we restored the scripts of \lambda\delta version 1

[helm.git] / helm / coq-contribs / LAMBDA-TYPES / pr3_props.v

diff --git a/helm/coq-contribs/LAMBDA-TYPES/pr3_props.v b/helm/coq-contribs/LAMBDA-TYPES/pr3_props.v
deleted file mode 100644 (file)
index b5c7df9..0000000
--- a/helm/coq-contribs/LAMBDA-TYPES/pr3_props.v
+++ /dev/null
@@ -1,127 +0,0 @@
-Require subst0_subst0.
-Require pr0_subst0.
-Require cpr0_defs.
-Require pr2_lift.
-Require pr2_gen.
-Require pr3_defs.
-
-(*#* #caption "main properties of the relation $\\PrT{}{}{}$" *)
-(*#* #clauses *)
-
-(*#* #stop file *)
-
-   Section pr3_context. (****************************************************)
-
-      Theorem pr3_pr0_pr2_t: (u1,u2:?) (pr0 u1 u2) ->
-                             (c:?; t1,t2:?; k:?) (pr2 (CTail c k u2) t1 t2) ->
-                             (pr3 (CTail c k u1) t1 t2).
-      Intros; Inversion H0; Clear H0; XAuto.
-      NewInduction i.
-(* case 1 : pr2_delta i = 0 *) 
-      DropGenBase; Inversion H0; Clear H0 H4 H5 H6 c k t.
-      Rewrite H7 in H; Clear H7 u2.
-      Pr0Subst0; XEAuto.
-(* case 2 : pr2_delta i > 0 *)
-      NewInduction k; DropGenBase; XEAuto.
-      Qed.
-
-      Theorem pr3_pr2_pr2_t: (c:?; u1,u2:?) (pr2 c u1 u2) ->
-                             (t1,t2:?; k:?) (pr2 (CTail c k u2) t1 t2) ->
-                             (pr3 (CTail c k u1) t1 t2).
-      Intros until 1; Inversion H; Clear H; Intros.
-(* case 1 : pr2_free *)
-      EApply pr3_pr0_pr2_t; [ Apply H0 | XAuto ].
-(* case 2 : pr2_delta *)
-      Inversion H; [ XAuto | NewInduction i0 ]. 
-(* case 2.1 : i0 = 0 *)
-      DropGenBase; Inversion H4; Clear H3 H4 H7 t t4.
-      Rewrite <- H9; Rewrite H10 in H; Rewrite <- H11 in H6; Clear H9 H10 H11 d0 k u0.
-      Subst0Subst0; Arith9'In H4 i; Clear H2 H H6 u2.
-      Pr0Subst0; Apply pr3_sing with t2:=x0; XEAuto.
-(* case 2.2 : i0 > 0 *)
-      Clear IHi0; NewInduction k; DropGenBase; XEAuto.
-      Qed.
-
-      Theorem pr3_pr2_pr3_t: (c:?; u2,t1,t2:?; k:?)
-                             (pr3 (CTail c k u2) t1 t2) ->
-                             (u1:?) (pr2 c u1 u2) ->
-                             (pr3 (CTail c k u1) t1 t2).
-      Intros until 1; XElim H; Intros.
-(* case 1 : pr3_refl *)
-      XAuto.
-(* case 2 : pr3_sing *)
-      EApply pr3_t.
-      EApply pr3_pr2_pr2_t; [ Apply H2 | Apply H ].
-      XAuto.
-      Qed.
-
-(*#* #caption "reduction inside context items" *)
-(*#* #cap #cap t1, t2 #alpha c in E, u1 in V1, u2 in V2, k in z *)
-
-      Theorem pr3_pr3_pr3_t: (c:?; u1,u2:?) (pr3 c u1 u2) ->
-                             (t1,t2:?; k:?) (pr3 (CTail c k u2) t1 t2) ->
-                             (pr3 (CTail c k u1) t1 t2).
-      Intros until 1; XElim H; Intros.
