Section ProofTheoryPatterns.
Context {L: Language}
{minL: MinimumLanguage L}
{pL: PropositionalLanguage L}
{Gamma: Provable L}
{minAX: MinimumAxiomatization L Gamma}
{ipAX: IntuitionisticPropositionalLogic L Gamma}.

Lemma Build_RightUnit': forall {e: expr} {prodp: expr -> expr -> expr},
(forall x: expr, |-- prodp x e <--> x) ->
RightUnit L Gamma e prodp.