matita/matita/contribs/limits/u0_exp.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "u0_class.ma".
  16
  17 (* EXPONENTIAL CLASS **************************************************)
  18
  19 definition u0_exp_eq (D,C): u0_predicate2 (u0_fun D C) ≝
  20                      λf,g. (u0_xeq … (u0_class_in D) … (u0_class_eq C) f g).
  21
  22 definition u0_exp (D,C): u0_class ≝
  23                   mk_u0_class (u0_fun D C) (is_u0_fun …) (u0_exp_eq D C).
  24
  25 definition u0_proj1 (D1,D2): u0_fun D1 (u0_exp D2 D1) ≝
  26                     mk_u0_fun … (λa. mk_u0_fun … (u0_k … a)).
  27
  28 (* Basic properties ***************************************************)
  29
  30 lemma u0_class_exp: ∀D,C. is_u0_class C → is_u0_class (u0_exp D C).
  31 /4 width=7 by mk_is_u0_class, u0_class_refl, u0_class_repl, u0_fun_hom1/ qed.
  32
  33 lemma u0_fun_proj1: ∀D2,D1. is_u0_class D1 → is_u0_fun … (u0_proj1 D1 D2).
  34 #D2 #D1 #HD1 @mk_is_u0_fun /3 width=1 by mk_is_u0_fun, u0_class_refl/
  35 qed.