ocaml 3.09 transition

[helm.git] / helm / coq-contribs / LAMBDA-TYPES / ty0_sred_props.v

diff --git a/helm/coq-contribs/LAMBDA-TYPES/ty0_sred_props.v b/helm/coq-contribs/LAMBDA-TYPES/ty0_sred_props.v
index 6fb7f17e102aed06dbb494924f997fcad46672ec..1606efc5c0e9fc217c6bb4c9b00175da44ee9a76 100644 (file)
--- a/helm/coq-contribs/LAMBDA-TYPES/ty0_sred_props.v
+++ b/helm/coq-contribs/LAMBDA-TYPES/ty0_sred_props.v
@@ -3,6 +3,7 @@ Require drop_props.
 Require pc3_props.
 Require pc3_gen.
 Require ty0_defs.
+Require ty0_gen.
 Require ty0_props.
 Require ty0_sred.
 
@@ -25,62 +26,62 @@ Require ty0_sred.
 (*#* #caption "generation lemma for lift" *)
 (*#* #cap #cap t2 #alpha c in C1, e in C2, t1 in T, x in T1, d in i *)
 
-      Theorem ty0_gen_lift : (g:?; c:?; t1,x:?; h,d:?)
-                             (ty0 g c (lift h d t1) x) ->
-                             (e:?) (wf0 g e) -> (drop h d c e) ->
-                             (EX t2 | (pc3 c (lift h d t2) x) & (ty0 g e t1 t2)).
+      Theorem ty0_gen_lift: (g:?; c:?; t1,x:?; h,d:?)
+                            (ty0 g c (lift h d t1) x) ->
+                            (e:?) (wf0 g e) -> (drop h d c e) ->
+                            (EX t2 | (pc3 c (lift h d t2) x) & (ty0 g e t1 t2)).
 
 (*#* #stop file *)
 
       Intros until 1; InsertEq H '(lift h d t1);
       UnIntro H d; UnIntro H t1; XElim H; Intros;
       Rename x0 into t3; Rename x1 into d0.
-(* case 1 : ty0_conv *)
+(* case 1: ty0_conv *)
       IH e; XEAuto.
-(* case 2 : ty0_sort *)
+(* case 2: ty0_sort *)
       LiftGenBase; Rewrite H0; Clear H0 t.
       EApply ex2_intro; [ Rewrite lift_sort; XAuto | XAuto ].
-(* case 3 : ty0_abbr *)
+(* case 3: ty0_abbr *)
       Apply (lt_le_e n d0); Intros.
-(* case 3.1 : n < d0 *)
+(* case 3.1: n < d0 *)
       LiftGenBase; DropS; Rewrite H3; Clear H3 t3.
       Rewrite (le_plus_minus (S n) d0); [ Idtac | XAuto ].
       Rewrite (lt_plus_minus n d0) in H5; [ DropDis; IH x1 | XAuto ].
       EApply ex2_intro;
       [ Rewrite lift_d; [ EApply pc3_lift; XEAuto | XEAuto ]
       | EApply ty0_abbr; XEAuto ].
-(* case 3.2 : n >= d0 *)
+(* case 3.2: n >= d0 *)
       Apply (lt_le_e n (plus d0 h)); Intros.
-(* case 3.2.1 : n < d0 + h *)
+(* case 3.2.1: n < d0 + h *)
       LiftGenBase.
-(* case 3.2.2 : n >= d0 + h *)
+(* case 3.2.2: n >= d0 + h *)
       Rewrite (le_plus_minus_sym h n) in H3; [ Idtac | XEAuto ].
       LiftGenBase; DropDis; Rewrite H3; Clear H3 t3.
       EApply ex2_intro; [ Idtac | EApply ty0_abbr; XEAuto ].
       Rewrite lift_free; [ Idtac | XEAuto | XAuto ].
       Rewrite <- plus_n_Sm; Rewrite <- le_plus_minus; XEAuto.
-(* case 4 : ty0_abst *)
+(* case 4: ty0_abst *)
       Apply (lt_le_e n d0); Intros.
-(* case 4.1 : n < d0 *)
+(* case 4.1: n < d0 *)
       LiftGenBase; Rewrite H3; Clear H3 t3.
       Rewrite (le_plus_minus (S n) d0); [ Idtac | XAuto ].
       Rewrite (lt_plus_minus n d0) in H5; [ DropDis; Rewrite H0; IH x1 | XAuto ].
       EApply ex2_intro; [ Rewrite lift_d | EApply ty0_abst ]; XEAuto.
-(* case 4.2 : n >= d0 *)
+(* case 4.2: n >= d0 *)
       Apply (lt_le_e n (plus d0 h)); Intros.
-(* case 4.2.1 : n < d0 + h *)
+(* case 4.2.1: n < d0 + h *)
       LiftGenBase.
-(* case 4.2.2 : n >= d0 + h *)
+(* case 4.2.2: n >= d0 + h *)
       Rewrite (le_plus_minus_sym h n) in H3; [ Idtac | XEAuto ].
       LiftGenBase; DropDis; Rewrite H3; Clear H3 t3.
       EApply ex2_intro; [ Idtac | EApply ty0_abst; XEAuto ].
       Rewrite lift_free; [ Idtac | XEAuto | XAuto ].
       Rewrite <- plus_n_Sm; Rewrite <- le_plus_minus; XEAuto.
-(* case 5 : ty0_bind *)
+(* case 5: ty0_bind *)
       LiftGenBase; Rewrite H5; Rewrite H8; Rewrite H8 in H2; Clear H5 t3.
       Move H0 after H2; IH e; IH '(CTail e (Bind b) x0); Ty0Correct.
       EApply ex2_intro; [ Rewrite lift_bind; XEAuto | XEAuto ].
-(* case 6 : ty0_appl *)
+(* case 6: ty0_appl *)
       LiftGenBase; Rewrite H3; Rewrite H6; Clear H3 c t3 x y.
       IH e; IH e; Pc3Gen; Pc3T; Pc3Gen; Pc3T.
       Move H3 after H12; Ty0Correct; Ty0SRed; Ty0GenBase; Wf0Ty0.
@@ -91,7 +92,7 @@ Require ty0_sred.
         [ EApply ty0_conv
         | EApply ty0_conv; [ EApply ty0_bind | Idtac | Idtac ] ]
       ]; XEAuto.
-(* case 7 : ty0_cast *)
+(* case 7: ty0_cast *)
       LiftGenBase; Rewrite H3; Rewrite H6; Rewrite H6 in H0.
       IH e; IH e; Pc3Gen; XEAuto.
       Qed.
@@ -107,7 +108,7 @@ Require ty0_sred.
                LApply H0; [ Clear H0 H1; Intros H0 | XAuto ];
                XElim H0; Intros
             | [ H0: (ty0 ?1 ?2 (lift ?3 ?4 ?5) ?6);
-                _ : (wf0 ?1 ?7) |- ? ] ->
+                 _: (wf0 ?1 ?7) |- ? ] ->
                LApply (ty0_gen_lift ?1 ?2 ?5 ?6 ?3 ?4); [ Clear H0; Intros H0 | XAuto ];
                LApply (H0 ?7); [ Clear H0; Intros H0 | XAuto ];
                LApply H0; [ Clear H0; Intros H0 | XAuto ];
@@ -121,22 +122,22 @@ Require ty0_sred.
 (*#* #caption "drop preserves well-formedness" *)
 (*#* #cap #alpha c in C1, e in C2, d in i *)
 
