theorem
  t<>0 implies t(.)(X (O) Y) = t(.)X (O) t(.)Y
proof
  assume
A1: t<>0;
  t(.)(X (O) Y) =t(.)(X (-) Y) (+) t(.)Y by Th63
    .=t(.)X (-) t(.)Y (+) t(.)Y by A1,Th64;
  hence thesis;
end;
