(* This file was automatically generated: do not edit *********************)
-include "LambdaDelta-1/pc3/props.ma".
+include "Basic-1/pc3/props.ma".
-include "LambdaDelta-1/pr3/fwd.ma".
+include "Basic-1/pr3/fwd.ma".
theorem pc3_gen_sort:
\forall (c: C).(\forall (m: nat).(\forall (n: nat).((pc3 c (TSort m) (TSort
(\lambda (e: T).(match e in T return (\lambda (_: T).nat) with [(TSort n0)
\Rightarrow n0 | (TLRef _) \Rightarrow m | (THead _ _ _) \Rightarrow m]))
(TSort m) (TSort n) H3) in H4))))) H0))))).
+(* COMMENTS
+Initial nodes: 153
+END *)
theorem pc3_gen_abst:
\forall (c: C).(\forall (u1: T).(\forall (u2: T).(\forall (t1: T).(\forall
B).(\forall (u: T).(pc3 (CHead c (Bind b) u) t1 t2))) (pc3_pr3_t c u1 x0 H16
u2 H5) (\lambda (b: B).(\lambda (u: T).(pc3_pr3_t (CHead c (Bind b) u) t1 x1
(H15 b u) t2 (H6 b u))))))))) H12)))))))) H7))))))) H3))))) H0))))))).
+(* COMMENTS
+Initial nodes: 715
+END *)
theorem pc3_gen_abst_shift:
\forall (c: C).(\forall (u: T).(\forall (t1: T).(\forall (t2: T).((pc3 c
(CHead c (Bind Abst) u) t1 t2) (\lambda (_: (pc3 c u u)).(\lambda (H2:
((\forall (b: B).(\forall (u0: T).(pc3 (CHead c (Bind b) u0) t1 t2))))).(H2
Abst u))) H0))))))).
+(* COMMENTS
+Initial nodes: 129
+END *)
theorem pc3_gen_lift:
\forall (c: C).(\forall (t1: T).(\forall (t2: T).(\forall (h: nat).(\forall
T).(eq T t (lift h d x0))) H5 (lift h d x1) H8) in (let H11 \def (eq_ind T x1
(\lambda (t: T).(pr3 e t1 t)) H9 x0 (lift_inj x1 x0 h d H10)) in (pc3_pr3_t e
t1 x0 H11 t2 H6)))))) H7))))) H4))))) H1))))))))).
+(* COMMENTS
+Initial nodes: 363
+END *)
theorem pc3_gen_not_abst:
\forall (b: B).((not (eq B b Abst)) \to (\forall (c: C).(\forall (t1:
Void) O c c (drop_refl c) u1) (THead (Bind Abst) u2 t2) (THead (Bind Abst) x0
x1) (pr3_head_12 c u2 x0 H8 (Bind Abst) t2 x1 (H9 Abst x0)))))))))) H6)))
H4))))) H1))))))))) b).
+(* COMMENTS
+Initial nodes: 2427
+END *)
theorem pc3_gen_lift_abst:
\forall (c: C).(\forall (t: T).(\forall (t2: T).(\forall (u2: T).(\forall
T).(\lambda (t1: T).(\forall (b: B).(\forall (u: T).(pr3 (CHead c (Bind b) u)
t2 (lift h (S d) t1)))))) x3 x4 H17 H16 H15))))))))) (lift_gen_bind Abst x1
x2 x0 h d H11)))))))) H7))))) H4))))) H1)))))))))).
+(* COMMENTS
+Initial nodes: 973
+END *)
theorem pc3_gen_sort_abst:
\forall (c: C).(\forall (u: T).(\forall (t: T).(\forall (n: nat).((pc3 c
(_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False
| (THead _ _ _) \Rightarrow True])) I (TSort n) H7) in (False_ind P
H8)))))))) H3))))) H0))))))).
+(* COMMENTS
+Initial nodes: 303
+END *)