reserve m,n for Nat,
  I for Program of SCM+FSA,
  s,s1,s2 for State of SCM+FSA,
  a for Int-Location,
  f for FinSeq-Location,
  p,p1,p2 for Instruction-Sequence of SCM+FSA;

theorem Th23:
  for I being Program of SCM+FSA holds I is InitHalting iff for s
  being State of SCM+FSA,p holds I is_halting_onInit s,p
proof
  let I be Program of SCM+FSA;
  hereby
    assume
A1: I is InitHalting;
    let s be State of SCM+FSA;
    let p;
A2:  I c= p+*I by FUNCT_4:25;
    iS c= Initialized s by FUNCT_4:25;
    then p+*I halts_on Initialized s by A2,A1;
    hence I is_halting_onInit s,p;
  end;
  assume
A3: for s being State of SCM+FSA,p holds I is_halting_onInit s,p;
  now
    let s be State of SCM+FSA;
    assume iS c= s;
    then
A4: s = Initialized s by FUNCT_4:98;
    let p;
    assume I c= p;
    then
A5:  p +* I = p by FUNCT_4:98;
    I is_halting_onInit s,p by A3;
    hence p halts_on s by A4,A5;
  end;
  hence thesis;
end;
