theorem
  (CX is negation_faithful & CX is with_examples implies
  (JH,valH(Al) |= p iff CX |- p)) implies
  (CX is negation_faithful & CX is with_examples implies
  (JH,valH(Al) |= 'not' p iff CX |- 'not' p))
  by HENMODEL:def 2,VALUAT_1:17;
