helm/software/matita/contribs/RELATIONAL/NLE/defs.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
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  13 (**************************************************************************)
  14
  15 set "baseuri" "cic:/matita/RELATIONAL/NLE/defs".
  16
  17 include "logic/equality.ma".
  18
  19 include "Nat/defs.ma".
  20
  21 inductive NLE: Nat \to Nat \to Prop \def
  22    | NLE_zero: \forall q. NLE zero q
  23    | NLE_succ: \forall p,q. NLE p q \to NLE (succ p) (succ q)
  24 .
  25
  26 (*CSC: the URI must disappear: there is a bug now *)
  27 interpretation "natural 'less or equal to'" 'leq x y =
  28    (cic:/matita/RELATIONAL/NLE/defs/NLE.ind#xpointer(1/1) x y).
  29
  30 (*CSC: the URI must disappear: there is a bug now *)
  31 interpretation "natural 'less than'" 'lt x y =
  32    (cic:/matita/RELATIONAL/NLE/defs/NLE.ind#xpointer(1/1)
  33       (cic:/matita/RELATIONAL/Nat/defs/Nat.ind#xpointer(1/1/2) x) y).