Mathlib Map

Theorems · Theorem · general topology

Ultrafilter.of_le

∀ {α : Type u} (f : Filter α) [inst : f.NeBot], ↑(Ultrafilter.of f) ≤ f
Defined in
Mathlib.Order.Filter.Ultrafilter.Defs
Cited by
15 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Filter.NeBot
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FirstOrder.Language.Theory.isSatisfiable_iff_isFinitelySatisfiable · cited by 3Theory.isSatisfiable_iff_…Filter.hyperfilter_le_cofinite · cited by 2Filter.hyperfilter_le_cof…Filter.totallyBounded_iff_filter · cited by 2Filter.totallyBounded_iff…isComplete_iff_ultrafilter · cited by 1isComplete_iff_ultrafilterIsFoelner.amenable · cited by 1IsFoelner.amenableCauchy.ultrafilter_of · cited by 1Cauchy.ultrafilter_ofIsAddFoelner.amenable · cited by 1IsAddFoelner.amenableUltrafilter.exists_ultrafilter_of_finite_inter_nonempty · cited by 1Ultrafilter.exists_ultraf…Filter.totallyBounded_iff_ultrafilter · cited by 1Filter.totallyBounded_iff…Filter.forall_neBot_le_iff · cited by 1Filter.forall_neBot_le_iffFilter.mem_iff_ultrafilter · cited by 1Filter.mem_iff_ultrafilterUltrafilter.ofComapInfPrincipal_eq_of_map · cited by 0Ultrafilter.ofComapInfPri…Ultrafilter.ofComapInfPrincipal_mem · cited by 0Ultrafilter.ofComapInfPri…Ultrafilter.of_coe · cited by 0Ultrafilter.of_coeFilter.TotallyBounded.exists_clusterPt · cited by 0TotallyBounded.exists_clu…Filter · cited by 8121FilterFilter.NeBot · cited by 853Filter.NeBotUltrafilter.toFilter · cited by 172Ultrafilter.toFilterUltrafilter.of · cited by 15Ultrafilter.ofUltrafilter.exists_le · cited by 2Ultrafilter.exists_leUltrafilter.of_leCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by15

Results whose statement or proof uses this declaration.