9 Section pc3_gen. (********************************************************)
11 Theorem pc3_gen_sort: (c:?; m,n:?) (pc3 c (TSort m) (TSort n)) -> m = n.
12 Intros; Pc3Unfold; Repeat Pr3GenBase.
13 Rewrite H0 in H; Clear H0 x c.
17 Theorem pc3_gen_abst: (c:?; u1,u2,t1,t2:?)
18 (pc3 c (TTail (Bind Abst) u1 t1)
19 (TTail (Bind Abst) u2 t2)
22 (b:?; u:?) (pc3 (CTail c (Bind b) u) t1 t2).
24 Pc3Unfold; Repeat Pr3GenBase; Rewrite H1 in H; Clear H1 x.
25 TGenBase; Rewrite H1 in H4; Rewrite H6 in H5.
29 Theorem pc3_gen_lift: (c:?; t1,t2:?; h,d:?)
30 (pc3 c (lift h d t1) (lift h d t2)) ->
31 (e:?) (drop h d c e) ->
34 Pc3Unfold; Repeat Pr3Gen; Rewrite H2 in H; Clear H2 x.
35 LiftGen; Rewrite H in H4; XEAuto.
38 Theorem pc3_gen_not_abst: (b:?) ~b=Abst -> (c:?; t1,t2,u1,u2:?)
39 (pc3 c (TTail (Bind b) u1 t1)
40 (TTail (Bind Abst) u2 t2)
42 (pc3 (CTail c (Bind b) u1) t1
43 (lift (1) (0) (TTail (Bind Abst) u2 t2))
46 Try EqFalse; Pc3Unfold; Repeat Pr3Gen;
47 Try (Rewrite H0 in H3; TGenBase);
48 Rewrite H1 in H0; Clear H H1 x;
49 EApply pc3_pr3_t; XEAuto.
52 Theorem pc3_gen_lift_abst: (c:?; t,t2,u2:?; h,d:?)
54 (TTail (Bind Abst) u2 t2)
56 (e:?) (drop h d c e) ->
57 (EX u1 t1 | (pr3 e t (TTail (Bind Abst) u1 t1)) &
58 (pr3 c u2 (lift h d u1)) &
59 (b:B; u:T)(pr3 (CTail c (Bind b) u) t2 (lift h (S d) t1))
62 Pc3Unfold; Repeat Pr3Gen; Rewrite H1 in H; Clear H1 x.
63 LiftGenBase; Rewrite H in H3; Rewrite H1 in H4; Rewrite H2 in H5; XEAuto.
68 Tactic Definition Pc3Gen :=
70 | [H: (pc3 ?1 (TSort ?2) (TSort ?3)) |- ? ] ->
71 LApply (pc3_gen_sort ?1 ?2 ?3); [ Clear H; Intros | XAuto ]
72 | [ _: (pc3 ?1 (lift ?2 ?3 ?4) (lift ?2 ?3 ?5));
73 _: (drop ?2 ?3 ?1 ?6) |- ? ] ->
74 LApply (pc3_gen_lift ?1 ?4 ?5 ?2 ?3); [ Intros H_x | XAuto ];
75 LApply (H_x ?6); [ Clear H_x; Intros | XAuto ]
76 | [ H: (pc3 ?1 (TTail (Bind Abst) ?2 ?3) (TTail (Bind Abst) ?4 ?5)) |- ? ] ->
77 LApply (pc3_gen_abst ?1 ?2 ?4 ?3 ?5);[ Clear H; Intros H | XAuto ];
79 | [ H: (pc3 ?1 (TTail (Bind ?2) ?3 ?4) (TTail (Bind Abst) ?5 ?6));
80 _: ~ ?2 = Abst |- ? ] ->
81 LApply (pc3_gen_not_abst ?2); [ Intros H_x | XAuto ];
82 LApply (H_x ?1 ?4 ?6 ?3 ?5); [ Clear H H_x; Intros | XAuto ]
83 | [ _: (pc3 ?1 (lift ?2 ?3 ?4) (TTail (Bind Abst) ?5 ?6));
84 _: (drop ?2 ?3 ?1 ?7) |- ? ] ->
85 LApply (pc3_gen_lift_abst ?1 ?4 ?6 ?5 ?2 ?3); [ Intros H_x | XAuto ];
86 LApply (H_x ?7); [ Clear H_x; Intros H_x | XAuto ];