
theorem Th47: :: Lemma 4.51
  for R, S being non empty RelStr st R is Dickson & S is quasi_ordered &
  the InternalRel of R c= the InternalRel of S &
  (the carrier of R) = (the carrier of S) holds S\~ is well_founded
proof
  let R, S be non empty RelStr such that
A1: R is Dickson and
A2: S is quasi_ordered and
A3: the InternalRel of R c= the InternalRel of S and
A4: the carrier of R = the carrier of S;
  S is Dickson by A1,A3,A4,Th27;
  hence thesis by A2,Th32;
end;
