 The first three De Morgan rules are valid on any compatibility frame if the standard evaluation clauses for \(\wedge\) and \(\vee\) are assumed, and they can be proved utilizing standard inference rules for \(\wedge\) and \(\vee\) (cf. Restall 2000). (The first two De Morgan rules are valid on any compatibility frame also if negation as impossibility, \(\osim\), is replaced by negation as unnecessity, \(\neg\).) Whereas the first two De Morgan laws, however, can be proved using only contraposition and inference rules for \(\wedge\) and \(\vee\), a derivation of the third De Morgan law requires the application of constructive contraposition: