reserve x for set,
  m,n for Nat,
  a,b for Int_position,
  i,j,k for Instruction of SCMPDS,
  s,s1,s2 for State of SCMPDS,
  k1,k2 for Integer,
  loc,l for Nat,
  I,J,K for Program of SCMPDS;

theorem
  for s being State of SCMPDS, i being Instruction of SCMPDS st InsCode
  i in {0,4,5,6,14} holds DataPart Exec(i,s) = DataPart s
proof
  let s be State of SCMPDS,i be Instruction of SCMPDS;
  assume
A1: InsCode i in {0,4,5,6,14};
  now
    let a be Int_position;
    per cases by A1,ENUMSET1:def 3;
    suppose
      InsCode i = 0;
      hence Exec(i,s).a = s.a by SCMPDS_2:86;
    end;
    suppose
      InsCode i = 14;
      then ex k1 st i = goto k1 by SCMPDS_2:26;
      hence Exec(i,s).a = s.a by SCMPDS_2:54;
    end;
    suppose
      InsCode i = 4;
      then ex b,k1,k2 st i = (b,k1)<>0_goto k2 by SCMPDS_2:30;
      hence Exec(i,s).a = s.a by SCMPDS_2:55;
    end;
    suppose
      InsCode i = 5;
      then ex b,k1,k2 st i = (b,k1)<=0_goto k2 by SCMPDS_2:31;
      hence Exec(i,s).a = s.a by SCMPDS_2:56;
    end;
    suppose
      InsCode i = 6;
      then ex b,k1,k2 st i = (b,k1)>=0_goto k2 by SCMPDS_2:32;
      hence Exec(i,s).a = s.a by SCMPDS_2:57;
    end;
  end;
  hence thesis by SCMPDS_4:8;
end;
