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;
