matita/contribs/LAMBDA-TYPES/Level-1/problems.ma

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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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 (* Problematic objects for disambiguation/typechecking ********************)
  16
  17 set "baseuri" "cic:/matita/LAMBDA-TYPES/Level-1/problems".
  18
  19 include "LambdaDelta/theory.ma".
  20
  21 (* Problem 1: disambiguation errors with these objects *)
  22
  23 (*  leq_trans (in problems-4)
  24  *)
  25
  26 (* Problem 2: assertion failure raised by type checker on this object *)
  27
  28 definition foo ≝
  29 \lambda g:G.\lambda c:C.\lambda t:T.
  30 \lambda P:T\to Prop.
  31 \lambda H:\forall t1:T.\forall H:tau0 g c t t1.P t1.
  32 \lambda H1:
  33  \forall t1:T.\forall H1:tau1 g c t t1.
  34   P t1 \to \forall t2:T.\forall H2:tau0 g c t1 t2.P t2.
  35  let rec f (t1:T) (H2:tau1 g c t t1) on H2 ≝
  36   match H2 return \lambda t2:T.\lambda H3:tau1 g c t t2.P t2 with
  37   [ tau1_tau0 => \lambda t2:T.\lambda H3:(tau0 g c t t2).H t2 H3
  38   | tau1_sing =>
  39      \lambda t2:T.\lambda H3:(tau1 g c t t2).\lambda t3:T.
  40       \lambda H4:tau0 g c t2 t3.H1 t2 H3 (f t2 H3) t3 H4
  41   ]
  42  in f.
  43
  44
  45 inductive tau1 (g:G) (c:C) (t1:T): T \to Prop \def
  46 | tau1_tau0: \forall (t2: T).((tau0 g c t1 t2) \to (tau1 g c t1 t2))
  47 | tau1_sing: \forall (t: T).((tau1 g c t1 t) \to (\forall (t2: T).((tau0 g c
  48 t t2) \to (tau1 g c t1 t2))))).