we restored the scripts of \lambda\delta version 1

[helm.git] / helm / coq-contribs / LAMBDA-TYPES / pr0_gen.v

diff --git a/helm/coq-contribs/LAMBDA-TYPES/pr0_gen.v b/helm/coq-contribs/LAMBDA-TYPES/pr0_gen.v
deleted file mode 100644 (file)
index bfe1895..0000000
--- a/helm/coq-contribs/LAMBDA-TYPES/pr0_gen.v
+++ /dev/null
@@ -1,99 +0,0 @@
-(*#* #stop file *)
-
-Require lift_gen.
-Require lift_props.
-Require subst0_gen.
-Require pr0_defs.
-Require pr0_lift.
-
-   Section pr0_gen_abbr. (***************************************************)
-
-      Theorem pr0_gen_abbr : (u1,t1,x:?) (pr0 (TTail (Bind Abbr) u1 t1) x) ->
-                             (EX u2 t2 | x = (TTail (Bind Abbr) u2 t2) &
-                                         (pr0 u1 u2) &
-                                         (pr0 t1 t2) \/
-                                         (EX y | (pr0 t1 y) & (subst0 (0) u2 y t2))
-                             ) \/
-                             (pr0 t1 (lift (1) (0) x)).
-      Intros.
-      Inversion H; Clear H; XDEAuto 6.
-      Qed.
-
-   End pr0_gen_abbr.
-
-   Section pr0_gen_void. (***************************************************)
-
-      Theorem pr0_gen_void : (u1,t1,x:?) (pr0 (TTail (Bind Void) u1 t1) x) ->
-                             (EX u2 t2 | x = (TTail (Bind Void) u2 t2) &
-                                         (pr0 u1 u2) & (pr0 t1 t2)
-                             ) \/
-                             (pr0 t1 (lift (1) (0) x)).
-      Intros.
-      Inversion H; Clear H; XEAuto.
-      Qed.
-
-   End pr0_gen_void.
-
-   Section pr0_gen_lift. (***************************************************)
-
-      Tactic Definition IH :=
-         Match Context With
-            | [ H: (_:?; _:?) ?0 = (lift ? ? ?) -> ?;
-                H0: ?0 = (lift ? ?2 ?3) |- ? ] ->
-               LApply (H ?3 ?2); [ Clear H H0; Intros H_x | XAuto ];
-               XElim H_x; Intro; Intros H_x; Intro;
-               Try Rewrite H_x; Try Rewrite H_x in H3; Clear H_x.
-
-(*#* #caption "generation lemma for lift" *)
-(*#* #cap #alpha t1 in U1, t2 in U2, x in T, d in i *)
-
-      Theorem pr0_gen_lift : (t1,x:?; h,d:?) (pr0 (lift h d t1) x) ->
-                             (EX t2 | x = (lift h d t2) & (pr0 t1 t2)).
-      Intros until 1; InsertEq H '(lift h d t1);
-      UnIntro H d; UnIntro H t1; XElim H; Clear y x; Intros;
-      Rename x into t3; Rename x0 into d.
-(* case 1 : pr0_r *)
-      XEAuto.
-(* case 2 : pr0_c *)
-      NewInduction k; LiftGen; Rewrite H3; Clear H3 t0;
-      IH; IH; XEAuto.
-(* case 3 : pr0_beta *)
-      LiftGen; Rewrite H3; Clear H3 t0.
-      LiftGen; Rewrite H3; Clear H3 H5 x1 k.
-      IH; IH; XEAuto.
-(* case 4 : pr0_upsilon *)
-      LiftGen; Rewrite H6; Clear H6 t0.
-      LiftGen; Rewrite H6; Clear H6 x1.
-      IH; IH; IH.
-      Rewrite <- lift_d; [ Simpl | XAuto ].
-      Rewrite <- lift_flat; XEAuto.
-(* case 5 : pr0_delta *)
-      LiftGen; Rewrite H4; Clear H4 t0.
-      IH; IH; Arith3In H3 d; Subst0Gen.
-      Rewrite H3; XEAuto.
-(* case 6 : pr0_zeta *)
-      LiftGen; Rewrite H2; Clear H2 t0.
-      Arith7In H4 d; LiftGen; Rewrite H2; Clear H2 x1.
-      IH; XEAuto.
-(* case 7 : pr0_zeta *)
-      LiftGen; Rewrite H1; Clear H1 t0.
-      IH; XEAuto.
-      Qed.
-
-   End pr0_gen_lift.
-
-      Tactic Definition Pr0Gen :=
-         Match Context With
-            | [ H: (pr0 (TTail (Bind Abbr) ?1 ?2) ?3) |- ? ] ->
-               LApply (pr0_gen_abbr ?1 ?2 ?3); [ Clear H; Intros H | XAuto ];
-               XElim H;
-               [ Intros H; XElim H; Do 4 Intro; Intros H_x;
-                 XElim H_x; [ Intros | Intros H_x; XElim H_x; Intros ]
-               | Intros ]
-            | [ H: (pr0 (TTail (Bind Void) ?1 ?2) ?3) |- ? ] ->
-               LApply (pr0_gen_void ?1 ?2 ?3); [ Clear H; Intros H | XAuto ];
-               XElim H; [ Intros H; XElim H; Intros | Intros ]
-            | [ H: (pr0 (lift ?0 ?1 ?2) ?3) |- ? ] ->
-               LApply (pr0_gen_lift ?2 ?3 ?0 ?1); [ Clear H; Intros H | XAuto ];
-               XElim H; Intros
-            | _ -> Pr0GenBase.