reserve n for Nat;
reserve i for Integer;
reserve r,s,t for Real;
reserve An,Bn,Cn,Dn for Point of TOP-REAL n;
reserve L1,L2 for Element of line_of_REAL n;
reserve A,B,C for Point of TOP-REAL 2;
reserve D for Point of TOP-REAL 2;
reserve a,b,c,d for Real;

theorem Th31:
  B <> C implies the_altitude(A,B,C) is being_line
  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
    A in L1 and
A2: L1 _|_ L2 by Def1;
    thus thesis by A1,A2,EUCLIDLP:67;
  end;
