expGrowthInf_eventually_monotone — Mathlib

English

expGrowthInf_eventually_monotone asserts that if u ≤ᶠ v then expGrowthInf u ≤ expGrowthInf v.

Русский

exp Growth Inf постепенно монотонно, если u не превышает v на tail, тогда inf-growth order не больше.

LaTeX

$$$u \\leq^{{\\,tail}} v \\Rightarrow \\expGrowthInf(u) \\leq \\expGrowthInf(v).$$$

Lean4

theorem expGrowthInf_eventually_monotone (h : u ≤ᶠ[atTop] v) : expGrowthInf u ≤ expGrowthInf v :=
  liminf_le_liminf (h.mono fun n uv ↦ monotone_div_right_of_nonneg n.cast_nonneg' (log_monotone uv))

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