ocaml 3.09 transition

[helm.git] / helm / coq-contribs / LAMBDA-TYPES / pc3_subst0.v

diff --git a/helm/coq-contribs/LAMBDA-TYPES/pc3_subst0.v b/helm/coq-contribs/LAMBDA-TYPES/pc3_subst0.v
index 4fd7e138a624026fe2ca6bf8a3de157e2e53a281..02a5d8a385bce027359f9be4bc0daa160b3b3355 100644 (file)
--- a/helm/coq-contribs/LAMBDA-TYPES/pc3_subst0.v
+++ b/helm/coq-contribs/LAMBDA-TYPES/pc3_subst0.v
@@ -4,6 +4,7 @@ Require subst0_subst0.
 Require fsubst0_defs.
 Require pr0_subst0.
 Require pc3_defs.
+Require pc3_props.
 
    Section pc3_fsubst0. (****************************************************)
 
@@ -15,11 +16,11 @@ Require pc3_defs.
 (* case 1: pr2_free *)
       Intros until 2; XElim H0; Intros.
 (* case 1.1: fsubst0_snd *)
-      Pr0Subst0; [ XAuto | Apply (pc3_pr3_u c1 x); XEAuto ].
+      Pr0Subst0; [ XAuto | Apply (pc3_pr2_u c1 x); XEAuto ].
 (* case 1.2: fsubst0_fst *)
       XAuto.
 (* case 1.3: fsubst0_both *)
-      Pr0Subst0; CSubst0Drop; [ XAuto | Apply (pc3_pr3_u c0 x); XEAuto ].
+      Pr0Subst0; CSubst0Drop; [ XAuto | Apply (pc3_pr2_u c0 x); XEAuto ].
 (* case 2 : pr2_delta *)
       Intros until 4; XElim H2; Intros.
 (* case 2.1: fsubst0_snd. *)
@@ -31,33 +32,33 @@ Require pc3_defs.
 (* case 2.2.2: i < i0, csubst0_snd *)
       CGenBase; Rewrite <- H8 in H5; Rewrite <- H9 in H5; Rewrite <- H9 in H6; Rewrite <- H10 in H6; Clear H8 H9 H10 c2 t3 x0 x1 x2.
       Subst0Subst0; Rewrite <- lt_plus_minus_r in H7; [ CSubst0Drop | XAuto ].
-      Apply (pc3_pr3_u c0 x); XEAuto.
+      Apply (pc3_pr2_u c0 x); XEAuto.
 (* case 2.2.3: i < i0, csubst0_fst *)
       CGenBase; Rewrite <- H8 in H6; Rewrite <- H9 in H5; Rewrite <- H9 in H6; Rewrite <- H10 in H5; Clear H8 H9 H10 c2 t3 x0 x1 x3.
       Apply pc3_pr2_r; XEAuto.
 (* case 2.2.4: i < i0, csubst0_both *)
       CGenBase; Rewrite <- H9 in H7; Rewrite <- H10 in H5; Rewrite <- H10 in H6; Rewrite <- H10 in H7; Rewrite <- H11 in H6; Clear H9 H10 H11 c2 t3 x0 x1 x3.
       Subst0Subst0; Rewrite <- lt_plus_minus_r in H8; [ CSubst0Drop | XAuto ].
-      Apply (pc3_pr3_u c0 x); XEAuto.
+      Apply (pc3_pr2_u c0 x); XEAuto.
 (* case 2.2.5: i >= i0 *)
       XEAuto.
 (* case 2.3: fsubst0_both *)
       Apply (lt_le_e i i0); Intros; CSubst0Drop.
 (* case 2.3.1 : i < i0, none *)
-      CSubst0Drop; Apply pc3_pr3_u2 with t0 := t1; XEAuto.
+      CSubst0Drop; Apply pc3_pr2_u2 with t0 := t1; XEAuto.
 (* case 2.3.2 : i < i0, csubst0_snd *)
       CGenBase; Rewrite <- H9 in H6; Rewrite <- H10 in H6; Rewrite <- H10 in H7; Rewrite <- H11 in H7; Clear H9 H10 H11 c2 t3 x0 x1 x2.
       Subst0Subst0; Rewrite <- lt_plus_minus_r in H8; [ CSubst0Drop | XAuto ].
-      Apply (pc3_pr3_u2 c0 t1); [ Idtac | Apply (pc3_pr3_u c0 x) ]; XEAuto.
+      Apply (pc3_pr2_u2 c0 t1); [ Idtac | Apply (pc3_pr2_u c0 x) ]; XEAuto.
 (* case 2.3.3: i < i0, csubst0_fst *)
       CGenBase; Rewrite <- H9 in H7; Rewrite <- H10 in H6; Rewrite <- H10 in H7; Rewrite <- H11 in H6; Clear H9 H10 H11 c2 t3 x0 x1 x3.
-      CSubst0Drop; Apply (pc3_pr3_u2 c0 t1); [ Idtac | Apply pc3_pr2_r ]; XEAuto.
+      CSubst0Drop; Apply (pc3_pr2_u2 c0 t1); [ Idtac | Apply pc3_pr2_r ]; XEAuto.
 (* case 2.3.4: i < i0, csubst0_both *)
       CGenBase; Rewrite <- H10 in H8; Rewrite <- H11 in H6; Rewrite <- H11 in H7; Rewrite <- H11 in H8; Rewrite <- H12 in H7; Clear H10 H11 H12 c2 t3 x0 x1 x3.
       Subst0Subst0; Rewrite <- lt_plus_minus_r in H9; [ CSubst0Drop | XAuto ].
-      Apply (pc3_pr3_u2 c0 t1); [ Idtac | Apply (pc3_pr3_u c0 x) ]; XEAuto.
+      Apply (pc3_pr2_u2 c0 t1); [ Idtac | Apply (pc3_pr2_u c0 x) ]; XEAuto.
 (* case 2.3.5: i >= i0 *)
-      CSubst0Drop; Apply (pc3_pr3_u2 c0 t1); XEAuto.
+      CSubst0Drop; Apply (pc3_pr2_u2 c0 t1); XEAuto.
       Qed.
 
