Local Open Scope logic_base.
Local Open Scope syntax.

Lemma allp_K
(BL: BinderLanguage)
{nBL: NormalBinderLanguage BL}
{pBL: PropositionalBinderLanguage BL}
{qL: QuantifierLanguage BL}
(BGamma: BindedProofTheory BL)
{nGamma: forall ts, NormalProofTheory (binded_L ts) (binded_Gamma ts)}
{mpGamma: forall ts, MinimunPropositionalLogic (binded_L ts) (binded_Gamma ts)}
{ipGamma: forall ts, IntuitionisticPropositionalLogic (binded_L ts) (binded_Gamma ts)}
{qGamma: QuantifierLogic BL BGamma}:
forall (t: type) (ts: list type) (x y: binded_expr (t :: ts)),
|-- allp (x --> y) --> (allp x --> allp y).