proposition: Lemma inter_realizer : forall A B t e, t↓e ⊩ A∩B <-> t↓e ⊩ A /\ t↓e ⊩ B.
proof: Proof. intros A B t e. split; intro Ht. split; subtyping. destruct Ht as [Ht₁ Ht₂]. start; (now apply Ht₁) || (now apply Ht₂). Qed.
imports: RelationClasses Morphisms ClassicalRealizability.ShallowEmbedding ClassicalRealizability.Tactics ClassicalRealizability.BasicResults