Theorems · Theorem · convex and discrete geometry
stdSimplex_subset_Icc
∀ (𝕜 : Type u_2) {ι : Type u_1} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : Fintype ι]
[IsOrderedAddMonoid 𝕜], stdSimplex 𝕜 ι ⊆ Set.Icc 0 1stdSimplex 𝕜 ι is a subset of the unit cube
- Defined in
- Mathlib.Analysis.Convex.StdSimplex
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 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 and proof · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Fintypestatement and proof · cited by 7,736
- PartialOrderstatement and proof · cited by 6,410
- Set.Iccstatement and proof · cited by 1,702
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- stdSimplexstatement and proof · cited by 76
- Set.mem_iInterproof · cited by 69
- Set.pi_univ_Iccproof · cited by 11
- mem_Icc_of_mem_stdSimplexproof · cited by 3
- Set.univ_pi_eq_iInterproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- isCompact_stdSimplexproof · cited by 1