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
  k > d implies for C being Chain of k,G holds C is Cycle of k,G
proof
  assume
A1: k > d;
  let C be Chain of k,G;
  consider k9 being Nat such that
A2: k = k9 + 1 by A1,NAT_1:6;
  reconsider k9 as Element of NAT by ORDINAL1:def 12;
  reconsider C9 = C as Chain of (k9 + 1),G by A2;
  del C9 = 0_(k9,G) by A1,A2,Th49;
  hence thesis by A2,Def14;
end;
