reserve l, m, n for Nat,
  i,j,k for Instruction of SCM+FSA,
  I,J,K for Program of SCM+FSA;
reserve a,b for Int-Location,
  f for FinSeq-Location,
  s,s1,s2 for State of SCM+FSA;

theorem Th7:
  for I,J being Program of SCM+FSA holds dom I c= dom (I ";" J)
proof
  let I,J be Program of SCM+FSA;
A1: card stop I -' 1 = card I by COMPOS_1:71;
  card stop Directed I = card stop I by Lm2;
  then dom (I ";" J) = dom Directed I \/ dom Reloc(J,card I)
   by FUNCT_4:def 1,A1
    .= dom I \/ dom Reloc(J,card I) by FUNCT_4:99;
  hence thesis by XBOOLE_1:7;
end;
