biSup_add — Mathlib

English

For Exists p, biSup_add' holds: (iSup i, iSup x with p i, f i) + a = iSup i, iSup x with p i, a + f i.

Русский

Для существования p, biSup_add' справедливо: (iSup i, iSup x с p i, f i) + a = iSup i, iSup x с p i, a + f i).

LaTeX

$$$ \exists p(i) \rightarrow \left( \iSup_i \iSup_x^{p(i)} f(i) + a = \iSup_i \iSup_x^{p(i)} (a + f(i)) \right) $$$

Lean4

theorem biSup_add {ι : Type*} {s : Set ι} (hs : s.Nonempty) (f : ι → ℕ∞) : (⨆ i ∈ s, f i) + a = ⨆ i ∈ s, f i + a :=
  biSup_add' hs _

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