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;

theorem Th30:
  for A be Subset of REAL n,x1,x2 holds A is being_line & x1 in A
  & x2 in A & x1<>x2 implies A=Line(x1,x2)
proof
  let A be Subset of REAL n;
  let x1,x2;
  assume that
A1: A is being_line and
A2: x1 in A & x2 in A & x1<>x2;
  ex y1,y2 st y1<>y2 & A=Line(y1,y2) by A1;
  then Line(x1,x2) c= A & A c= Line(x1,x2) by A2,EUCLID_4:10,11;
  hence thesis by XBOOLE_0:def 10;
end;
