Theorems · Theorem · convex and discrete geometry

segment_single_subset_stdSimplex

∀ (𝕜 : Type u_2) {ι : Type u_1} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : Fintype ι]
  [inst_3 : DecidableEq ι] [ZeroLEOneClass 𝕜] [IsOrderedRing 𝕜] (i j : ι),
  segment 𝕜 (Pi.single i 1) (Pi.single j 1) ⊆ stdSimplex 𝕜 ι

The edges are contained in the simplex.

Defined in

Mathlib.Analysis.Convex.StdSimplex

Cited by

1 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderFintypeDecidableEqZeroLEOneClassIsOrderedRing