fact: Definition hom_prod_algebra_mapout (f : Homomorphism C (ProdAlgebra I A)) (i:I) : Homomorphism C (A i) := hom_compose (hom_proj_prod_algebra I A i) f.
imports: HoTT.Types.Bool HoTT.Types.Forall HoTT.Classes.theory.ua_homomorphism