invMulSubgroup_eq_mul_inv — Mathlib

English

There is a finite type structure on the subtype of elements of invMulSubgroup.

Русский

Существует структура конечного типа на подмножество элементов invMulSubgroup.

LaTeX

$$$\text{Fintype}(\text{Subtype}\;\{x \mid x \in \text{invMulSubgroup}\})$$$

Lean4

theorem invMulSubgroup_eq_mul_inv (A : Finset G) (h) : (invMulSubgroup A h : Set G) = A * A⁻¹ :=
  by
  rw [invMulSubgroup_eq_inv_mul, eq_comm]
  norm_cast
  exact mul_inv_eq_inv_mul_of_doubling_lt_two (by qify at h ⊢; linarith)

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