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 incsub:
  F c= G & not F is consistent implies not G is consistent
  proof
    assume A2: F c= G & not F is consistent;then
    consider p such that A1: F |- p & F |- 'not' p;
    G |- p & G |- 'not' p by monmp,A1,A2;
    hence not G is consistent;
  end;
