(* This file was automatically generated: do not edit *********************)
-include "LambdaDelta-1/pc3/props.ma".
+include "Basic-1/pc3/props.ma".
theorem pc3_ind_left__pc3_left_pr3:
\forall (c: C).(\forall (t1: T).(\forall (t2: T).((pr3 c t1 t2) \to
(t: T).(pc3_left_r c t)) (\lambda (t0: T).(\lambda (t3: T).(\lambda (H0: (pr2
c t3 t0)).(\lambda (t4: T).(\lambda (_: (pr3 c t0 t4)).(\lambda (H2:
(pc3_left c t0 t4)).(pc3_left_ur c t3 t0 H0 t4 H2))))))) t1 t2 H)))).
+(* COMMENTS
+Initial nodes: 87
+END *)
theorem pc3_ind_left__pc3_left_trans:
\forall (c: C).(\forall (t1: T).(\forall (t2: T).((pc3_left c t1 t2) \to
(H2: ((\forall (t5: T).((pc3_left c t4 t5) \to (pc3_left c t0
t5))))).(\lambda (t5: T).(\lambda (H3: (pc3_left c t4 t5)).(pc3_left_ux c t0
t3 H0 t5 (H2 t5 H3)))))))))) t1 t2 H)))).
+(* COMMENTS
+Initial nodes: 195
+END *)
theorem pc3_ind_left__pc3_left_sym:
\forall (c: C).(\forall (t1: T).(\forall (t2: T).((pc3_left c t1 t2) \to
(_: (pc3_left c t0 t4)).(\lambda (H2: (pc3_left c t4
t0)).(pc3_ind_left__pc3_left_trans c t4 t0 H2 t3 (pc3_left_ur c t0 t3 H0 t3
(pc3_left_r c t3))))))))) t1 t2 H)))).
+(* COMMENTS
+Initial nodes: 163
+END *)
theorem pc3_ind_left__pc3_left_pc3:
\forall (c: C).(\forall (t1: T).(\forall (t2: T).((pc3 c t1 t2) \to
x)).(\lambda (H2: (pr3 c t2 x)).(pc3_ind_left__pc3_left_trans c t1 x
(pc3_ind_left__pc3_left_pr3 c t1 x H1) t2 (pc3_ind_left__pc3_left_sym c t2 x
(pc3_ind_left__pc3_left_pr3 c t2 x H2)))))) H0))))).
+(* COMMENTS
+Initial nodes: 105
+END *)
theorem pc3_ind_left__pc3_pc3_left:
\forall (c: C).(\forall (t1: T).(\forall (t2: T).((pc3_left c t1 t2) \to
T).(\lambda (t3: T).(\lambda (H0: (pr2 c t0 t3)).(\lambda (t4: T).(\lambda
(_: (pc3_left c t0 t4)).(\lambda (H2: (pc3 c t0 t4)).(pc3_t t0 c t3
(pc3_pr2_x c t3 t0 H0) t4 H2))))))) t1 t2 H)))).
+(* COMMENTS
+Initial nodes: 147
+END *)
theorem pc3_ind_left:
\forall (c: C).(\forall (P: ((T \to (T \to Prop)))).(((\forall (t: T).(P t
c t1 t3)).(\lambda (H5: (P t1 t3)).(H1 t1 t2 H3 t3
(pc3_ind_left__pc3_pc3_left c t1 t3 H4) H5))))))) t t0
(pc3_ind_left__pc3_left_pc3 c t t0 H2))))))))).
+(* COMMENTS
+Initial nodes: 225
+END *)