mk_div_mk — Mathlib

English

The membership of an element in divPairs can be simplified to the div condition.

Русский

Членство элемента в divPairs упрощается до условия деления.

LaTeX

$$@[simp] theorem mem_divPairs : x ∈ divPairs f s ↔ f x.1 / f x.2 ∈ s$$

Lean4

@[to_additive (attr := simp)]
theorem mk_div_mk (m₁ m₂ : M) (s₁ s₂ : (⊤ : Submonoid M)) :
    mk m₁ s₁ / mk m₂ s₂ = .mk (m₁ * s₂) ⟨s₁ * m₂, Submonoid.mem_top _⟩ := by simp [div_eq_mul_inv, mk_mul]; rfl

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