matita/matita/contribs/lambdadelta/basic_1/pr3/pr1.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 include "basic_1/pr3/defs.ma".
  18
  19 include "basic_1/pr1/fwd.ma".
  20
  21 lemma pr3_pr1:
  22  \forall (t1: T).(\forall (t2: T).((pr1 t1 t2) \to (\forall (c: C).(pr3 c t1
  23 t2))))
  24 \def
  25  \lambda (t1: T).(\lambda (t2: T).(\lambda (H: (pr1 t1 t2)).(pr1_ind (\lambda
  26 (t: T).(\lambda (t0: T).(\forall (c: C).(pr3 c t t0)))) (\lambda (t:
  27 T).(\lambda (c: C).(pr3_refl c t))) (\lambda (t0: T).(\lambda (t3:
  28 T).(\lambda (H0: (pr0 t3 t0)).(\lambda (t4: T).(\lambda (_: (pr1 t0
  29 t4)).(\lambda (H2: ((\forall (c: C).(pr3 c t0 t4)))).(\lambda (c:
  30 C).(pr3_sing c t0 t3 (pr2_free c t3 t0 H0) t4 (H2 c))))))))) t1 t2 H))).
  31