matita/contribs/LOGIC/PRed/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 set "baseuri" "cic:/matita/LOGIC/PRed/defs".
  16
  17 (* SINGLE STEP PARALLEL REDUCTION
  18    For cut elimination
  19 *)
  20
  21 include "datatypes/Proof.ma".
  22
  23 inductive PRed: Proof \to Proof \to Prop \def
  24    | pred_lref: \forall i. PRed (lref i) (lref i)
  25    | pred_parx: \forall h. PRed (parx h) (parx h)
  26    | pred_impw: \forall p1,p2. PRed p1 p2 \to PRed (impw p1) (impw p2)
  27    | pred_impr: \forall p1,p2. PRed p1 p2 \to PRed (impr p1) (impr p2)
  28    | pred_impi: \forall p1,p2. PRed p1 p2 \to \forall q1,q2. PRed q1 q2 \to
  29                 \forall r1,r2. PRed r1 r2 \to
  30                 PRed (impi p1 q1 r1) (impi p2 q2 r2)
  31    | pred_scut: \forall p1,p2. PRed p1 p2 \to \forall q1,q2. PRed q1 q2 \to
  32                 PRed (scut p1 q1) (scut p2 q2)
  33 .
  34
  35 (*CSC: the URI must disappear: there is a bug now *)
  36 interpretation
  37    "single step parallel reduction in B->"
  38    'parred x y = (cic:/matita/LOGIC/PRed/defs/PRed.ind#xpointer(1/1) x y)
  39 .