reserve x,y,z for set;
reserve f,f1,f2,f3 for FinSequence,
  p,p1,p2,p3 for set,
  i,k for Nat;

theorem Th32:
  <*z*>|--z = {} & <*z*>-|z = {}
proof
  z in { z } by TARSKI:def 1;
  then
A1: z in rng<*z*> by FINSEQ_1:39;
A2: z..<*z*> = 1 by Th18;
  len<*z*> = 1 by FINSEQ_1:39;
  hence <*z*>|--z = {} by A1,A2,FINSEQ_4:49;
  thus thesis by A1,A2,FINSEQ_4:40;
end;
