reserve x,y,z for set;
reserve I,J,K for Element of Segm 9,
  i,a,a1,a2 for Nat,
  b,b1,b2,c,c1 for Element of SCM-Data-Loc;

theorem Th1:
   (SCM-VAL*SCM-OK).NAT = NAT
proof
   NAT in dom SCM-OK by Lm3,PARTFUN1:def 2;
   then
A1: (SCM-VAL*SCM-OK).NAT = SCM-VAL.(SCM-OK.NAT) by FUNCT_1:13;
   (SCM-VAL*SCM-OK).NAT = SCM-VAL.0 by A1,Def2,Lm3;
  hence thesis;
end;
