theorem Th3: {} LTLB_WFF |= A iff not 'not' A is satisfiable
  proof
    hereby
      assume
A1:   {}l |= A;
      assume 'not' A is satisfiable;
      then consider M,n such that
A2:   (SAT M).[n,'not' A] = 1;
A3:   M |= {}l;
      (SAT M).[n,A] = 0 by A2,LTLAXIO1:5;
      hence contradiction by A3,A1,LTLAXIO1:def 12;
    end;
    assume
A4: not 'not' A is satisfiable;
    assume not {}l |= A;
    then consider M such that
    M |= {}l and
A5: not M |= A;
    consider n such that
A6: not (SAT M).[n,A] = 1 by A5;
    (SAT M).[n,'not' A] = 1 by A6,XBOOLEAN:def 3,LTLAXIO1:5;
    hence contradiction by A4;
  end;
