Theorems · Theorem · general topology
Real.dist_le_of_mem_Icc
∀ {x y x' y' : ℝ}, x ∈ Set.Icc x' y' → y ∈ Set.Icc x' y' → dist x y ≤ y' - x'- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Real
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
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
- LE.le.transproof · cited by 3,151
- absproof · cited by 1,814
- Set.Iccstatement and proof · cited by 1,702
- Dist.diststatement · cited by 1,539
- neg_subproof · cited by 272
- abs_of_nonposproof · cited by 53
- sub_nonposproof · cited by 29
- Set.Icc_subset_uIccproof · cited by 12
- Real.dist_le_of_mem_uIccproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Real.dist_le_of_mem_Icc_01proof · cited by 4
- Real.ediam_eqproof · cited by 4
- TopologicalSpace.exists_isInducing_l_inftyproof · cited by 1