reserve x,y for set;
reserve s,r for Real;
reserve r1,r2 for Real;
reserve n for Nat;
reserve p,q,q1,q2 for Point of TOP-REAL 2;

theorem
  for r being Real,p being Point of TOP-REAL 2 holds
  p in Horizontal_Line(r) iff p`2=r
proof
  let r be Real,p be Point of TOP-REAL 2;
  hereby
    assume p in Horizontal_Line(r);
    then ex q being Point of TOP-REAL 2 st q=p & q`2=r;
    hence p`2=r;
  end;
  assume p`2 = r;
  hence thesis;
end;
