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_1:32
  for A be Subset of REAL n st A is being_line holds ex x2 st x1<>x2 & x2 in A
proof
  let A be Subset of REAL n;
  assume A is being_line;
  then consider y1,y2 such that
A1: y1 in A and
A2: y2 in A & y1<>y2 by Th13;
  x1 = y1 implies x1<>y2 & y2 in A by A2;
  hence thesis by A1;
end;
