(* This file was automatically generated: do not edit *********************)
-include "Basic-1/pr3/defs.ma".
+include "basic_1/pr3/defs.ma".
-include "Basic-1/pr1/defs.ma".
+include "basic_1/pr1/fwd.ma".
theorem pr3_pr1:
\forall (t1: T).(\forall (t2: T).((pr1 t1 t2) \to (\forall (c: C).(pr3 c t1
t2))))
\def
- \lambda (t1: T).(\lambda (t2: T).(\lambda (H: (pr1 t1 t2)).(pr1_ind (\lambda
-(t: T).(\lambda (t0: T).(\forall (c: C).(pr3 c t t0)))) (\lambda (t:
-T).(\lambda (c: C).(pr3_refl c t))) (\lambda (t0: T).(\lambda (t3:
-T).(\lambda (H0: (pr0 t3 t0)).(\lambda (t4: T).(\lambda (_: (pr1 t0
-t4)).(\lambda (H2: ((\forall (c: C).(pr3 c t0 t4)))).(\lambda (c:
-C).(pr3_sing c t0 t3 (pr2_free c t3 t0 H0) t4 (H2 c))))))))) t1 t2 H))).
-(* COMMENTS
-Initial nodes: 95
-END *)
+ \lambda (t1: T).(\lambda (t2: T).(\lambda (H: (pr1 t1 t2)).(let TMP_1 \def
+(\lambda (t: T).(\lambda (t0: T).(\forall (c: C).(pr3 c t t0)))) in (let
+TMP_2 \def (\lambda (t: T).(\lambda (c: C).(pr3_refl c t))) in (let TMP_5
+\def (\lambda (t0: T).(\lambda (t3: T).(\lambda (H0: (pr0 t3 t0)).(\lambda
+(t4: T).(\lambda (_: (pr1 t0 t4)).(\lambda (H2: ((\forall (c: C).(pr3 c t0
+t4)))).(\lambda (c: C).(let TMP_3 \def (pr2_free c t3 t0 H0) in (let TMP_4
+\def (H2 c) in (pr3_sing c t0 t3 TMP_3 t4 TMP_4)))))))))) in (pr1_ind TMP_1
+TMP_2 TMP_5 t1 t2 H)))))).