reserve a,b,s,t,u,lambda for Real,
  n for Nat;
reserve x,x1,x2,x3,y1,y2 for Element of REAL n;

theorem :: AFF_1:30
  for A,C be Subset of REAL n,x1,x2 holds A is being_line & C is
  being_line & x1 in A & x2 in A & x1 in C & x2 in C implies x1=x2 or A=C
proof
  let A,C be Subset of REAL n;
  let x1,x2;
  assume that
A1: A is being_line and
A2: C is being_line and
A3: x1 in A & x2 in A and
A4: x1 in C & x2 in C;
  assume
A5: x1<>x2;
  then A = Line(x1,x2) by A1,A3,Lm3;
  hence thesis by A2,A4,A5,Lm3;
end;
