matitaB/matita/contribs/character/classes/defs.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 "preamble.ma".
  16
  17 (* NOTE: OEIS sequence identifiers
  18    P(n): A016777 "3n+1"
  19    T(n): A155504 "(3h+1)*3^(k+1)"
  20 *)
  21
  22 inductive P: nat → Prop ≝
  23    | p1: P 1
  24    | p2: ∀i,j. T i → P j → P (i + j)
  25 with T: nat → Prop ≝
  26    | t1: ∀i. P i → T (i * 3)
  27    | t2: ∀i. T i → T (i * 3)
  28 .
  29
  30 inductive S: nat → Prop ≝
  31    | s1: ∀i. P i → S (i * 2)
  32    | s2: ∀i. T i → S (i * 2)
  33 .