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 Th13: ::AFF_1:31
  for A be Subset of REAL n st A is being_line holds ex x1,x2 st
  x1 in A & x2 in A & x1<>x2
proof
  let A be Subset of REAL n;
  assume A is being_line;
  then consider x1,x2 such that
A1: x1<>x2 and
A2: A = Line(x1,x2);
  x1 in A & x2 in A by A2,Th9;
  hence thesis by A1;
end;
