theorem
  <*p*>:-p = <*p*> & <*p*>-:p = <*p*>
proof
  p in { p } by TARSKI:def 1;
  then
A1: p in rng<*p*> by FINSEQ_1:39;
  hence <*p*>:-p = <*p*>^(<*p*>|--p )by Th41
    .= <*p*>^{} by Th32
    .= <*p*> by FINSEQ_1:34;
  thus <*p*>-:p = (<*p*>-|p)^<*p*> by A1,Th40
    .= {}^<*p*> by Th32
    .= <*p*> by FINSEQ_1:34;
end;
