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 Th96:
  L1,L2 are_coplane iff ex P st L1 c= P & L2 c= P
proof
  thus L1,L2 are_coplane implies ex P st L1 c= P & L2 c= P
  proof
    assume L1,L2 are_coplane;
    then consider x1,x2,x3 being Element of REAL n such that
A1: L1 c= plane(x1,x2,x3) & L2 c= plane(x1,x2,x3);
    set P = plane(x1,x2,x3);
    take P;
    thus thesis by A1,Th90;
  end;
  now
    assume ex P st L1 c= P & L2 c= P;
    then consider P such that
A2: L1 c= P & L2 c= P;
    P in plane_of_REAL n;
    then ex P9 being Subset of REAL n st P = P9 & ex x1,x2,x3 being Element of
    REAL n st P9 = plane(x1,x2,x3);
    hence L1,L2 are_coplane by A2;
  end;
  hence thesis;
end;
