Definition nelstructonforall {X : UU} {n : nat} (P : X -> UU) (f : X -> nat) (sx : nelstruct n X) (fs : ∏ x : X , nelstruct (f x) (P x)) : nelstruct (stnprod (f ∘ sx)) (∏ x : X , P x) := invweq (weqcomp (weqonsecbase P sx) (weqstnprod (P ∘ sx) (f ∘ sx) (λ i : ⟦ n ⟧, fs (sx i)))).
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.DecidablePropositions. Require Import UniMath.MoreFoundations.NegativePropositions. Require Import UniMath.MoreFoundations.Subtypes.