Theorems · Theorem · general topology
dist_pi_le_iff
∀ {β : Type u_2} {X : β → Type u_3} [inst : Fintype β] [inst_1 : (b : β) → PseudoMetricSpace (X b)]
{f g : (b : β) → X b} {r : ℝ}, 0 ≤ r → (dist f g ≤ r ↔ ∀ (b : β), dist (f b) (g b) ≤ r)- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Pi
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypePseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- NNRealproof · cited by 4,310
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- NNReal.toRealproof · cited by 1,260
- nndist_pi_le_iffproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- pi_norm_le_iff_of_nonnegproof · cited by 18
- pi_norm_le_iff_of_nonneg'proof · cited by 5
- closedBall_piproof · cited by 2
- diam_stdSimplex_leproof · cited by 1
- Real.dist_le_of_mem_pi_Iccproof · cited by 1
- LipschitzOnWith.extend_piproof · cited by 1
- stdSimplex_subset_closedBallproof · cited by 1
- sphere_piproof · cited by 0
- dist_pi_const_leproof · cited by 0
- dist_pi_le_iff'proof · cited by 0