Theorems · Theorem · convex and discrete geometry
convex_stdSimplex
∀ (𝕜 : Type u_2) (ι : Type u_1) [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : Fintype ι] [IsOrderedRing 𝕜], Convex 𝕜 (stdSimplex 𝕜 ι)
- Defined in
- Mathlib.Analysis.Convex.StdSimplex
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Fintypestatement and proof · cited by 7,736
- PartialOrderstatement and proof · cited by 6,410
- Finset.sumproof · cited by 5,195
- mul_oneproof · cited by 3,885
- Finset.univproof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- IsOrderedRingstatement and proof · cited by 777
- Convexstatement · cited by 551
- mul_nonnegproof · cited by 397
- smul_eq_mulproof · cited by 357
- Finset.sum_add_distribproof · cited by 131
Cited by3
Results whose statement or proof uses this declaration.
- convexHull_basis_eq_stdSimplexproof · cited by 2
- segment_single_subset_stdSimplexproof · cited by 1
- isPathConnected_stdSimplexproof · cited by 0