reserve X for set, R,R1,R2 for Relation;
reserve x,y,z for set;
reserve n,m,k for Nat;

theorem Th18:
  iter(R,n).:X = {} & m >= n implies iter(R,m).:X = {}
  proof assume
A1: iter(R,n).:X = {} & m >= n; then
    consider k such that
A2: m = n+k by NAT_1:10;
    thus iter(R,m).:X = (iter(R,n)*iter(R,k)).:X by A2,FUNCT_7:77
    .= iter(R,k).:{} by A1,RELAT_1:126
    .= {};
  end;
