reserve x,y for set;
reserve N for PT_net_Str;

theorem Th21:
  for N being Pnet for x being Element of Elements(N) for X being
  set holds Elements(N) <> {} & x in X implies enter(N,x) in Entr(N,X)
proof
  let N be Pnet;
  let x be Element of Elements(N);
  let X be set;
  assume that
A1: Elements(N) <> {} and
A2: x in X;
  enter(N,x) c= Elements N by A1,Th16;
  hence thesis by A2,Def13;
end;
