pc3_props.
+Require csub0_defs.   
+
+   Section csub0_pc3. (*****************************************************)
+
+      Theorem csub0_pr2: (g:?; c1:?; t1,t2:?) (pr2 c1 t1 t2) ->
+                         (c2:?) (csub0 g c1 c2) -> (pr2 c2 t1 t2).
+      Intros until 1; XElim H; Intros.
+(* case 1: pr2_free *)
+      XAuto.
+(* case 2: pr2_delta *)
+      CSub0Drop; XEAuto.
+      Qed.
+
+      Hints Resolve csub0_pr2.
+
+      Opaque pc3.
+
+      Theorem csub0_pc3: (g:?; c1:?; t1,t2:?) (pc3 c1 t1 t2) ->
+                         (c2:?) (csub0 g c1 c2) -> (pc3 c2 t1 t2).
+      Intros until 1; XElimUsing pc3_ind_left H; XEAuto.
+      Qed.
+
+   End csub0_pc3.
+
+      Hints Resolve csub0_pc3 : ltlc.
+   
+   Section csub0_ty0. (*****************************************************)
+
+      Theorem csub0_ty0: (g:?; c1:?; t1,t2:?) (ty0 g c1 t1 t2) ->
+                         (c2:?) (wf0 g c2) -> (csub0 g c1 c2) ->
+                         (ty0 g c2 t1 t2).
+      Intros until 1; XElim H; Intros.
+(* case 1: ty0_conv *)
+      EApply ty0_conv; XEAuto.
+(* case 2: ty0_sort *)
+      XEAuto.
+(* case 3: ty0_abbr *)
+      CSub0Drop; EApply ty0_abbr; XEAuto.
+(* case 4: ty0_abst *)
+      CSub0Drop; [ EApply ty0_abst | EApply ty0_abbr ]; XEAuto.
+(* case 5: ty0_bind *)
+      EApply ty0_bind; XEAuto.
+(* case 6: ty0_appl *)
+      EApply ty0_appl; XEAuto.
+(* case 7: ty0_cast *)
+      EApply ty0_cast; XAuto.
+      Qed.
+
+      Theorem csub0_ty0_ld: (g:?; c:?; u,v:?) (ty0 g c u v) -> (t1,t2:?)
+                            (ty0 g (CTail c (Bind Abst) v) t1 t2) ->
+                            (ty0 g (CTail c (Bind Abbr) u) t1 t2).
+      Intros; EApply csub0_ty0; XEAuto.
+      Qed.
+
+   End csub0_ty0.
+
+      Hints Resolve csub0_ty0 csub0_ty0_ld : ltlc.
+
+      Tactic Definition CSub0Ty0 :=
+         Match Context With
+            [ _: (ty0 ?1 ?2 ?4 ?); _: (ty0 ?1 ?2 ?3 ?7); _: (pc3 ?2 ?4 ?7);
+              H: (ty0 ?1 (CTail ?2 (Bind Abst) ?4) ?5 ?6) |- ? ] ->
+               LApply (csub0_ty0_ld ?1 ?2 ?3 ?4); [ Intros H_x | EApply ty0_conv; XEAuto ];
+               LApply (H_x ?5 ?6); [ Clear H_x H; Intros | XAuto ].