theorem Th77:
  Q is struct-invariant implies
  for p being Element of Args(o,Q) st
  for t being Element of Q st t in rng p holds t is y-omitting
  for t being Element of Q st t = Den(o,Q).p holds t is y-omitting
  proof assume ZZ: Q is struct-invariant;
    let p be Element of Args(o,Q);
    assume Z0: for t being Element of Q st t in rng p holds
    t is y-omitting;
    let t be Element of Q;
    assume t = Den(o,Q).p;
    then
A1: t = (canonical_homomorphism Q).(the_result_sort_of o).(Den(o,Free(S,Y)).p)
    by MSAFREE4:67;
    Args(o,Q) c= Args(o, Free(S,Y)) by MSAFREE4:41;
    then reconsider q = p as Element of Args(o,Free(S,Y));
A2: Den(o,Free(S,Y)).q = o-term q by MSAFREE4:13;
    now let v; assume
A5:   v in rng p;
      then reconsider d = v as Element of Q by RELAT_1:167;
      d is y-omitting by Z0,A5;
      hence v is y-omitting;
    end;
    then
A3: o-term q is y-omitting by Th54A;
    the_sort_of (o-term q) = the_result_sort_of o by Th8;
    then t = (canonical_homomorphism Q).(o-term q) by A1,A2,ABBR;
    hence thesis by ZZ,A3,Th68;
  end;
