reserve n,m,k,k1,k2,i,j for Nat;
reserve x,y,z for object,X,Y,Z for set;
reserve A for Subset of X;
reserve B,A1,A2,A3 for SetSequence of X;
reserve Si for SigmaField of X;
reserve S,S1,S2,S3 for SetSequence of Si;

theorem Th1:
  for f be sequence of Y
   holds f.(n + m) in {f.k: n <= k}
proof
  n <= n + m by NAT_1:11;
  hence thesis;
end;
