Section DerivableRules.
Context {L: Language}
{minL: MinimunLanguage L}
{pL: PropositionalLanguage L}
{Gamma: ProofTheory L}
{minAX: MinimunAxiomatization L Gamma}
{ipGamma: IntuitionisticPropositionalLogic L Gamma}.

(* Specifications: *)
Lemma falsep_andp: forall x: expr,
|-- FF && x <--> FF.
Lemma andp_falsep: forall x: expr,
|-- x && FF <--> FF.
Lemma andp_orp_distr_l: forall x y z: expr,
|-- (x || y) && z <--> (x && z) || (y && z).
Lemma andp_orp_distr_r: forall x y z: expr,
|-- x && (y || z) <--> (x && y) || (x && z).