
theorem Th21:
  for S1,S2 being unsplit gate`1=arity non empty ManySortedSign
for x being set st x in InnerVertices S1 holds x in InnerVertices (S1+*S2) & x
  in InnerVertices (S2+*S1)
proof
  let S1,S2 be unsplit gate`1=arity non empty ManySortedSign;
  S1 tolerates S2 by CIRCCOMB:47;
  then InnerVertices (S1+*S2) = InnerVertices S1 \/ InnerVertices S2 &
  InnerVertices (S2+*S1) = InnerVertices S2 \/ InnerVertices S1 by CIRCCOMB:11;
  hence thesis by XBOOLE_0:def 3;
end;
