Theorems · Theorem · general topology
Filter.isCompl_principal
∀ {α : Type u} (s : Set α), IsCompl (Filter.principal s) (Filter.principal sᶜ)- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Top.topproof · cited by 9,680
- Filterstatement and proof · cited by 8,121
- Bot.botproof · cited by 4,720
- Compl.complstatement · cited by 2,925
- Filter.principalstatement and proof · cited by 740
- IsComplstatement · cited by 351
- Set.union_compl_selfproof · cited by 57
- Filter.principal_univproof · cited by 46
- Filter.inf_principalproof · cited by 29
- Filter.principal_emptyproof · cited by 19
- Set.inter_compl_selfproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- Filter.mem_inf_principal'proof · cited by 2