intros. Opaque Seqtl. simpl. unfold eq_part. intro x. split.
intro H. destruct x. simpl in subtype_prf.
simpl. unfold subtype_image_equal. simpl. exact subtype_prf.
intro H. simpl. auto. Qed.
Transparent Seqtl.

Lemma incexc3_basecase:forall(G:Setoid)(A:part_set G)
(AH:seq 0 A)(AH':full A =' seq_set AH)(AH'':distinct AH)
(c:Nat)(V:seq c(part_set G))
(Va:forall(i:fin c)(g:G),in_part g(V i)->in_part g A)
(Vb:forall(g:G)(H:in_part g A),exists i:fin c,in_part g(V i))
(Vc:forall(g:G)(H:in_part g A)(i i':fin c),
in_part g(V i)->in_part g(V i')->i =' i')
(V':seq c Nat)(V'a:forall(i:fin c),has_n_elements(V' i)(V i)),
nsum c V' =' 0.