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;
reserve P,P0,P1,P2 for Element of plane_of_REAL n;

theorem
  for L1,L2 st L1 is being_line & L2 is being_line & L1 <> L2 & L1 meets
  L2 holds ex P st L1 c= P & L2 c= P & P is being_plane
proof
  let L1,L2;
  assume that
A1: L1 is being_line and
A2: L2 is being_line and
A3: L1 <> L2 and
A4: L1 meets L2;
  consider x such that
A5: x in L1 and
A6: not x in L2 by A1,A2,A3,Th79;
A7: ex P st x in P & L2 c= P & P is being_plane by A2,A6,Th100;
  consider y such that
A8: y in L1 and
A9: y in L2 by A4,Th49;
  L1 = Line(x,y) by A1,A5,A6,A8,A9,Th30;
  hence thesis by A7,A9,Th95;
end;
