Notation "''Sym_' T" := (Sym (Phant T))
(at level 8, T at level 2, format "''Sym_' T") : group_scope.
Notation "''Sym_' T" := (Sym_group (Phant T)) : Group_scope.
Notation "''Alt_' T" := (Alt (Phant T))
(at level 8, T at level 2, format "''Alt_' T") : group_scope.
Notation "''Alt_' T" := (Alt_group (Phant T)) : Group_scope.

(* Specifications: *)
Lemma trivial_Alt_2 (T : finType) : #|T| <= 2 -> 'Alt_T = 1.
Lemma simple_Alt_3 (T : finType) : #|T| = 3 -> simple 'Alt_T.
Lemma not_simple_Alt_4 (T : finType) : #|T| = 4 -> ~~ simple 'Alt_T.
Lemma simple_Alt5_base (T : finType) : #|T| = 5 -> simple 'Alt_T.
Section Restrict.