reserve AS for AffinSpace;
reserve a,a9,b,b9,c,d,o,p,q,r,s,x,y,z,t,u,w for Element of AS;
reserve A,C,D,K for Subset of AS;
reserve AP for AffinPlane;
reserve a,b,c,d,x,p,q for Element of AP;
reserve A,C for Subset of AP;

theorem
  not a,b // c,d implies ex p st LIN a,b,p & LIN c,d,p
proof
  assume not a,b // c,d;
  then consider p such that
A1: a,b // a,p and
A2: c,d // c,p by DIRAF:46;
A3: LIN c,d,p by A2;
  LIN a,b,p by A1;
  hence thesis by A3;
end;
