Theorems · Theorem · general topology
Filter.EventuallyLE.trans_eq
∀ {α : Type u} {β : Type v} [inst : Preorder β] {l : Filter α} {f g h : α → β}, f ≤ᶠ[l] g → g =ᶠ[l] h → f ≤ᶠ[l] h- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Filter.EventuallyEqstatement and proof · cited by 1,912
- Filter.EventuallyLEstatement and proof · cited by 383
- Filter.EventuallyEq.leproof · cited by 46
- Filter.EventuallyLE.transproof · cited by 27
Cited by8
Results whose statement or proof uses this declaration.
- MeasureTheory.condExp_monoproof · cited by 6
- MeasureTheory.condExpInd_nonnegproof · cited by 1
- MeasureTheory.Submartingale.zero_le_of_predictableproof · cited by 1
- ProbabilityTheory.Kernel.ae_null_of_compProd_nullproof · cited by 1
- ProbabilityTheory.Kernel.ae_null_of_comp_nullproof · cited by 1
- MeasureTheory.Measure.measure_ae_null_of_prod_nullproof · cited by 1
- MeasureTheory.condExpIndSMul_nonnegproof · cited by 1
- MeasureTheory.condExpL2_indicator_nonnegproof · cited by 1