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 Th14:
  for I,J being Program of SCM+FSA holds Directed (I ";" J) = I ";" Directed J
proof
  let I,J be Program of SCM+FSA;
A1: card stop I -' 1 = card I by COMPOS_1:71;
A2: card stop Directed I = card stop I by Lm2;
  hence I ";" Directed J
     = Directed I +*
        (Reloc(J,card I) +~ (halt SCM+FSA,goto(card J + card I))) by Th13,A1
    .= Directed I +*
        (Reloc(J,card I) +~ (halt SCM+FSA,goto(card(I ";" J)))) by Th11
    .= Directed I+~(halt SCM+FSA,goto card (I ";" J))+*
      (Reloc(J,card I)+~(halt SCM+FSA,goto card (I ";" J))) by FUNCT_4:127
    .= Directed (I ";" J) by FUNCT_7:117,A1,A2;
end;
