iSupIndep_iff_pairwiseDisjoint — Mathlib

English

For two indices i and j covering all indices, iSupIndep t is equivalent to Disjoint (t i) (t j).

Русский

Для двух индексов i и j, покрывающих все индексы, iSupIndep t эквивалентно Disjoint (t i) (t j).

LaTeX

$$$\\\\forall i \\\\neq j,\\\\forall huniv,\\\\ (huniv k) \\\\Rightarrow iSupIndep t \\\\iff Disjoint (t i) (t j)$$$

Lean4

theorem iSupIndep_iff_pairwiseDisjoint {f : ι → α} : iSupIndep f ↔ Pairwise (Disjoint on f) :=
  ⟨iSupIndep.pairwiseDisjoint, fun hs _ => disjoint_iSup_iff.2 fun _ => disjoint_iSup_iff.2 fun hij => hs hij.symm⟩

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