mul_lt_mul_of_lt_of_lt — Mathlib

English

For odd n, a^n = b^n ⇔ a = b.

Русский

Для нечетного n, a^n = b^n ⇔ a = b.

LaTeX

$$$a^n = b^n \iff a = b$$$

Lean4

protected theorem mul_lt_mul_of_lt_of_lt [PosMulStrictMono R] {a b c d : R} (hab : a < b) (hcd : c < d) :
    a * c < b * d := by
  -- TODO: This should be an instance but it currently times out

  have := posMulStrictMono_iff_mulPosStrictMono.1 ‹_›
  obtain rfl | hc := eq_zero_or_pos c
  · rw [mul_zero]
    exact mul_pos ((zero_le _).trans_lt hab) hcd
  · exact mul_lt_mul_of_pos' hab hcd hc ((zero_le _).trans_lt hab)

Похожие утверждения