
theorem Th6:
  for S1,S2 being unsplit gate`1=arity non empty ManySortedSign st
  InputVertices S1 is without_pairs & InnerVertices S2 is Relation holds
  InputVertices S1 c= InputVertices (S1+*S2) & InputVertices (S1+*S2) = (
  InputVertices S1) \/ (InputVertices S2 \ InnerVertices S1)
proof
  let S1,S2 be unsplit gate`1=arity non empty ManySortedSign;
  assume InputVertices S1 is without_pairs & InnerVertices S2 is Relation;
  then S1 tolerates S2 & InnerVertices S2 misses InputVertices S1 by
CIRCCOMB:47;
  hence thesis by Th4;
end;
