reserve x,y,z for set,
  k for Nat;
reserve J,J1,K for Element of Segm 13,
  a for Nat,
  b,b1,b2,c,c1,c2 for Element of SCM+FSA-Data-Loc,
  f,f1,f2 for Element of SCM+FSA-Data*-Loc;

theorem Th4:
  (SCM*-VAL*SCM+FSA-OK).NAT = NAT
proof
A1: SCM+FSA-OK.NAT = 0 by Lm4;
  thus (SCM*-VAL*SCM+FSA-OK).NAT
     = SCM*-VAL.(SCM+FSA-OK.NAT) by Lm3,FUNCT_1:13
    .= NAT by A1;
end;
