reserve a,a1,a2,a3,b,b1,b2,b3,r,s,t,u for Real;
reserve n for Nat;
reserve x0,x,x1,x2,x3,y0,y,y1,y2,y3 for Element of REAL n;
reserve L,L0,L1,L2 for Element of line_of_REAL n;

theorem
  for x,L st (not x in L) & L is being_line holds ex L0 st x in L0 & L0
  // L & L0 <> L
proof
  let x,L;
  assume that
A1: not x in L and
A2: L is being_line;
  ex L0 st x in L0 & L0 // L by A2,Th72;
  hence thesis by A1;
end;