-      Theorem wf0_drop : (c,e:?; d,h:?) (drop h d c e) ->
-                         (g:?) (wf0 g c) -> (wf0 g e).
+      Theorem wf0_drop: (c,e:?; d,h:?) (drop h d c e) ->
+                        (g:?) (wf0 g c) -> (wf0 g e).
 
 (*#* #stop proof *)
 
       XElim c.
-(* case 1 : CSort *)
+(* case 1: CSort *)
       Intros; DropGenBase; Rewrite H; XAuto.
-(* case 2 : CTail k *)
+(* case 2: CTail k *)
       Intros c IHc; XElim k; (
       XElim d;
       [ XEAuto
       | Intros d IHd; Intros;
         DropGenBase; Rewrite H; Rewrite H1 in H0; Clear IHd H H1 e t;
         Inversion H0; Clear H3 H4 b0 u ]).
-(* case 2.1 : Bind, d > 0 *)
+(* case 2.1: Bind, d > 0 *)
       Ty0Gen; XEAuto.
       Qed.
 
@@ -145,8 +146,8 @@ Require ty0_sred.
 (*#* #caption "type reduction" *)
 (*#* #cap #cap c, t1, t2 #alpha u in T *)
 
-      Theorem ty0_tred : (g:?; c:?; u,t1:?) (ty0 g c u t1) ->
-                         (t2:?) (pr3 c t1 t2) -> (ty0 g c u t2).
+      Theorem ty0_tred: (g:?; c:?; u,t1:?) (ty0 g c u t1) ->
+                        (t2:?) (pr3 c t1 t2) -> (ty0 g c u t2).
 
 (*#* #stop proof *)
 
@@ -158,13 +159,13 @@ Require ty0_sred.
 (*#* #caption "subject conversion" *)
 (*#* #cap #cap c, u1, u2, t1, t2 *)
 
-      Theorem ty0_sconv : (g:?; c:?; u1,t1:?) (ty0 g c u1 t1) ->
-                          (u2,t2:?) (ty0 g c u2 t2) ->
-                          (pc3 c u1 u2) -> (pc3 c t1 t2).
+      Theorem ty0_sconv: (g:?; c:?; u1,t1:?) (ty0 g c u1 t1) ->
+                         (u2,t2:?) (ty0 g c u2 t2) ->
+                         (pc3 c u1 u2) -> (pc3 c t1 t2).
 
 (*#* #stop file *)
 
-      Intros; Pc3Confluence; Repeat Ty0SRed; XEAuto.
+      Intros; Pc3Unfold; Repeat Ty0SRed; XEAuto.
       Qed.