From mathcomp Require Import all_ssreflect.
(** * Using [exists] *)
Goal forall w:seq nat,
(exists w1 w2: seq nat, w = (w1 ++ w2)%list /\ (length w)==0%nat) -> w = [::].
Proof.
move=> w [w1 [w2]].
by case; case: w; case: w1; case: w2.
Qed.