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 Th44:
  A,B,C is_a_triangle implies A <> the_foot_of_the_altitude(A,B,C)
  proof
    assume
A1: A,B,C is_a_triangle;
    assume
A2: A = the_foot_of_the_altitude(A,B,C);
A3: A,B,C are_mutually_distinct by A1,EUCLID_6:20;
    then A in Line(B,C) by A2,Th35;
    hence contradiction by A1,A3,MENELAUS:13;
  end;
