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 semnot:
  (SAT M).('not' A)=1 iff (SAT M).A=0
  proof
    hereby assume(SAT M).('not' A)=1;then
      'not' (SAT M).A = 1 by semnot2;
      hence (SAT M).A=0;
    end;
    assume A2: (SAT M).A=0;
    thus(SAT M).('not' A)= 'not' (SAT M).A by semnot2 .=1 by A2;
  end;
