theorem OMIT4:
  for S,X for B being non empty FinSequence of the carrier of S
  for D being B-sorts FinSequence of Free(S,X)
  for V being B-sorts FinSequence of Union X st V is D-omitting
  for b1,b2 being Element of dom B holds D.b1 is V.b2-omitting
  proof
    let S,X;
    let B be non empty FinSequence of the carrier of S;
    let D be B-sorts FinSequence of Free(S,X);
    let V be B-sorts FinSequence of Union X;
    assume Z0: V is D-omitting;
    let b1,b2 be Element of dom B;
    dom D = dom B & dom V = dom B by SORTS,SORTS2;
    then D.b1 in rng D & V.b2 in rng V by FUNCT_1:def 3;
    then V.b2 nin vf (D.b1) by Z0,XBOOLE_0:3;
    hence D.b1 is V.b2-omitting by Th92;
  end;
