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 Th41:
  for I being Program of SCM+FSA holds I is InitHalting iff for s
  being State of SCM+FSA,p holds I is_halting_on Initialized s,p
proof
  let I be Program of SCM+FSA;
  thus I is InitHalting implies
  for s be State of SCM+FSA,p holds I is_halting_on Initialized s,p
    by Th23,Th27;
  assume for s being State of SCM+FSA,p holds I is_halting_on Initialized s,p;
  then for s be State of SCM+FSA,p holds I is_halting_onInit s,p by Th27;
  hence thesis by Th23;
