reserve p,q,r,s,A,B for Element of PL-WFF,
  F,G,H for Subset of PL-WFF,
  k,n for Element of NAT,
  f,f1,f2 for FinSequence of PL-WFF;
reserve M for PLModel;

theorem
  p => (p 'or' q) is tautology
  proof
    let M;
    thus (SAT M).(p => (p 'or' q)) = (SAT M).p => (SAT M).(p 'or' q) by Def11
    .= (SAT M).p => ((SAT M).p 'or' (SAT M).q) by semdis2
    .= 1 by XBOOLEAN:123;
  end;
