theorem Th10:
  ((qs, w)-response).1 = (the OFun of sfsm).qs
proof
  1 <= len w + 1 by NAT_1:12;
  then 1 in Seg (len w + 1) by FINSEQ_1:1;
  hence ((qs, w)-response).1 = (the OFun of sfsm).((qs, w)-admissible.1) by
Def7
    .= (the OFun of sfsm).qs by Def2;
end;
