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

theorem
  for i being Instruction of SCM+FSA holds (Directed Macro i). 1 = goto  2
proof
  let i be Instruction of SCM+FSA;
A1: (Macro i). 1 = halt SCM+FSA by COMPOS_1:59;
   1 in { 0, 1} by TARSKI:def 2;
  then
A2:  1 in dom Macro i by COMPOS_1:61;
A3: halt SCM+FSA in dom (halt SCM+FSA .--> goto  2) by TARSKI:def 1;
A4: dom id the InstructionsF of SCM+FSA = the InstructionsF of SCM+FSA;
  card Macro i = 2 & rng Macro i c= the InstructionsF of SCM+FSA
   by COMPOS_1:56,RELAT_1:def 19;
  hence (Directed Macro i). 1 = (((id the InstructionsF of SCM+FSA) +* (
  halt SCM+FSA,goto  2))* Macro i). 1 by FUNCT_7:116
    .= (((id the InstructionsF of SCM+FSA) +* (halt SCM+FSA .--> goto
  2))* Macro i). 1 by A4,FUNCT_7:def 3
    .= ((id the InstructionsF of SCM+FSA) +* (halt SCM+FSA .--> goto  2
  )). halt SCM+FSA by A2,A1,FUNCT_1:13
    .= (halt SCM+FSA .--> goto  2).halt SCM+FSA by A3,FUNCT_4:13
    .= goto  2 by FUNCOP_1:72;
end;
