let k be Element of NAT ; :: thesis: for d being non zero Element of NAT
for G being Grating of d holds del (0_ ((k + 1),G)) = 0_ (k,G)
let d be non zero Element of NAT ; :: thesis: for G being Grating of d holds del (0_ ((k + 1),G)) = 0_ (k,G)
let G be Grating of d; :: thesis: del (0_ ((k + 1),G)) = 0_ (k,G)

now

let A be Cell of k,G; :: thesis: ( A in del (0_ ((k + 1),G)) iff A in 0_ (k,G) )
card ((star A) /\ (0_ ((k + 1),G))) = 2 * 0 ;
hence ( A in del (0_ ((k + 1),G)) iff A in 0_ (k,G) ) by Th52; :: thesis: verum

end;

hence del (0_ ((k + 1),G)) = 0_ (k,G) by SUBSET_1:3; :: thesis: verum