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 Th49:
  k + 1 > d implies for C being Chain of (k + 1),G holds del C = 0_(k,G)
proof
  assume
A1: k + 1 > d;
  let C be Chain of (k + 1),G;
  for A being object holds not A in del C by A1,Th48;
  hence thesis by XBOOLE_0:def 1;
end;
