Theorems · Theorem · general topology
Icc_mem_nhdsGE_of_mem
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [ClosedIciTopology α] {a b c : α},
b ∈ Set.Ico c a → Set.Icc c a ∈ nhdsWithin b (Set.Ici b)- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- Filterstatement · cited by 8,121
- nhdsWithinstatement · cited by 1,912
- Set.Iccstatement · cited by 1,702
- Set.Icistatement · cited by 1,070
- Set.Icostatement and proof · cited by 799
- Filter.mem_of_supersetproof · cited by 308
- ClosedIciTopologystatement and proof · cited by 156
- Set.Ico_subset_Icc_selfproof · cited by 41
- Ico_mem_nhdsGE_of_memproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Icc_mem_nhdsGEproof · cited by 6
- norm_image_sub_le_of_norm_deriv_le_segment'proof · cited by 4
- eq_of_derivWithin_eqproof · cited by 0