Theorems · Theorem · general topology
Real.dist_le_of_mem_pi_Icc
∀ {ι : Type u_1} [inst : Fintype ι] {x y x' y' : ι → ℝ}, x ∈ Set.Icc x' y' → y ∈ Set.Icc x' y' → dist x y ≤ dist x' y'- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Real
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- LE.le.transproof · cited by 3,151
- Set.Iccstatement and proof · cited by 1,702
- Dist.diststatement · cited by 1,539
- dist_nonnegproof · cited by 126
- Set.Icc_subset_uIccproof · cited by 12
- dist_pi_le_iffproof · cited by 10
- dist_le_pi_distproof · cited by 3
- Real.dist_le_of_mem_uIccproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- BoxIntegral.Box.diam_Icc_le_of_distortion_leproof · cited by 1