(***)
intros E A n v i j X Z1 Z2. simpl. unfold eq_part. intro x.
split. intro G0. elim(classic(x=' v j)). intro G1. simpl.
elim(omit_removes' v Z1). intros i' i'H. exists i'.
apply Trans with(v j). exact G1. exact i'H. intro G1.
assert(G2:~x=' v i). unfold not. intro G2. apply G1.
apply Trans with(v i). exact G2. exact Z2. set(x':=
Map_to_equal_subsets X(Id A)(Build_subtype(P:=A)
(subtype_elt:=x)G0)). elim(has_index x'). intros i' i'H.
simpl. assert(G3:~i =' i'). unfold not. intro G3.
apply G2. apply Trans with(seq_set v x'). simpl.
apply Refl. apply Trans with(v i'). exact i'H.
apply Map_compatible_prf. apply Sym. exact G3.
elim(omit_removes' v G3). intros m mH. exists m.
apply Trans with(v i'). apply Trans with(seq_set v x').
simpl. apply Refl. exact i'H. exact mH.
intro G1. simpl in G1. elim G1. clear G1. intros m mH.
apply in_part_comp_l with(omit v i m). 2:exact mH.
apply in_part_comp_r with(seq_set v). 2:exact(Sym X).
apply omit_seq_in_seq_set. Qed.

(* Specifications: *)
Lemma existbij_c:forall(E:Setoid)(A:part_set E),
(forall(c:Nat)(v:seq c E)(H:A =' seq_set v),~distinct v)
->
(exists k:Nat,exists w:seq k E,A =' seq_set w /\ ~distinct w)
->False.