Theorems · Theorem · general topology
PiNat.mem_cylinder_iff_dist_le
∀ {E : ℕ → Type u_1} {x y : (n : ℕ) → E n} {n : ℕ}, y ∈ PiNat.cylinder x n ↔ dist y x ≤ (1 / 2) ^ n- Defined in
- Mathlib.Topology.MetricSpace.PiNat
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- Dist.diststatement · cited by 1,539
- eq_or_neproof · cited by 1,117
- LT.lt.trans_leproof · cited by 678
- one_divproof · cited by 624
- inv_powproof · cited by 140
- PiNat.cylinderstatement · cited by 26
- PiNat.firstDiffproof · cited by 23
- PiNat.diststatement · cited by 12
- PiNat.dist_eq_of_neproof · cited by 7
- PiNat.apply_eq_of_lt_firstDiffproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- PiNat.exists_disjoint_cylinderproof · cited by 2
- MeasureTheory.measurablySeparable_range_of_disjointproof · cited by 1
- PiNat.lipschitz_with_one_iff_forall_dist_image_le_of_mem_cylinderproof · cited by 0
- PiNat.isOpen_iff_distproof · cited by 0