reserve Y for non empty set,
  G for Subset of PARTITIONS(Y),
  a,b,c,u for Function of Y,BOOLEAN,
  PA for a_partition of Y;

theorem
  All(a 'imp' b,PA,G) = 'not' (Ex(a '&' 'not' b,PA,G))
proof
  'not' All('not' a 'or' b,PA,G) = Ex('not' ('not' a 'or' b),PA,G) & 'not'
  ( 'not' a 'or' b)=('not' 'not' a) '&' ('not' b) by BVFUNC_1:13,BVFUNC_2:18;
  hence thesis by Th26;
end;
