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Theorems · Theorem · functional analysis

AbsConvex.empty

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : SeminormedRing 𝕜] [inst_1 : SMul 𝕜 E] [inst_2 : AddCommMonoid E]
  [inst_3 : PartialOrder 𝕜], AbsConvex 𝕜 ∅
Defined in
Mathlib.Analysis.LocallyConvex.AbsConvex
Cited by
1 results in Mathlib
Foundations
Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedRingSMulAddCommMonoidPartialOrder
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Around this declaration

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

absConvexHull_empty · cited by 1absConvexHull_emptySet · cited by 53352SetAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderSeminormedRing · cited by 446SeminormedRingAbsConvex · cited by 31AbsConvexconvex_empty · cited by 5convex_emptybalanced_empty · cited by 1balanced_emptyAbsConvex.emptyCITED BYCITES

Cites7

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

Cited by1

Results whose statement or proof uses this declaration.