ext — Mathlib

English

Two CancelMonoid structures are equal if their multiplication coincide.

Русский

Две CancelMonoid структуры равны, если совпадает умножение.

LaTeX

$$$\forall x,y, x *_{m_1} y = x *_{m_2} y \Rightarrow m_1 = m_2$$$

Lean4

@[to_additive (attr := ext)]
theorem ext {M : Type u} ⦃m₁ m₂ : RightCancelMonoid M⦄
    (h_mul :
      (letI := m₁;
          HMul.hMul :
          M → M → M) =
        (letI := m₂;
          HMul.hMul :
          M → M → M)) :
    m₁ = m₂ :=
  RightCancelMonoid.toMonoid_injective <| Monoid.ext h_mul

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