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Theorems · Theorem · convex and discrete geometry

stdSimplex.vertex.congr_simp

∀ {S : Type u_1} [inst : Semiring S] [inst_1 : PartialOrder S] {X : Type u_2} [inst_2 : Fintype X]
  [inst_3 : IsOrderedRing S] [inst_4 : DecidableEq X] (x x_1 : X), x = x_1 → stdSimplex.vertex x = stdSimplex.vertex x_1
Defined in
Mathlib.Analysis.Convex.StdSimplex
Cited by
1 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringPartialOrderFintypeIsOrderedRingDecidableEq
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

TopCat.toSSetObj₁Equiv_apply_zero · cited by 0TopCat.toSSetObj₁Equiv_ap…Semiring · cited by 13802SemiringFintype · cited by 7736FintypeSet.Elem · cited by 7166Set.ElemPartialOrder · cited by 6410PartialOrderIsOrderedRing · cited by 777IsOrderedRingstdSimplex · cited by 76stdSimplexstdSimplex.vertex · cited by 12stdSimplex.vertexvertex.congr_simpCITED BYCITES

Cites7

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Cited by1

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