theorem Th72:
  r|= H1 'R' H2 iff r |= 'not' ( ('not' H1) 'U' ('not' H2))
proof
  set H01= Evaluate(H1,AtomicKai);
  set H02= Evaluate(H2,AtomicKai);
  set nH1= 'not' H1;
  set nH2= 'not' H2;
  r|= H1 'R' H2 iff r|= H01 'R' H02 by Th55;
  then
A1: r|= H1 'R' H2 iff r |= 'not' ( ('not' H01) 'U' ('not' H02)) by Def55;
  'not' H01 = Evaluate(nH1,AtomicKai) & 'not' H02 = Evaluate(nH2,AtomicKai
  ) by Th50;
  then r |= nH1 'U' nH2 iff r |= 'not' H01 'U' 'not' H02 by Th54;
  hence thesis by A1,Th57,Th64;
end;
