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 Th35: 'not' (p '&&' q) => (('not' p) 'or' ('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 '&&' q)) = v.(p '&&' q) => v.tf by LTLAXIO1:def 15
    .= v.p '&' v.q => v.tf by LTLAXIO1:31;
A4: v.(('not' p) 'or' ('not' q)) = v.('not' p) 'or' v.('not' q) by Th5
    .= (v.p => v.tf) 'or' v.('not' q) by LTLAXIO1:def 15
    .= (v.p => v.tf) 'or' (v.q => v.tf) by LTLAXIO1:def 15;
A5: v.q = 1 or v.q = 0 by XBOOLEAN:def 3;
   thus v.('not' (p '&&' q) => (('not' p) 'or' ('not' q))) =
   v.('not' (p '&&' q)) => v.(('not' p) 'or' ('not' q)) by LTLAXIO1:def 15
   .= 1 by A2,A5,A1,A4,A3;
 end;
