Theorems · Theorem · general topology
Real.dist_le_of_mem_uIcc
∀ {x y x' y' : ℝ}, x ∈ Set.uIcc x' y' → y ∈ Set.uIcc x' y' → dist x y ≤ dist x' y'- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Real
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Dist.diststatement · cited by 1,539
- Set.uIccstatement and proof · cited by 393
- Set.uIcc_commproof · cited by 18
- Set.uIcc_subset_uIccproof · cited by 6
- Set.abs_sub_le_of_uIcc_subset_uIccproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Real.dist_le_of_mem_Iccproof · cited by 3
- Real.dist_le_of_mem_pi_Iccproof · cited by 1