proposition: Lemma fset_map_correct `{FSet A} `{FSet B} (f : A → B) `{!Setoid_Morphism f} : singleton ∘ f = fset_map f ∘ singleton.
proof: Proof. Proof (fset_extend_correct _). Lemma fset_map_correct_applied `{FSet A} `{FSet B} (f : A → B) `{!Setoid_Morphism f} x : {{ f x }} = fset_map f {{ x }}. Proof. pose proof (fset_car_setoid A). now apply (setoids.ext_equiv_applied (fset_map_correct f)). Qed.
imports: MathClasses.theory.lattices MathClasses.varieties.monoids MathClasses.implementations.bool MathClasses.implementations.list_finite_set MathClasses.orders.lattices MathClasses.interfaces.abstract_algebra MathClasses.interfaces.finite_sets MathClasses.interfaces.orders