mk'_mul_mk' — Mathlib

English

Difference of fractions equals mk' of a subtraction on numerators and scaled by denominators.

Русский

Разность дробей равна mk' разности числителей и вычитанных знаменателей.

LaTeX

$$$mk' f m_1 s_1 - mk' f m_2 s_2 = mk' f (s_2\\cdot m_1 - s_1\\cdot m_2) (s_1 s_2)$$$

Lean4

theorem mk'_mul_mk' {M M' : Type*} [Semiring M] [Semiring M'] [Algebra R M] [Algebra R M'] (f : M →ₐ[R] M')
    [IsLocalizedModule S f.toLinearMap] (m₁ m₂ : M) (s₁ s₂ : S) :
    mk' f.toLinearMap m₁ s₁ * mk' f.toLinearMap m₂ s₂ = mk' f.toLinearMap (m₁ * m₂) (s₁ * s₂) :=
  mk'_mul_mk'_of_map_mul f.toLinearMap (map_mul f) m₁ m₂ s₁ s₂

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