mul — Mathlib

English

If s is totally bounded, then its inverse is totally bounded (repeat instance).

Русский

Если s полностью ограничено, то и s^{-1} полностью ограничено (повторение).

LaTeX

$$$TotallyBounded(s) \\Rightarrow TotallyBounded(s^{-1})$$$

Lean4

@[to_additive]
theorem mul (hf : TendstoUniformlyOnFilter f g l l') (hf' : TendstoUniformlyOnFilter f' g' l l') :
    TendstoUniformlyOnFilter (f * f') (g * g') l l' := fun u hu =>
  ((uniformContinuous_mul.comp_tendstoUniformlyOnFilter (hf.prodMk hf')) u hu).diag_of_prod_left

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