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 p => (q => p) is ctaut
  proof
    let g;
    set v = VAL g;
A1: v.p = 1 or v.p = 0 by XBOOLEAN:def 3;
    thus v.(p => (q => p)) = v.p => v.(q => p) by LTLAXIO1:def 15
    .= v.p => (v.q => v.p) by LTLAXIO1:def 15
    .= 1 by A1;
  end;
