theorem Th15:
  tfsm1, tfsm2-are_equivalent & tfsm2, tfsm3-are_equivalent
  implies tfsm1, tfsm3-are_equivalent
proof
  assume that
A1: tfsm1, tfsm2-are_equivalent and
A2: tfsm2, tfsm3-are_equivalent;
  let w1 be FinSequence of IAlph;
  set IS3 = the InitS of tfsm3;
  set IS1 = the InitS of tfsm1, IS2 = the InitS of tfsm2;
  thus (IS1, w1)-response = (IS2, w1)-response by A1
    .= (IS3, w1)-response by A2;
end;
