matita/matita/tests/esempio_oliboni.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 "logic/equality.ma".
  16 include "nat/nat.ma".
  17
  18 universe constraint Type[0] < Type[1].
  19 universe constraint Type[1] < Type[2].
  20 universe constraint CProp[0] < CProp[1].
  21 universe constraint Type[0] ≤ CProp[0].
  22 universe constraint CProp[0] ≤ Type[0].
  23 universe constraint Type[1] ≤ CProp[1].
  24 universe constraint CProp[1] ≤ Type[1].
  25
  26 ninductive A : Type[0] ≝
  27  | K : nat → A
  28  | W : nat → A.
  29
  30 nlet rec A_rect (Q_:∀x_3:A.Type[0]) H_K H_W x_3 on x_3 :Q_ x_3≝
  31 match x_3 with [K x_4⇒H_K x_4|W x_5⇒H_W x_5].
  32
  33 nlemma yy : ∀x,y. K x = W y → False.
  34 #x; #y; #H;
  35 nchange with
  36   (match K x return λ_.Prop with [ K _ ⇒ False | W _ ⇒ True]);
  37 nrewrite > H; nwhd; napply I;
  38 nqed.
  39
  40 nlemma xx : ∀x,y. K x = K y → x = y.
  41 # x; #y; #H;
  42 nchange with
  43   (match K x return λ_.Prop with [ K a ⇒ a = y | W b ⇒ b = y]);
  44 nrewrite > H; nwhd; napply (refl_eq ??);
  45 nqed.
  46
  47 naxiom P : Prop.
  48
  49 nlemma ww : ∀a,b:A. a = b → P.
  50 #a; #b;
  51 ncases a; ncases b;
  52 #x; #y; #H;
  53 ##[
  54
  55 ##| nelim (yy ?? H);
  56 ##| nelim (yy ?? H);
  57
  58 ##]
  59
  60
  61
  62