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 Th53:
  L is being_line implies ex x1 st x1 <> x0 & x1 in L
proof
  assume L is being_line;
  then consider y1,y2 such that
A1: y1 in L and
A2: y2 in L & y1 <> y2 by EUCLID_4:13;
  now
    per cases;
    case
A3:   y1 = x0;
      take y2;
      thus y2 <> x0 & y2 in L by A2,A3;
    end;
    case
A4:   y1 <> x0;
      take y1;
      thus y1 <> x0 & y1 in L by A1,A4;
    end;
  end;
  hence thesis;
end;
