theorem Th30:
  B <> C implies A in the_altitude(A,B,C)
  proof
    assume B <> C;
    then consider L1,L2 be Element of line_of_REAL 2 such that
A1: the_altitude(A,B,C) = L1  and
    L2 = Line(B,C) and
A2: A in L1 and
    L1 _|_ L2 by Def1;
    thus thesis by A1,A2;
  end;
