reserve a,a1,a2,v,v1,v2,x for object;
reserve V,A for set;
reserve m,n for Nat;
reserve S,S1,S2 for FinSequence;

theorem Th8:
  for f,g being finite Function holds
  f tolerates g & f in NDSS(V,A) & g in NDSS(V,A) implies
  f \/ g in NDSS(V,A)
  proof
    let f,g be finite Function;
    assume
A1: f tolerates g;
    assume f in NDSS(V,A) & g in NDSS(V,A);
    then f is NominativeSet of V,A & g is NominativeSet of V,A by Th4;
    then f \/ g is V-defined A-valued;
    then f \/ g is PartFunc of V,A by A1,RELSET_1:4,PARTFUN1:51;
    hence f \/ g in NDSS(V,A);
  end;
