include "basic_1/pc3/props.ma".
-theorem pc3_gen_sort:
+lemma pc3_gen_sort:
\forall (c: C).(\forall (m: nat).(\forall (n: nat).((pc3 c (TSort m) (TSort
n)) \to (eq nat m n))))
\def
\Rightarrow m | (THead _ _ _) \Rightarrow m])) (TSort m) (TSort n) H3) in
H4))))) H0))))).
-theorem pc3_gen_abst:
+lemma pc3_gen_abst:
\forall (c: C).(\forall (u1: T).(\forall (u2: T).(\forall (t1: T).(\forall
(t2: T).((pc3 c (THead (Bind Abst) u1 t1) (THead (Bind Abst) u2 t2)) \to
(land (pc3 c u1 u2) (\forall (b: B).(\forall (u: T).(pc3 (CHead c (Bind b) u)
(CHead c (Bind b) u) t1 x1 (H15 b u) t2 (H6 b u))))))))) H12))))))))
H7))))))) H3))))) H0))))))).
-theorem pc3_gen_abst_shift:
+lemma pc3_gen_abst_shift:
\forall (c: C).(\forall (u: T).(\forall (t1: T).(\forall (t2: T).((pc3 c
(THead (Bind Abst) u t1) (THead (Bind Abst) u t2)) \to (pc3 (CHead c (Bind
Abst) u) t1 t2)))))
((\forall (b: B).(\forall (u0: T).(pc3 (CHead c (Bind b) u0) t1 t2))))).(H2
Abst u))) H0))))))).
-theorem pc3_gen_lift:
+lemma pc3_gen_lift:
\forall (c: C).(\forall (t1: T).(\forall (t2: T).(\forall (h: nat).(\forall
(d: nat).((pc3 c (lift h d t1) (lift h d t2)) \to (\forall (e: C).((drop h d
c e) \to (pc3 e t1 t2))))))))
(\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))))))))).
-theorem pc3_gen_not_abst:
+lemma pc3_gen_not_abst:
\forall (b: B).((not (eq B b Abst)) \to (\forall (c: C).(\forall (t1:
T).(\forall (t2: T).(\forall (u1: T).(\forall (u2: T).((pc3 c (THead (Bind b)
u1 t1) (THead (Bind Abst) u2 t2)) \to (pc3 (CHead c (Bind b) u1) t1 (lift (S
t2) (THead (Bind Abst) x0 x1) (pr3_head_12 c u2 x0 H8 (Bind Abst) t2 x1 (H9
Abst x0)))))))))) H6))) H4))))) H1))))))))) b).
-theorem pc3_gen_lift_abst:
+lemma pc3_gen_lift_abst:
\forall (c: C).(\forall (t: T).(\forall (t2: T).(\forall (u2: T).(\forall
(h: nat).(\forall (d: nat).((pc3 c (lift h d t) (THead (Bind Abst) u2 t2))
\to (\forall (e: C).((drop h d c e) \to (ex3_2 T T (\lambda (u1: T).(\lambda
t2 (lift h (S d) t1)))))) x3 x4 H17 H16 H15))))))))) (lift_gen_bind Abst x1
x2 x0 h d H11)))))))) H7))))) H4))))) H1)))))))))).
-theorem pc3_gen_sort_abst:
+lemma pc3_gen_sort_abst:
\forall (c: C).(\forall (u: T).(\forall (t: T).(\forall (n: nat).((pc3 c
(TSort n) (THead (Bind Abst) u t)) \to (\forall (P: Prop).P)))))
\def