theorem Th70:
  r|= 'not' (H1 'or' H2) iff r |= ('not' H1) '&' ('not' H2)
proof
  r|= 'not' (H1 'or' H2) iff r|/= H1 'or' H2 by Th64;
  then r|= 'not' (H1 'or' H2) iff not (r |= H1 or r |= H2) by Th66;
  then r|= 'not' (H1 'or' H2) iff r |= 'not' H1 & r |= 'not' H2 by Th64;
  hence thesis by Th65;
end;
