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 Th5: (VAL g).(p 'or' q) = (VAL g).p 'or' (VAL g).q
  proof
    set v = VAL g;
A1: v.tf = FALSE by LTLAXIO1:def 15;
    thus v.(p 'or' q) = v.(('not' p) '&&' ('not' q)) => v.tf by LTLAXIO1:def 15
    .= v.('not' p) '&' v.('not' q) => v.tf by LTLAXIO1:31
    .= (v.p => v.tf) '&' v.('not' q) => v.tf by LTLAXIO1:def 15
    .= (v.p => v.tf) '&' (v.q => v.tf) => v.tf by LTLAXIO1:def 15
    .= v.p 'or' v.q by A1;
  end;
