quotient_eq_of_quotient_subgroup_eq'

English

Every class in the quotient has a nonempty orbit in α.

Русский

У каждой орбиты класс в α непустая.

LaTeX

$$$x \text{.orbit} \;\neq \emptyset$ for every $x$ in the quotient.$$

Lean4

@[to_additive]
theorem quotient_eq_of_quotient_subgroup_eq' {H : Subgroup G} {a b : α}
    (h : (Quotient.mk'' a : orbitRel.Quotient H α) = Quotient.mk'' b) :
    (Quotient.mk'' a : orbitRel.Quotient G α) = Quotient.mk'' b :=
  orbitRel.quotient_eq_of_quotient_subgroup_eq h

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