subgroup_quotient_eq_iff — Mathlib

English

Equality of quotients respects subgroup and quotient relations between orbits.

Русский

Равенство квартих выражений сохраняется между орбитами подгрупп и общими орбитами.

LaTeX

$$Theorem: subgroup_quotient_eq_iff ...$$

Lean4

@[to_additive]
theorem subgroup_quotient_eq_iff {H : Subgroup G} {x : orbitRel.Quotient G α} {a b : x.orbit} :
    (⟦a⟧ : orbitRel.Quotient H x.orbit) = ⟦b⟧ ↔ (⟦↑a⟧ : orbitRel.Quotient H α) = ⟦↑b⟧ :=
  by
  simp_rw [← @Quotient.mk''_eq_mk, Quotient.eq'']
  exact orbitRel.Quotient.mem_subgroup_orbit_iff.symm

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