       Theorem pc3_pr2_fsubst0_back: (c1:?; t,t1:?) (pr2 c1 t t1) ->
@@ -68,11 +69,11 @@ Require pc3_defs.
 (* case 1: pr2_free *)
       Intros until 2; XElim H0; Intros.
 (* case 1.1: fsubst0_snd. *)
-      Apply (pc3_pr3_u c1 t2); XEAuto.
+      Apply (pc3_pr2_u c1 t2); XEAuto.
 (* case 1.2: fsubst0_fst. *)
       XAuto.
 (* case 1.3: fsubst0_both. *)
-      CSubst0Drop; Apply (pc3_pr3_u c0 t2); XEAuto.
+      CSubst0Drop; Apply (pc3_pr2_u c0 t2); XEAuto.
 (* case 2: pr2_delta *)
       Intros until 4; XElim H2; Intros.
 (* case 2.1: fsubst0_snd. *)
@@ -84,58 +85,52 @@ Require pc3_defs.
 (* case 2.2.2: i < i0, csubst0_bind *)
       CGenBase; Rewrite <- H8 in H5; Rewrite <- H9 in H5; Rewrite <- H9 in H6; Rewrite <- H10 in H6; Clear H8 H9 H10 c2 t3 x0 x1 x2.
       Subst0Subst0; Rewrite <- lt_plus_minus_r in H7; [ CSubst0Drop | XAuto ].
-      Apply (pc3_pr3_u c0 x); XEAuto.
+      Apply (pc3_pr2_u c0 x); XEAuto.
 (* case 2.2.3: i < i0, csubst0_fst *)
       CGenBase; Rewrite <- H8 in H6; Rewrite <- H9 in H5; Rewrite <- H9 in H6; Rewrite <- H10 in H5; Clear H8 H9 H10 c2 t3 x0 x1 x3.
       Apply pc3_pr2_r; XEAuto.
 (* case 2.2.4: i < i0, csubst0_both *)
       CGenBase; Rewrite <- H9 in H7; Rewrite <- H10 in H5; Rewrite <- H10 in H6; Rewrite <- H10 in H7; Rewrite <- H11 in H6; Clear H9 H10 H11 c2 t3 x0 x1 x3.
       Subst0Subst0; Rewrite <- lt_plus_minus_r in H8; [ CSubst0Drop | XAuto ].
-      Apply (pc3_pr3_u c0 x); XEAuto.
+      Apply (pc3_pr2_u c0 x); XEAuto.
 (* case 2.2.5: i >= i0 *)
       XEAuto.
 (* case 2.3: fsubst0_both *)
       Apply (lt_le_e i i0); Intros; CSubst0Drop.
 (* case 2.3.1 : i < i0, none *)
-      CSubst0Drop; Apply pc3_pr3_u with t2:=t2; Try Apply pc3_pr3_r; XEAuto.
+      CSubst0Drop; Apply pc3_pr2_u with t2:=t2; Try Apply pc3_pr3_r; XEAuto.
 (* case 2.3.2 : i < i0, csubst0_snd *)
       CGenBase; Rewrite <- H9 in H6; Rewrite <- H10 in H6; Rewrite <- H10 in H7; Rewrite <- H11 in H7; Clear H9 H10 H11 c2 t3 x0 x1 x2.
       Subst0Subst0; Rewrite <- lt_plus_minus_r in H8; [ CSubst0Drop | XAuto ].
-      Apply (pc3_pr3_u c0 x); [ Idtac | Apply (pc3_pr3_u2 c0 t0) ]; XEAuto.
+      Apply (pc3_pr2_u c0 x); [ Idtac | Apply (pc3_pr2_u2 c0 t0) ]; XEAuto.
 (* case 2.3.3: i < i0, csubst0_fst *)
       CGenBase; Rewrite <- H9 in H7; Rewrite <- H10 in H6; Rewrite <- H10 in H7; Rewrite <- H11 in H6; Clear H9 H10 H11 c2 t3 x0 x1 x3.
-      CSubst0Drop; Apply (pc3_pr3_u c0 t0); [ Idtac | Apply pc3_pr2_r ]; XEAuto.
+      CSubst0Drop; Apply (pc3_pr2_u c0 t0); [ Idtac | Apply pc3_pr2_r ]; XEAuto.
 (* case 2.3.4: i < i0, csubst0_both *)
       CGenBase; Rewrite <- H10 in H8; Rewrite <- H11 in H6; Rewrite <- H11 in H7; Rewrite <- H11 in H8; Rewrite <- H12 in H7; Clear H10 H11 H12 c2 t3 x0 x1 x3.
       Subst0Subst0; Rewrite <- lt_plus_minus_r in H9; [ CSubst0Drop | XAuto ].
-      Apply (pc3_pr3_u c0 x); [ Idtac | Apply (pc3_pr3_u2 c0 t0) ]; XEAuto.
+      Apply (pc3_pr2_u c0 x); [ Idtac | Apply (pc3_pr2_u2 c0 t0) ]; XEAuto.
 (* case 2.3.5: i >= i0 *)
-      CSubst0Drop; Apply (pc3_pr3_u c0 t0); XEAuto.
+      CSubst0Drop; Apply (pc3_pr2_u c0 t0); XEAuto.
       Qed.
 
