right_bot_eq_right_quot — Mathlib

English

right_bot_eq_right_quot: Quotient (H : Set G) (⊥ : Subgroup G) = Quotient (QuotientGroup.rightRel H).

Русский

Правая факторизация ⊥ по H эквивалентна фактор-множество G/H по rightRel.

LaTeX

$$$ \\mathrm{Quotient}(H : \\text{Set } G)(\\bot) = \\; \\text{Quotient}(\\text{QuotientGroup.rightRel } H) $$$

Lean4

theorem right_bot_eq_right_quot (H : Subgroup G) :
    Quotient (H : Set G) (⊥ : Subgroup G) = _root_.Quotient (QuotientGroup.rightRel H) :=
  by
  unfold Quotient
  congr
  ext
  simp_rw [← rel_bot_eq_right_group_rel H]

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