Theorems · Theorem · general topology
PiNat.eq_of_dist_eq_zero
∀ {E : ℕ → Type u_1} (x y : (n : ℕ) → E n), dist x y = 0 → x = y- Defined in
- Mathlib.Topology.MetricSpace.PiNat
- Cited by
- 0 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Dist.diststatement and proof · cited by 1,539
- eq_or_neproof · cited by 1,117
- one_divproof · cited by 624
- inv_powproof · cited by 140
- PiNat.firstDiffproof · cited by 23
- PiNat.diststatement · cited by 12
- PiNat.dist_eq_of_neproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- PiNat.metricSpaceproof · cited by 3
- PiNat.metricSpaceOfDiscreteUniformityproof · cited by 0