mul_le_one — Mathlib

English

If a ≤ 1 and b ≤ 1, then a·b ≤ 1.

Русский

Если a ≤ 1 и b ≤ 1, то a·b ≤ 1.

LaTeX

$$$$\forall a,b \in \alpha:\; a \le 1 \land b \le 1 \Rightarrow a\,b \le 1.$$$$

Lean4

/-- Assumes left covariance.
The lemma assuming right covariance is `Right.mul_le_one`. -/
@[to_additive /-- Assumes left covariance.
    The lemma assuming right covariance is `Right.add_nonpos`. -/
    ]
theorem mul_le_one [MulLeftMono α] {a b : α} (ha : a ≤ 1) (hb : b ≤ 1) : a * b ≤ 1 :=
  mul_le_of_le_of_le_one ha hb

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