Notation "A / H" := (quotient A H) : group_scope.Implicit Types A : {set gT}.Implicit Types (C D : {set coset_of H}) (L M : {group coset_of H}).Notation "A / H" := (quotient_group A H) : Group_scope.

(* Specifications: *)
Lemma quotientT : setT / H = setT.
Lemma quotient0 : set0 / H = set0.
Lemma quotient1 : 1 / H = 1.
Lemma quotientV A : A^-1 / H = (A / H)^-1.
Lemma trivg_quotient : H / H = 1.
Lemma quotient_abelian A : abelian A -> abelian (A / H).
Lemma quotientMidr A : A * H / H = A / H.
Lemma quotientMidl A : H * A / H = A / H.
Lemma quotient_isom : isom G (G / H) (restrm nHG (coset H)).
Lemma quotient_isog : isog G (G / H).
Lemma quotient1_isom : isom A (A / 1) (coset 1).
Lemma quotient1_isog : isog A (A / 1).