one_lt_mul — Mathlib

English

If a > 1 and b > 1, then 1 < a·b.

Русский

Если a > 1 и b > 1, тогда 1 < a·b.

LaTeX

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

Lean4

/-- Assumes left covariance.
The lemma assuming right covariance is `Right.one_lt_mul`. -/
@[to_additive Left.add_pos /-- Assumes left covariance.
    The lemma assuming right covariance is `Right.add_pos`. -/
    ]
theorem one_lt_mul [MulLeftStrictMono α] {a b : α} (ha : 1 < a) (hb : 1 < b) : 1 < a * b :=
  lt_mul_of_lt_of_one_lt ha hb

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