mk'_eq_iff — Mathlib

English

Given a multiplicative map hf, the mk'_mul_mk'_of_map_mul expresses the product law for mk' fractions.

Русский

Дано отображение hf, mk'_mul_mk'_of_map_mul задаёт закон умножения дробей mk'.

LaTeX

$$$mk'_mul_mk'_of_map_mul f hf m_1 m_2 s_1 s_2 = mk' f m_1 s_1 * mk' f m_2 s_2 = mk' f (m_1 m_2) (s_1 s_2)$$$

Lean4

theorem mk'_eq_iff {m : M} {s : S} {m' : M'} : mk' f m s = m' ↔ f m = s • m' := by
  rw [← smul_inj f s, Submonoid.smul_def, ← mk'_smul, ← Submonoid.smul_def, mk'_cancel]

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