helm/software/matita/tests/esempio_oliboni.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
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  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 CProp[1] < CProp[2].
  22 universe constraint Type[0] ≤ CProp[0].
  23 universe constraint CProp[0] ≤ Type[0].
  24 universe constraint Type[1] ≤ CProp[1].
  25 universe constraint CProp[1] ≤ Type[1].
  26 universe constraint Type[2] ≤ CProp[2].
  27 universe constraint CProp[2] ≤ Type[2].
  28
  29 ninductive A : Type[0] ≝
  30  | K : nat → A
  31  | W : nat → A.
  32
  33 nlet rec A_rect (Q_:∀x_3:A.Type[0]) H_K H_W x_3 on x_3 :Q_ x_3≝
  34 match x_3 with [K x_4⇒H_K x_4|W x_5⇒H_W x_5].
  35
  36 nlemma yy : ∀x,y. K x = W y → False.
  37 #x; #y; #H;
  38 nchange with
  39   (match K x return λ_.Prop with [ K _ ⇒ False | W _ ⇒ True]);
  40 nrewrite > H; nwhd; napply I;
  41 nqed.
  42
  43 nlemma xx : ∀x,y. K x = K y → x = y.
  44 # x; #y; #H;
  45 nchange with
  46   (match K x return λ_.Prop with [ K a ⇒ a = y | W b ⇒ b = y]);
  47 nrewrite > H; nwhd; napply (refl_eq ??);
  48 nqed.
  49
  50 naxiom P : Prop.
  51
  52 nlemma ww : ∀a,b:A. a = b → P.
  53 #a; #b;
  54 ncases a; ncases b;
  55 #x; #y; #H;
  56 ##[
  57
  58 ##| nelim (yy ?? H);
  59 ##| nelim (yy ?? H);
  60
  61 ##]
  62
  63
  64
  65