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 Th49:
  L1 meets L2 iff ex x st x in L1 & x in L2
proof
  thus L1 meets L2 implies ex x st x in L1 & x in L2
  proof
    assume L1 meets L2;
    then consider x being object such that
A1: x in L1 and
A2: x in L2 by XBOOLE_0:3;
    reconsider x as Element of REAL n by A1;
    take x;
    thus thesis by A1,A2;
  end;
  thus thesis by XBOOLE_0:3;
end;
