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
  (SAT M).(A => B) = 1 iff (SAT M).A = 0 or (SAT M).B = 1
  proof
A3:   (SAT M).B = TRUE or (SAT M).B = FALSE by XBOOLEAN:def 3;
      hereby
        assume (SAT M).(A => B) = 1;then
        (SAT M).A => (SAT M).B = 1 by Def11;
        hence (SAT M).A = 0 or (SAT M).B = 1 by A3;
      end;
      assume
A4:   (SAT M).A = 0 or (SAT M).B = 1;
      thus (SAT M).(A => B) = (SAT M).A => (SAT M).B by Def11
      .= 1 by A4;
    end;
