reserve m for Nat;
reserve P for Instruction-Sequence of SCM+FSA;

theorem Th7:
  for I,J being Program of SCM+FSA, x being set holds x in dom I
  implies (I ";" J).x = (Directed I).x
proof
  let I,J be Program of SCM+FSA;
  let x be set;
  assume x in dom I;
  then
A1: x in dom Directed I by FUNCT_4:99;
  Directed I c= I ";" J by SCMFSA6A:16;
  hence thesis by A1,GRFUNC_1:2;
end;
