reserve p,q,r,s,A,B for Element of PL-WFF,
  F,G,H for Subset of PL-WFF,
  k,n for Element of NAT,
  f,f1,f2 for FinSequence of PL-WFF;
reserve M for PLModel;

theorem semcon2:
  (SAT M).(A '&' B) = (SAT M).A '&' (SAT M).B
  proof
    thus (SAT M).(A '&' B) = 'not' (SAT M).(A => 'not' B) by semnot2
    .= 'not' ((SAT M).A => (SAT M).('not' B)) by Def11
    .= 'not' ((SAT M).A => 'not' (SAT M).B) by semnot2
    .= (SAT M).A '&' (SAT M).B;
  end;
