reserve a,b,s,t,u,lambda for Real,
  n for Nat;
reserve x,x1,x2,x3,y1,y2 for Element of REAL n;
reserve p1,p2,q1,q2 for Point of TOP-REAL n;

theorem :: AFF_1:30
  for A,C being Subset of TOP-REAL n holds A is being_line & C is
  being_line & p1 in A & p2 in A & p1 in C & p2 in C implies p1=p2 or A=C
proof
  let A,C be Subset of TOP-REAL n;
  assume that
A1: A is being_line and
A2: C is being_line and
A3: p1 in A & p2 in A and
A4: p1 in C & p2 in C;
  assume
A5: p1<>p2;
  then A = Line(p1,p2) by A1,A3,Lm9;
  hence thesis by A2,A4,A5,Lm9;
end;
