Theorems · Theorem · general topology
dist_le_pi_dist
∀ {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) (b : β), dist (f b) (g b) ≤ dist f g- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Pi
- Cited by
- 3 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- nndist_le_pi_nndistproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Real.dist_le_of_mem_pi_Iccproof · cited by 1
- BoxIntegral.hasIntegral_GP_pderivproof · cited by 1
- LipschitzOnWith.extend_piproof · cited by 1