theorem Th71:
  r|= 'not' (H1 '&' H2) iff r |= ('not' H1) 'or' ('not' H2)
proof
  r|= 'not' (H1 '&' H2) iff r|/= H1 '&' H2 by Th64;
  then r|= 'not' (H1 '&' H2) iff not (r |= H1 & r |= H2) by Th65;
  then r|= 'not' (H1 '&' H2) iff (r |= 'not' H1 or r |= 'not' H2) by Th64;
  hence thesis by Th66;
end;
