(* This file was automatically generated: do not edit *********************)
-include "LambdaDelta-1/pc1/defs.ma".
+include "Basic-1/pc1/defs.ma".
-include "LambdaDelta-1/pr1/pr1.ma".
+include "Basic-1/pr1/pr1.ma".
theorem pc1_pr0_r:
\forall (t1: T).(\forall (t2: T).((pr0 t1 t2) \to (pc1 t1 t2)))
\lambda (t1: T).(\lambda (t2: T).(\lambda (H: (pr0 t1 t2)).(ex_intro2 T
(\lambda (t: T).(pr1 t1 t)) (\lambda (t: T).(pr1 t2 t)) t2 (pr1_pr0 t1 t2 H)
(pr1_refl t2)))).
+(* COMMENTS
+Initial nodes: 43
+END *)
theorem pc1_pr0_x:
\forall (t1: T).(\forall (t2: T).((pr0 t2 t1) \to (pc1 t1 t2)))
\lambda (t1: T).(\lambda (t2: T).(\lambda (H: (pr0 t2 t1)).(ex_intro2 T
(\lambda (t: T).(pr1 t1 t)) (\lambda (t: T).(pr1 t2 t)) t1 (pr1_refl t1)
(pr1_pr0 t2 t1 H)))).
+(* COMMENTS
+Initial nodes: 43
+END *)
theorem pc1_refl:
\forall (t: T).(pc1 t t)
\def
\lambda (t: T).(ex_intro2 T (\lambda (t0: T).(pr1 t t0)) (\lambda (t0:
T).(pr1 t t0)) t (pr1_refl t) (pr1_refl t)).
+(* COMMENTS
+Initial nodes: 31
+END *)
theorem pc1_pr0_u:
\forall (t2: T).(\forall (t1: T).((pr0 t1 t2) \to (\forall (t3: T).((pc1 t2
T).(\lambda (H2: (pr1 t2 x)).(\lambda (H3: (pr1 t3 x)).(ex_intro2 T (\lambda
(t: T).(pr1 t1 t)) (\lambda (t: T).(pr1 t3 t)) x (pr1_sing t2 t1 H x H2)
H3)))) H1)))))).
+(* COMMENTS
+Initial nodes: 97
+END *)
theorem pc1_s:
\forall (t2: T).(\forall (t1: T).((pc1 t1 t2) \to (pc1 t2 t1)))
t1) (\lambda (x: T).(\lambda (H1: (pr1 t1 x)).(\lambda (H2: (pr1 t2
x)).(ex_intro2 T (\lambda (t: T).(pr1 t2 t)) (\lambda (t: T).(pr1 t1 t)) x H2
H1)))) H0)))).
+(* COMMENTS
+Initial nodes: 79
+END *)
theorem pc1_head_1:
\forall (u1: T).(\forall (u2: T).((pc1 u1 u2) \to (\forall (t: T).(\forall
(\lambda (t0: T).(pr1 (THead k u1 t) t0)) (\lambda (t0: T).(pr1 (THead k u2
t) t0)) (THead k x t) (pr1_head_1 u1 x H1 t k) (pr1_head_1 u2 x H2 t k)))))
H0)))))).
+(* COMMENTS
+Initial nodes: 133
+END *)
theorem pc1_head_2:
\forall (t1: T).(\forall (t2: T).((pc1 t1 t2) \to (\forall (u: T).(\forall
T).(\lambda (H1: (pr1 t1 x)).(\lambda (H2: (pr1 t2 x)).(ex_intro2 T (\lambda
(t: T).(pr1 (THead k u t1) t)) (\lambda (t: T).(pr1 (THead k u t2) t)) (THead
k u x) (pr1_head_2 t1 x H1 u k) (pr1_head_2 t2 x H2 u k))))) H0)))))).
+(* COMMENTS
+Initial nodes: 133
+END *)
theorem pc1_t:
\forall (t2: T).(\forall (t1: T).((pc1 t1 t2) \to (\forall (t3: T).((pc1 t2
x1)).(ex_intro2 T (\lambda (t: T).(pr1 t1 t)) (\lambda (t: T).(pr1 t3 t)) x1
(pr1_t x0 t1 H5 x1 H7) (pr1_t x t3 H3 x1 H8))))) (pr1_confluence t2 x0 H6 x
H2))))) H4))))) H1)))))).
+(* COMMENTS
+Initial nodes: 203
+END *)
theorem pc1_pr0_u2:
\forall (t0: T).(\forall (t1: T).((pr0 t0 t1) \to (\forall (t2: T).((pc1 t0
\def
\lambda (t0: T).(\lambda (t1: T).(\lambda (H: (pr0 t0 t1)).(\lambda (t2:
T).(\lambda (H0: (pc1 t0 t2)).(pc1_t t0 t1 (pc1_pr0_x t1 t0 H) t2 H0))))).
+(* COMMENTS
+Initial nodes: 35
+END *)
theorem pc1_head:
\forall (u1: T).(\forall (u2: T).((pc1 u1 u2) \to (\forall (t1: T).(\forall
T).(\lambda (t2: T).(\lambda (H0: (pc1 t1 t2)).(\lambda (k: K).(pc1_t (THead
k u2 t1) (THead k u1 t1) (pc1_head_1 u1 u2 H t1 k) (THead k u2 t2)
(pc1_head_2 t1 t2 H0 u2 k)))))))).
+(* COMMENTS
+Initial nodes: 71
+END *)