-      Theorem pc3_pc2_fsubst0: (c1:?; t1,t:?) (pc2 c1 t1 t) ->
-                               (i:?; u,c2,t2:?) (fsubst0 i u c1 t1 c2 t2) ->
-                               (e:?) (drop i (0) c1 (CTail e (Bind Abbr) u)) ->
-                               (pc3 c2 t2 t).
-      Intros until 1; XElim H; Intros.
-(* case 1: pc2_r *)
-      EApply pc3_pr2_fsubst0; XEAuto.
-(* case 2: pc2_x *)
-      Apply pc3_s; EApply pc3_pr2_fsubst0_back; XEAuto.
-      Qed.
+      Opaque pc3.
 
       Theorem pc3_fsubst0: (c1:?; t1,t:?) (pc3 c1 t1 t) ->
                            (i:?; u,c2,t2:?) (fsubst0 i u c1 t1 c2 t2) ->
                            (e:?) (drop i (0) c1 (CTail e (Bind Abbr) u)) ->
                            (pc3 c2 t2 t).
-      Intros until 1; XElim H.
-(* case 1: pc3_r *)
+      Intros until 1; XElimUsing pc3_ind_left H.
+(* case 1: pc3_refl *)
       Intros until 1; XElim H; Intros; Try CSubst0Drop; XEAuto.
-(* case 2: pc3_u *)
+(* case 2: pc3_pr2_u *)
+      Intros until 4; XElim H2; Intros;
+      (Apply (pc3_t t2); [ EApply pc3_pr2_fsubst0; XEAuto | XEAuto ]).
+(* case 2: pc3_pr2_u2 *)
       Intros until 4; XElim H2; Intros;
-      (Apply (pc3_t t2); [ EApply pc3_pc2_fsubst0; XEAuto | XEAuto ]).
+      (Apply (pc3_t t0); [ Apply pc3_s; EApply pc3_pr2_fsubst0_back; XEAuto | XEAuto ]).
       Qed.
 
    End pc3_fsubst0.
 
-      Hints Resolve pc3_fsubst0.
+      Hints Resolve pc3_fsubst0 : ltlc.