Section RotRcons.
Variable T : Type.
Implicit Types (x : T) (s : seq T).
Canonical seq_eqMixin := EqMixin eqseqP.
Canonical seq_eqType := Eval hnf in EqType (seq T) seq_eqMixin.

Lemma exists_cons {P : T -> Prop} {a s} :
(exists2 x, x \in a::s & P x) <-> P a \/ exists2 x, x \in s & P x.