theorem Th35:
  B*^A c= C*^A & A <> {} implies B c= C
proof
  assume
A1: B*^A c= C*^A;
  B*^A c= C*^A & B*^A <> C*^A iff B*^A c< C*^A;
  then (A <> {} implies B = C) or B in C by A1,Th33,Th34,ORDINAL1:11;
  hence thesis by ORDINAL1:def 2;
end;
