Theorems · Theorem · general topology
eventually_gt_nhds
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [ClosedIicTopology α] {a b : α},
b < a → ∀ᶠ (x : α) in nhds a, b < x- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Quot.sound
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.
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- nhdsstatement · cited by 5,554
- Filter.Eventuallystatement · cited by 3,134
- ClosedIicTopologystatement and proof · cited by 115
- Ioi_mem_nhdsproof · cited by 27
Cited by8
Results whose statement or proof uses this declaration.
- Filter.Tendsto.eventually_const_ltproof · cited by 6
- ConvexOn.slope_le_of_hasDerivWithinAt_Iioproof · cited by 5
- EReal.continuous_toENNRealproof · cited by 4
- Complex.Gamma_mul_Gamma_add_halfproof · cited by 2
- Real.deriv_Gamma_natproof · cited by 2
- eventually_nhdsWithin_sign_eq_of_deriv_posproof · cited by 2
- deriv_norm_ofReal_cpowproof · cited by 1
- MeasureTheory.aecover_Iio_of_Icoproof · cited by 1