
theorem
  for A,B,C be Point of TOP-REAL 2 st
  A,B,C is_a_triangle & angle(B,A,C) = PI/2 holds
    angle(C,B,A) + angle(A,C,B) = PI/2
  proof
    let A,B,C be Point of TOP-REAL 2 such that
A1: A,B,C is_a_triangle and
A2: angle(B,A,C) = PI/2;
A3: A,B,C are_mutually_distinct by A1,EUCLID_6:20;
    angle(B,A,C)+angle(A,C,B)+angle(C,B,A)=PI by A2,COMPTRIG:5,A3,EUCLID_3:47;
    hence thesis by A2;
  end;
