proposition: Lemma transport_adjunction (A : Type) (B : A -> Type) (R: forall a :A, crelation (B a)) : forall (a a' : A) (p : a = a') (x : B a) (y : B a'), ((R _ x (transport_r B p y) -> R _ (transport B p x) y)) * (R _ (transport B p x) y -> (R _ x (transport_r B p y))).
proof: Proof. intros a a' p x y. split. - destruct p. now unfold transport_r. - destruct p. now unfold transport_r. Defined.
imports: Category.Lib Category.Theory.Category Category.Theory.Isomorphism Equations.Prop.Logic