Iic_mul_Iio_subset' — Mathlib

English

For all a,b, the product Iic(a)·Iio(b) is contained in Iio(ab): Iic(a)·Iio(b) ⊆ Iio(ab).

Русский

Для любых a,b произведение Iic(a) и Iio(b) contained в Iio(ab).

LaTeX

$$$$ Iic(a) \\cdot Iio(b) \\subseteq Iio(a b). $$$$

Lean4

@[to_additive Iic_add_Iio_subset]
theorem Iic_mul_Iio_subset' (a b : α) : Iic a * Iio b ⊆ Iio (a * b) :=
  by
  have := mulRightMono_of_mulRightStrictMono α
  rintro x ⟨y, hya, z, hzb, rfl⟩
  exact mul_lt_mul_of_le_of_lt hya hzb

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