for i being Nat
for X0, Y0 being finite natural-membered set st X0 <N< Y0 & i < card X0 holds
( rng ((Sgm0 (X0 \/ Y0)) | (card X0)) = X0 & ((Sgm0 (X0 \/ Y0)) | (card X0)) . i = (Sgm0 (X0 \/ Y0)) . i )