Theorems · Theorem · global analysis

tangentConeAt_mono_field

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : AddCommGroup E] [inst_1 : SMul 𝕜 E] [inst_2 : TopologicalSpace E] {s : Set E}
  {x : E} {𝕜' : Type u_3} [inst_3 : Monoid 𝕜'] [inst_4 : SMul 𝕜 𝕜'] [inst_5 : MulAction 𝕜' E] [IsScalarTower 𝕜 𝕜' E],
  tangentConeAt 𝕜 s x ⊆ tangentConeAt 𝕜' s x

Given x ∈ s and a semiring extension 𝕜 ⊆ 𝕜', the tangent cone of s at x with respect to 𝕜 is contained in the tangent cone of s at x with respect to 𝕜'.

Defined in

Mathlib.Analysis.Calculus.TangentCone.Basic

Cited by

3 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupSMulTopologicalSpaceMonoidSMulMulActionIsScalarTower