Theorems · Theorem · general topology
Icc_mem_nhds
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderClosedTopology α] {a b x : α},
a < x → x < b → Set.Icc a b ∈ nhds x- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- nhdsstatement · cited by 5,554
- Set.Iccstatement · cited by 1,702
- OrderClosedTopologystatement and proof · cited by 445
- Filter.mem_of_supersetproof · cited by 308
- Set.Ioo_subset_Icc_selfproof · cited by 54
- Ioo_mem_nhdsproof · cited by 27
Cited by20
Results whose statement or proof uses this declaration.
- Manifold.pathELength_eq_lintegral_mfderivWithin_Iccproof · cited by 5
- intervalIntegral.integral_deriv_of_contDiffOn_Iccproof · cited by 4
- intervalIntegral.continuous_primitiveproof · cited by 3
- exists_isLocalExtr_Iooproof · cited by 3
- taylor_integral_remainder_auxproof · cited by 2
- intervalIntegral.integral_derivWithin_Icc_of_contDiffOn_Iccproof · cited by 1
- intervalIntegral.integral_mul_deriv_eq_deriv_mul_of_hasDerivWithinAtproof · cited by 1
- intervalIntegral.integral_deriv_mul_eq_sub_of_hasDerivWithinAtproof · cited by 1
- BoundedVariationOn.ae_differentiableAt_of_mem_uIccproof · cited by 1
- ODE.picard_eq_of_hasDerivAtproof · cited by 1
- pi_Icc_mem_nhdsproof · cited by 1