Theorems · Theorem · order theory
Filter.liminf_congr
∀ {β : Type u_2} {α : Type u_6} [inst : ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β},
(∀ᶠ (a : α) in f, u a = v a) → Filter.liminf u f = Filter.liminf v f- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- ConditionallyCompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Filter.Eventuallystatement and proof · cited by 3,134
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Filter.liminfstatement · cited by 198
- Filter.limsup_congrproof · cited by 20
Cited by14
Results whose statement or proof uses this declaration.
- LinearGrowth.linearGrowthInf_topproof · cited by 5
- ExpGrowth.expGrowthInf_mul_leproof · cited by 2
- MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_leproof · cited by 2
- LinearGrowth.linearGrowthInf_infproof · cited by 1
- ENNReal.liminf_toReal_eqproof · cited by 1
- ExpGrowth.expGrowthInf_infproof · cited by 1
- LinearGrowth.linearGrowthInf_add_leproof · cited by 1
- ExpGrowth.le_expGrowthInf_mulproof · cited by 1
- LinearGrowth.linearGrowthInf_negproof · cited by 0
- ExpGrowth.expGrowthInf_congrproof · cited by 0
- LinearGrowth.le_linearGrowthInf_addproof · cited by 0
- ExpGrowth.expGrowthInf_invproof · cited by 0