reserve A,B,p,q,r,s for Element of LTLB_WFF,
  i,j,k,n for Element of NAT,
  X for Subset of LTLB_WFF,
  f,f1 for FinSequence of LTLB_WFF,
  g for Function of LTLB_WFF,BOOLEAN;

theorem 'not' (p 'or' q) => (('not' p) '&&' ('not' q)) is ctaut
  proof
    let g;
    set v = VAL g;
A1: v.tf = 0 by LTLAXIO1:def 15;
A2: v.p = 1 or v.p = 0 by XBOOLEAN:def 3;
A3: v.(('not' p) '&&' ('not' q)) = v.('not' p) '&' v.('not' q) by LTLAXIO1:31
    .= (v.p => v.tf) '&' v.('not' q) by LTLAXIO1:def 15
    .= (v.p => v.tf) '&' (v.q => v.tf) by LTLAXIO1:def 15;
A4: v.('not' (p 'or' q)) = v.(p 'or' q) => v.tf by LTLAXIO1:def 15
    .= v.p 'or' v.q => v.tf by Th5;
A5: v.q = 1 or v.q = 0 by XBOOLEAN:def 3;
    thus v.('not' (p 'or' q) => (('not' p) '&&' ('not' q)))
    = v.('not' (p 'or' q)) => v.(('not' p) '&&' ('not' q)) by LTLAXIO1:def 15
    .= 1 by A2,A5,A1,A3,A4;
  end;
