reserve X,x,y,z for set;
reserve n,m,k,k9,d9 for Nat;
reserve d for non zero Nat;
reserve i,i0,i1 for Element of Seg d;
reserve l,r,l9,r9,l99,r99,x,x9,l1,r1,l2,r2 for Element of REAL d;
reserve Gi for non trivial finite Subset of REAL;
reserve li,ri,li9,ri9,xi,xi9 for Real;
reserve G for Grating of d;

theorem Th59:
  for G being Grating of d9 + 1, C being Chain of (d9 + 1),G holds
  del C` = del C
proof
  let G be Grating of d9 + 1, C be Chain of (d9 + 1),G;
  thus del C` = del(C + Omega(G)) by Th55
    .= del C + del Omega(G) by Th58
    .= del C + 0_(d9,G) by Th57
    .= del C;
end;
