mul_div_assoc — Mathlib

English

In a Euclidean domain, dividing by 1 leaves the number unchanged: p / 1 = p.

Русский

В евклидовом кольце деление на 1 не изменяет число: p / 1 = p.

LaTeX

$$$ p / 1 = p $$$

Lean4

theorem mul_div_assoc (x : R) {y z : R} (h : z ∣ y) : x * y / z = x * (y / z) :=
  by
  by_cases hz : z = 0
  · subst hz
    rw [div_zero, div_zero, mul_zero]
  rcases h with ⟨p, rfl⟩
  rw [mul_div_cancel_left₀ _ hz, mul_left_comm, mul_div_cancel_left₀ _ hz]

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