
theorem Th10:
  for A, B being Sequence st A^B is Ordinal-yielding
  holds A is Ordinal-yielding & B is Ordinal-yielding
proof
  let A, B be Sequence;
  assume A^B is Ordinal-yielding;
  then consider c being Ordinal such that
    A1: rng(A^B) c= c by ORDINAL2:def 4;
  rng A c= rng(A^B) by ORDINAL4:39;
  hence A is Ordinal-yielding by A1, XBOOLE_1:1, ORDINAL2:def 4;
  rng B c= rng(A^B) by ORDINAL4:40;
  hence B is Ordinal-yielding by A1, XBOOLE_1:1, ORDINAL2:def 4;
end;
