reserve S for locally_directed OrderSortedSign;
reserve o for Element of the carrier' of S;

theorem
  for U1,U2 be non-empty OSAlgebra of S, F be ManySortedFunction of U1,
U2 st F is_epimorphism U1,U2 & F is order-sorted holds QuotOSAlg (U1,OSCng F),
  U2 are_isomorphic
proof
  let U1,U2 be non-empty OSAlgebra of S, F be ManySortedFunction of U1,U2;
  assume F is_epimorphism U1,U2 & F is order-sorted;
  then OSHomQuot(F) is_isomorphism QuotOSAlg (U1,OSCng F),U2 by Th18;
  hence thesis;
end;
