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 Th32: ('not' (p => q)) => ('not' q) is ctaut
  proof
    let g;
    set v = VAL g;
A1: v.tf = 0 by LTLAXIO1:def 15;
A2: v.q = 1 or v.q = 0 by XBOOLEAN:def 3;
    thus v.(('not' (p => q)) => ('not' q)) = v.('not' (p => q)) => v.('not' q)
    by LTLAXIO1:def 15
    .= (v.(p => q) => v.tf) => v.('not' q) by LTLAXIO1:def 15
    .= v.p => v.q => v.tf => v.('not' q) by LTLAXIO1:def 15
    .= v.p => v.q => v.tf => (v.q => v.tf) by LTLAXIO1:def 15
    .= 1 by A2,A1;
  end;
