Theorems · Theorem · general topology
Filter.seq_assoc
∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} (x : Filter α) (g : Filter (α → β)) (h : Filter (β → γ)),
h.seq (g.seq x) = ((Filter.map (fun x1 x2 => x1 ∘ x2) h).seq g).seq x- Defined in
- Mathlib.Order.Filter.Map
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Set.imageproof · cited by 5,609
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- Filter.mapstatement and proof · cited by 819
- Filter.image_mem_mapproof · cited by 39
- Set.seqproof · cited by 19
- Filter.seqstatement and proof · cited by 15
- Filter.seq_mem_seqproof · cited by 6
- Filter.mem_map_iff_exists_imageproof · cited by 6
- Filter.le_seqproof · cited by 5
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