Theorems · Theorem · real analysis
nhdsGT_le_nhdsNE
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : Preorder α] (a : α), nhdsWithin a (Set.Ioi a) ≤ nhdsWithin a {a}ᶜ- Defined in
- Mathlib.Topology.Order.LeftRight
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpacePreorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Filterstatement · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Compl.complstatement · cited by 2,925
- nhdsWithinstatement · cited by 1,912
- Set.Ioistatement · cited by 1,463
- ne_of_gtproof · cited by 637
- nhdsWithin_monoproof · cited by 82
Cited by10
Results whose statement or proof uses this declaration.
- sub_mem_posTangentConeAt_of_openSegment_subsetproof · cited by 2
- HasLineDerivAt.tendsto_slope_zero_rightproof · cited by 2
- Monotone.ae_hasDerivAtproof · cited by 1
- HasDerivAt.tendsto_slope_zero_rightproof · cited by 1
- isLocalMax_of_derivproof · cited by 1
- deriv_neg_right_of_sign_derivproof · cited by 1
- mem_posTangentConeAt_of_frequently_memproof · cited by 1
- deriv_pos_right_of_sign_derivproof · cited by 0
- isLocalMin_of_derivproof · cited by 0
- DirichletCharacter.LFunctionTrivChar_isBigO_near_one_horizontalproof · cited by 0