
theorem
  for n be Nat for x,y being FinSequence holds
  InnerVertices ((n+1)-BitGFA0Str(x,y)) = InnerVertices (n-BitGFA0Str(x,y)) \/
  InnerVertices BitGFA0Str(x .(n+1), y.(n+1), n-BitGFA0CarryOutput(x,y))
proof
  let n be Nat;
  let x,y be FinSequence;
  set Sn = n-BitGFA0Str(x,y);
  set SSn = BitGFA0Str(x .(n+1), y.(n+1), n-BitGFA0CarryOutput(x, y));
  InnerVertices (Sn +* SSn) = InnerVertices (Sn) \/ InnerVertices (SSn)
  by FACIRC_1:27;
  hence thesis by Th7;
end;
