we restored the scripts of \lambda\delta version 1

[helm.git] / helm / coq-contribs / LAMBDA-TYPES / pr2_gen.v

diff --git a/helm/coq-contribs/LAMBDA-TYPES/pr2_gen.v b/helm/coq-contribs/LAMBDA-TYPES/pr2_gen.v
deleted file mode 100644 (file)
index 98d1282..0000000
--- a/helm/coq-contribs/LAMBDA-TYPES/pr2_gen.v
+++ /dev/null
@@ -1,78 +0,0 @@
-(*#* #stop file *)
-
-Require subst0_gen.
-Require subst0_lift.
-Require drop_props.
-Require pr0_gen.
-Require pr0_subst0.
-Require pr2_defs.
-
-   Section pr2_gen. (********************************************************)
-
-      Theorem pr2_gen_abbr: (c:?; u1,t1,x:?)
-                            (pr2 c (TTail (Bind Abbr) u1 t1) x) ->
-                            (EX u2 t2 | x = (TTail (Bind Abbr) u2 t2) &
-                                        (pr2 c u1 u2) & (OR
-                                        (b:?; u:?) (pr2 (CTail c (Bind b) u) t1 t2) |
-                                       (EX u | (pr0 u1 u) & (pr2 (CTail c (Bind Abbr) u) t1 t2)) |
-                                       (EX y z | (pr2 (CTail c (Bind Abbr) u1) t1 y) & (pr0 y z) & (pr2 (CTail c (Bind Abbr) u1) z t2))
-                            )) \/ (b:?; u:?)
-                           (pr2 (CTail c (Bind b) u) t1 (lift (1) (0) x)).
-      Intros; Inversion H; 
-      Pr0Gen; Try Rewrite H1 in H2; Try Subst0Gen; Try Pr0Subst0; XDEAuto 10.
-      Qed.
-
-      Theorem pr2_gen_void: (c:?; u1,t1,x:?)
-                            (pr2 c (TTail (Bind Void) u1 t1) x) ->
-                            (EX u2 t2 | x = (TTail (Bind Void) u2 t2) &
-                                        (pr2 c u1 u2) & (b:?; u:?)
-                                        (pr2 (CTail c (Bind b) u) t1 t2)
-                            ) \/ (b:?; u:?)
-                            (pr2 (CTail c (Bind b) u) t1 (lift (1) (0) x)).
-      Intros; Inversion H; 
-      Try Pr0Gen; Try Rewrite H1 in H2; Try Subst0Gen; XDEAuto 7.
-      Qed.
-
-(*#* #caption "generation lemma for lift" *)
-(*#* #cap #cap c #alpha e in D, t1 in U1, t2 in U2, x in T, d in i *)
-
-      Theorem pr2_gen_lift: (c:?; t1,x:?; h,d:?) (pr2 c (lift h d t1) x) ->
-                            (e:?) (drop h d c e) ->
-                            (EX t2 | x = (lift h d t2) & (pr2 e t1 t2)).
-      Intros.
-      Inversion H; Clear H; Pr0Gen.
-(* case 1 : pr2_free *)
-      XEAuto.
-(* case 2 : pr2_delta *)
-      Rewrite H in H3; Clear H H4 t t2.
-      Apply (lt_le_e i d); Intros.
-(* case 2.1 : i < d *)
-      Rewrite (lt_plus_minus i d) in H0; [ Idtac | XAuto ]. 
-      Rewrite (lt_plus_minus i d) in H3; [ Idtac | XAuto ].
-      DropDis; Rewrite H0 in H3; Clear H0 u. 
-      Subst0Gen; Rewrite <- lt_plus_minus in H0; XEAuto.
-(* case 2.2 : i >= d *)
-      Apply (lt_le_e i (plus d h)); Intros.
-(* case 2.2.1 : i < d + h *)
-      EApply subst0_gen_lift_false; [ Apply H | Apply H4 | XEAuto ].
-(* case 2.2.2 : i >= d + h *)
-      DropDis; Subst0Gen; XEAuto.
-      Qed.
-
-   End pr2_gen.
-
-      Tactic Definition Pr2Gen :=
-         Match Context With
-            | [ H: (pr2 ?1 (TTail (Bind Abbr) ?2 ?3) ?4) |- ? ] ->
-               LApply (pr2_gen_abbr ?1 ?2 ?3 ?4); [ Clear H; Intros H | XAuto ];
-               XDecompose H  
-            | [ H: (pr2 ?1 (TTail (Bind Void) ?2 ?3) ?4) |- ? ] ->
-               LApply (pr2_gen_void ?1 ?2 ?3 ?4); [ Clear H; Intros H | XAuto ];
-               XDecompose H
-            | [ H0: (pr2 ?1 (lift ?2 ?3 ?4) ?5);
-                H1: (drop ?2 ?3 ?1 ?6) |- ? ] ->
-               LApply (pr2_gen_lift ?1 ?4 ?5 ?2 ?3); [ Clear H0; Intros H0 | XAuto ];
-               LApply (H0 ?6); [ Clear H0; Intros H0 | XAuto ];
-               XDecompose H0
-            | _ -> Pr2GenBase.
-