matita/matita/contribs/limits/u0_predicates.ma

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   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                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "preamble.ma".
  16
  17 (* RELATIONS **********************************************************)
  18
  19 definition u0_predicate1: Type[0] → Type[1] ≝ λT.T → Prop.
  20
  21 definition u0_predicate2: Type[0] → Type[1] ≝ λT.T → u0_predicate1 T.
  22
  23 definition u1_predicate1: Type[1] → Type[2] ≝ λT.T → Prop.
  24
  25 definition u0_quantifier: Type[0] → Type[2] ≝ λT. u1_predicate1 (u0_predicate1 T).
  26
  27 record is_u0_reflexive (T:Type[0]) (All:u0_quantifier T) (R:u0_predicate2 T): Prop ≝
  28 {
  29    u0_refl: All (λa. R a a)
  30 }.
  31
  32 record can_u0_replace1 (T:Type[0]) (All:u0_quantifier T) (Q:u0_predicate2 T) (R:u0_predicate1 T): Prop ≝
  33 {
  34    u0_repl1: All (λa. R a → All (λb. Q b a → R b))
  35 }.
  36 (*
  37 record can_u0_replac2 (T:Type[0]) (All:u0_quantifier T) (Q:u0_predicate2 T) (R:u0_predicate2 T): Prop ≝
  38 {
  39    u0_reflexivity: All (λa. R a a)
  40 }.
  41 *)