An algebraic approach to zero-order production logic interpretation is based on modelling inference process by finding connections between mathematical lattices elements (LP-inference). An algebraic structure arising in this approach is an LP-structure — boolean lattice with additional binary relation defined over it. An additional relation is built using recursive rules that reflect natural rules of logical inference. Authors previous works advance this approach by introducing the concept of production-logical equations on boolean lattice and proposing the method for solving such equations which corresponds to inference in zero-order logic. This method ignores the usage of contrapositive inference rule that is natural for zero-order logic as the other inference rules defined in LP-structures theory. This paper provides additional research on inference process bringing the ability to use the contrapositive rule to the concept of production-logical equations on boolean lattice. The theorem proved allows applying the previously obtained results regarding production-logical equations on boolean lattice without amendments by simply replacing an initial relation over lattice with its contrapositive closure. It is also shown that such a replacement does not affect an initial set of lattice. The practical significance of the provided study is connected with applying production-logical equations for building production systems that use logical connections of zero-order propositional language in its rules. Adding contrapositive rule to the process of inference will allow one to reduce the number of queries to the external source of information by exhaustive usage of knowledge from an initial set of rules.