Theorems · Theorem · general topology
PiNat.mem_cylinder_iff_le_firstDiff
∀ {E : ℕ → Type u_1} {x y : (n : ℕ) → E n}, x ≠ y → ∀ (i : ℕ), x ∈ PiNat.cylinder y i ↔ i ≤ PiNat.firstDiff x y- Defined in
- Mathlib.Topology.MetricSpace.PiNat
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- LT.lt.trans_leproof · cited by 678
- PiNat.cylinderstatement and proof · cited by 26
- PiNat.firstDiffstatement and proof · cited by 23
- PiNat.apply_eq_of_lt_firstDiffproof · cited by 6
- PiNat.apply_firstDiff_neproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- PiNat.exists_lipschitz_retraction_of_isClosedproof · cited by 2
- PiNat.disjoint_cylinder_of_longestPrefix_ltproof · cited by 1