Theorems · Theorem · real analysis
nhdsLT_le_nhdsNE
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : Preorder α] (a : α), nhdsWithin a (Set.Iio a) ≤ nhdsWithin a {a}ᶜ- Defined in
- Mathlib.Topology.Order.LeftRight
- Cited by
- 8 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.Iiostatement · cited by 1,166
- ne_of_ltproof · cited by 203
- nhdsWithin_monoproof · cited by 82
Cited by8
Results whose statement or proof uses this declaration.
- Monotone.ae_hasDerivAtproof · cited by 1
- isLocalMax_of_derivproof · cited by 1
- deriv_pos_left_of_sign_derivproof · cited by 1
- StieltjesFunction.ae_hasDerivAtproof · cited by 1
- HasDerivAt.tendsto_slope_zero_leftproof · cited by 0
- deriv_neg_left_of_sign_derivproof · cited by 0
- isLocalMin_of_derivproof · cited by 0
- HasLineDerivAt.tendsto_slope_zero_leftproof · cited by 0