theorem Th46:
  B <> C implies 0 <= the_length_of_the_altitude(A,B,C)
  proof
    assume B <> C;
    then the_length_of_the_altitude(A,B,C)
           = |.A-the_foot_of_the_altitude(A,B,C).| by Def3;
    hence thesis;
  end;