-(* case 1 : pr3_refl *)
-      XAuto.
-(* case 2 : pr3_sing *)
-      EApply pr3_pr2_pr3_t; [ Apply H1; XAuto | XAuto ].
-      Qed.
-
-   End pr3_context.
-
-      Tactic Definition Pr3Context :=
-         Match Context With
-            | [ H1: (pr0 ?2 ?3); H2: (pr2 (CTail ?1 ?4 ?3) ?5 ?6) |- ? ] ->
-               LApply (pr3_pr0_pr2_t ?2 ?3); [ Intros H_x | XAuto ];
-               LApply (H_x ?1 ?5 ?6 ?4); [ Clear H_x H2; Intros | XAuto ]
-            | [ H1: (pr0 ?2 ?3); H2: (pr3 (CTail ?1 ?4 ?3) ?5 ?6) |- ? ] ->
-               LApply (pr3_pr2_pr3_t ?1 ?3 ?5 ?6 ?4); [ Clear H2; Intros H2 | XAuto ];
-               LApply (H2 ?2); [ Clear H2; Intros | XAuto ]
-            | [ H1: (pr2 ?1 ?2 ?3); H2: (pr2 (CTail ?1 ?4 ?3) ?5 ?6) |- ? ] ->
-               LApply (pr3_pr2_pr2_t ?1 ?2 ?3); [ Intros H_x | XAuto ];
-               LApply (H_x ?5 ?6 ?4); [ Clear H_x H2; Intros | XAuto ]
-            | [ H1: (pr2 ?1 ?2 ?3); H2: (pr3 (CTail ?1 ?4 ?3) ?5 ?6) |- ? ] ->
-               LApply (pr3_pr2_pr3_t ?1 ?3 ?5 ?6 ?4); [ Clear H2; Intros H2 | XAuto ];
-               LApply (H2 ?2); [ Clear H2; Intros | XAuto ]
-            | [ H1: (pr3 ?1 ?2 ?3); H2: (pr3 (CTail ?1 ?4 ?3) ?5 ?6) |- ? ] ->
-               LApply (pr3_pr3_pr3_t ?1 ?2 ?3); [ Intros H_x | XAuto ];
-               LApply (H_x ?5 ?6 ?4); [ Clear H_x H2; Intros | XAuto ].
-
-   Section pr3_lift. (*******************************************************)
-
-(*#* #caption "conguence with lift" *)
-(*#* #cap #cap c, t1, t2 #alpha e in D, d in i *)
-
-      Theorem pr3_lift: (c,e:?; h,d:?) (drop h d c e) ->
-                        (t1,t2:?) (pr3 e t1 t2) ->
-                        (pr3 c (lift h d t1) (lift h d t2)).
-      Intros until 2; XElim H0; Intros; XEAuto.
-      Qed.
-
-   End pr3_lift.
-
-      Hints Resolve pr3_lift : ltlc.
-
-   Section pr3_cpr0. (*******************************************************)
-
-      Theorem pr3_cpr0_t: (c1,c2:?) (cpr0 c2 c1) -> (t1,t2:?) (pr3 c1 t1 t2) ->
-                          (pr3 c2 t1 t2).
-      Intros until 1; XElim H; Intros.
-(* case 1 : cpr0_refl *)
-      XAuto.
-(* case 2 : cpr0_comp *)
-      Pr3Context; Clear H1.
-      XElim H2; Intros.
-(* case 2.1 : pr3_refl *)
-      XAuto.
-(* case 2.2 : pr3_sing *)
-      EApply pr3_t; [ Idtac | XEAuto ]. Clear H2 H3 c1 c2 t1 t2 t4 u2.
-      Inversion_clear H1.
-(* case 2.2.1 : pr2_free *)
-      XAuto.
-(* case 2.2.1 : pr2_delta *)
-      Cpr0Drop; Pr0Subst0; Apply pr3_sing with t2:=x; XEAuto.
-      Qed.
-
-   End pr3_cpr0.