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
  for I,J being Program of SCM+FSA holds I +* (I ";" J) = (I ";" J)
proof
  let I,J be Program of SCM+FSA;
A1: for x be object st x in dom (I ";" J)
    holds (I +* (I ";" J)).x = (I ";" J).x by FUNCT_4:13;
  dom (I +* (I ";" J)) = dom I \/ dom (I ";" J) by FUNCT_4:def 1
    .= dom (I ";" J) by Th7,XBOOLE_1:12;
  hence thesis by A1,FUNCT_1:2;
end;
