ext — Mathlib

English

Two CancelCommMonoid structures are equal if their multiplications agree.

Русский

Две CancelCommMonoid структуры равны, если совпадает их умножение.

LaTeX

$$$m_1 = m_2 \text{ if } (\forall x,y, x *_{m_1} y = x *_{m_2} y)$$$

Lean4

@[to_additive (attr := ext)]
theorem ext {M : Type*} ⦃m₁ m₂ : CancelCommMonoid M⦄
    (h_mul :
      (letI := m₁;
          HMul.hMul :
          M → M → M) =
        (letI := m₂;
          HMul.hMul :
          M → M → M)) :
    m₁ = m₂ :=
  CancelCommMonoid.toCommMonoid_injective <| CommMonoid.ext h_mul

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