Mathlib Map

Theorems · Theorem · convex and discrete geometry

Pi.isAffineMap_eval

∀ {R : Type u_2} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : IsStrictOrderedRing R] {ι : Type u_3}
  {X : ι → Type u_4} [inst_3 : (i : ι) → Convexity.ConvexSpace R (X i)] {i : ι}, Convexity.IsAffineMap R fun x => x i
Defined in
Mathlib.Geometry.Convex.ConvexSpace.Prod
Cited by
2 results in Mathlib
Foundations
Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringPartialOrderIsStrictOrderedRingConvexity.ConvexSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Pi.convexCombPair_apply · cited by 1Pi.convexCombPair_applyPi.iConvexComb_apply · cited by 0Pi.iConvexComb_applySemiring · cited by 13802SemiringPartialOrder · cited by 6410PartialOrderIsStrictOrderedRing · cited by 2490IsStrictOrderedRingConvexity.ConvexSpace · cited by 176Convexity.ConvexSpaceConvexity.StdSimplex · cited by 123Convexity.StdSimplexConvexity.IsAffineMap · cited by 33Convexity.IsAffineMapPi.sConvexComb_apply · cited by 1Pi.sConvexComb_applyPi.isAffineMap_evalCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.