sequence_mono — Mathlib

English

If hg(s,t) holds for all s,t, then (iInf f).lift' g = iInf (f i).lift' g.

Русский

Если hg выполняется, то (iInf f).lift' g = iInf (f i).lift' g.

LaTeX

$$$(iInf f).lift' g = \\bigwedge_i (f(i).lift' g)$$$

Lean4

theorem sequence_mono : ∀ as bs : List (Filter α), Forall₂ (· ≤ ·) as bs → sequence as ≤ sequence bs
  | [], [], Forall₂.nil => le_rfl
  | _ :: as, _ :: bs, Forall₂.cons h hs => seq_mono (map_mono h) (sequence_mono as bs hs)

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