Theorems · Theorem · convex and discrete geometry
single_mem_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] (i : ι), Pi.single i 1 ∈ stdSimplex 𝕜 ι- Defined in
- Mathlib.Analysis.Convex.StdSimplex
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · 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
- Finset.univproof · cited by 3,473
- le_rflproof · cited by 1,558
- Pi.singlestatement · cited by 518
- zero_le_oneproof · cited by 316
- ZeroLEOneClassstatement and proof · cited by 304
- stdSimplexstatement · cited by 76
- Finset.sum_pi_single'proof · cited by 18
- le_update_iffproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- ite_eq_mem_stdSimplexproof · cited by 1
- stdSimplexHomeomorphUnitInterval_onestatement · cited by 1
- stdSimplexHomeomorphUnitInterval_zerostatement · cited by 1
- segment_single_subset_stdSimplexproof · cited by 1
- SSet.stdSimplex.δ_one_toSSetObjIproof · cited by 1
- SSet.stdSimplex.δ_zero_toSSetObjIproof · cited by 1
- stdSimplexEquivIcc_onestatement · cited by 0
- stdSimplexEquivIcc_zerostatement · cited by 0
- diam_stdSimplexproof · cited by 0
- isPathConnected_stdSimplexproof · cited by 0