Theorems · Theorem · functional analysis
dist_midpoint_midpoint_le
∀ {V : Type u_1} [inst : SeminormedAddCommGroup V] [inst_1 : NormedSpace ℝ V] (p₁ p₂ p₃ p₄ : V),
dist (midpoint ℝ p₁ p₂) (midpoint ℝ p₃ p₄) ≤ (dist p₁ p₃ + dist p₂ p₄) / 2- Defined in
- Mathlib.Analysis.Normed.Affine.AddTorsor
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 157 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.
- Realstatement and proof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Dist.diststatement and proof · cited by 1,539
- midpointstatement and proof · cited by 123
- Real.norm_ofNatproof · cited by 23
- dist_midpoint_midpoint_le'proof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Urysohns.CU.continuous_limproof · cited by 3
- nndist_midpoint_midpoint_leproof · cited by 0