The quotient of QPF is itself a QPF

The quotients are here defined using a surjective function and its right inverse. They are very similar to the abs and repr functions found in the definition of MvQPF

def MvQPF.quotientQPF {n : ℕ} {F : TypeVec n → Type u} [MvFunctor F] [q : MvQPF F] {G : TypeVec n → Type u} [MvFunctor G] {FG_abs : {α : TypeVec n} → F α → G α} {FG_repr : {α : TypeVec n} → G α → F α} (FG_abs_repr : ∀ {α : TypeVec n} (x : G α), FG_abs α (FG_repr α x) = x) (FG_abs_map : ∀ {α β : TypeVec n} (f : TypeVec.Arrow α β) (x : F α), FG_abs β (MvFunctor.map f x) = MvFunctor.map f (FG_abs α x)) : MvQPF G

If F is a QPF then G is a QPF as well. Can be used to construct MvQPF instances by transporting them across surjective functions

def MvQPF.Quot1 {n : ℕ} {F : TypeVec n → Type u} (R : ⦃α : TypeVec n⦄ → F α → F α → Prop) (α : TypeVec n) : Type u

Functorial quotient type

instance MvQPF.Quot1.inhabited {n : ℕ} {F : TypeVec n → Type u} (R : ⦃α : TypeVec n⦄ → F α → F α → Prop) {α : TypeVec n} [Inhabited (F α)] : Inhabited (MvQPF.Quot1 R α)

def MvQPF.Quot1.map {n : ℕ} {F : TypeVec n → Type u} (R : ⦃α : TypeVec n⦄ → F α → F α → Prop) [MvFunctor F] (Hfunc : ⦃α β : TypeVec n⦄ → (a b : F α) → (f : TypeVec.Arrow α β) → R α a b → R β (MvFunctor.map f a) (MvFunctor.map f b)) ⦃α : TypeVec n⦄ ⦃β : TypeVec n⦄ (f : TypeVec.Arrow α β) : MvQPF.Quot1 R α → MvQPF.Quot1 R β

map of the Quot1 functor

def MvQPF.Quot1.mvFunctor {n : ℕ} {F : TypeVec n → Type u} (R : ⦃α : TypeVec n⦄ → F α → F α → Prop) [MvFunctor F] (Hfunc : ⦃α β : TypeVec n⦄ → (a b : F α) → (f : TypeVec.Arrow α β) → R α a b → R β (MvFunctor.map f a) (MvFunctor.map f b)) : MvFunctor (MvQPF.Quot1 R)

mvFunctor instance for Quot1 with well-behaved R

noncomputable def MvQPF.relQuot {n : ℕ} {F : TypeVec n → Type u} (R : ⦃α : TypeVec n⦄ → F α → F α → Prop) [MvFunctor F] [q : MvQPF F] (Hfunc : ⦃α β : TypeVec n⦄ → (a b : F α) → (f : TypeVec.Arrow α β) → R α a b → R β (MvFunctor.map f a) (MvFunctor.map f b)) : MvQPF (MvQPF.Quot1 R)

Quot1 is a QPF