some reorganization and some corrections

[helm.git] / helm / coq-contribs / LAMBDA-TYPES / cpr0_props.v

diff --git a/helm/coq-contribs/LAMBDA-TYPES/cpr0_props.v b/helm/coq-contribs/LAMBDA-TYPES/cpr0_props.v
deleted file mode 100644 (file)
index 1050288..0000000
--- a/helm/coq-contribs/LAMBDA-TYPES/cpr0_props.v
+++ /dev/null
@@ -1,103 +0,0 @@
-(*#* #stop file *)
-
-Require pr0_subst0.
-Require pr3_defs.
-Require pr3_props.
-Require cpr0_defs.
-
-   Section cpr0_drop. (******************************************************)
-
-      Theorem cpr0_drop : (c1,c2:?) (cpr0 c1 c2) -> (h:?; e1:?; u1:?; k:?)
-                          (drop h (0) c1 (CTail e1 k u1)) ->
-                          (EX e2 u2 | (drop h (0) c2 (CTail e2 k u2)) &
-                                      (cpr0 e1 e2) & (pr0 u1 u2)
-                          ).
-      Intros until 1; XElim H.
-(* case 1 : cpr0_refl *)
-      XEAuto.
-(* case 2 : cpr0_cont *)
-      XElim h.
-(* case 2.1 : h = 0 *)
-      Intros; DropGenBase.
-      Inversion H2; Rewrite H6 in H1; Rewrite H4 in H; XEAuto.
-(* case 2.2 : h > 0 *)
-      XElim k; Intros; DropGenBase.
-(* case 2.2.1 : Bind *)
-      LApply (H0 n e1 u0 k); [ Clear H0 H3; Intros H0 | XAuto ].
-      XElim H0; XEAuto.
-(* case 2.2.2 : Flat *)
-      LApply (H0 (S n) e1 u0 k); [ Clear H0 H3; Intros H0 | XAuto ].
-      XElim H0; XEAuto.
-      Qed.
-
-      Theorem cpr0_drop_back : (c1,c2:?) (cpr0 c2 c1) -> (h:?; e1:?; u1:?; k:?)
-                               (drop h (0) c1 (CTail e1 k u1)) ->
-                               (EX e2 u2 | (drop h (0) c2 (CTail e2 k u2)) &
-                                           (cpr0 e2 e1) & (pr0 u2 u1)
-                               ).
-      Intros until 1; XElim H.
-(* case 1 : cpr0_refl *)
-      XEAuto.
-(* case 2 : cpr0_cont *)
-      XElim h.
-(* case 2.1 : h = 0 *)
-      Intros; DropGenBase.
-      Inversion H2; Rewrite H6 in H1; Rewrite H4 in H; XEAuto.
-(* case 2.2 : h > 0 *)
-      XElim k; Intros; DropGenBase.
-(* case 2.2.1 : Bind *)
-      LApply (H0 n e1 u0 k); [ Clear H0 H3; Intros H0 | XAuto ].
-      XElim H0; XEAuto.
-(* case 2.2.2 : Flat *)
-      LApply (H0 (S n) e1 u0 k); [ Clear H0 H3; Intros H0 | XAuto ].
-      XElim H0; XEAuto.
-      Qed.
-
-   End cpr0_drop.
-
-      Tactic Definition Cpr0Drop :=
-         Match Context With
-            | [ _: (drop ?1 (0) ?2 (CTail ?3 ?4 ?5));
-                _: (cpr0 ?2 ?6) |- ? ] ->
-               LApply (cpr0_drop ?2 ?6); [ Intros H_x | XAuto ];
-               LApply (H_x ?1 ?3 ?5 ?4); [ Clear H_x; Intros H_x | XAuto ];
-               XElim H_x; Intros
-            | [ _: (drop ?1 (0) ?2 (CTail ?3 ?4 ?5));
-                _: (cpr0 ?6 ?2) |- ? ] ->
-               LApply (cpr0_drop_back ?2 ?6); [ Intros H_x | XAuto ];
-               LApply (H_x ?1 ?3 ?5 ?4); [ Clear H_x; Intros H_x | XAuto ];
-               XElim H_x; Intros
-            | [ _: (drop ?1 (0) (CTail ?2 ?7 ?8) (CTail ?3 ?4 ?5));
-                _: (cpr0 ?2 ?6) |- ? ] ->
-               LApply (cpr0_drop (CTail ?2 ?7 ?8) (CTail ?6 ?7 ?8)); [ Intros H_x | XAuto ];
-               LApply (H_x ?1 ?3 ?5 ?4); [ Clear H_x; Intros H_x | XAuto ];
-               XElim H_x; Intros
-            | [ _: (drop ?1 (0) (CTail ?2 ?7 ?8) (CTail ?3 ?4 ?5));
-                _: (cpr0 ?6 ?2) |- ? ] ->
-               LApply (cpr0_drop_back (CTail ?2 ?7 ?8) (CTail ?6 ?7 ?8)); [ Intros H_x | XAuto ];
-               LApply (H_x ?1 ?3 ?5 ?4); [ Clear H_x; Intros H_x | XAuto ];
-               XElim H_x; Intros.
-
-   Section cpr0_pr3. (*******************************************************)
-
-      Theorem cpr0_pr3_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_cont *)
-      Pr3Context.
-      XElim H1; Intros.
-(* case 2.1 : pr3_r *)
-      XAuto.
-(* case 2.2 : pr3_u *)
-      EApply pr3_t; [ Idtac | XEAuto ]. Clear H2 H3 c1 c2 t1 t2 t4 u2.
-      Inversion_clear H1.
-(* case 2.2.1 : pr2_pr0 *)
-      XAuto.
-(* case 2.2.1 : pr2_delta *)
-      Cpr0Drop; Pr0Subst0.
-      EApply pr3_u; [ EApply pr2_delta; XEAuto | XAuto ].
-      Qed.
-
-   End cpr0_pr3.