Mathlib Map

Theorems · Theorem · group theory

Set.smul_subset_iff

∀ {α : Type u_2} {β : Type u_3} [inst : SMul α β] {s : Set α} {t u : Set β}, s • t ⊆ u ↔ ∀ a ∈ s, ∀ b ∈ t, a • b ∈ u
Defined in
Mathlib.Algebra.Group.Pointwise.Set.Scalar
Cited by
6 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SMul
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

IsClosed.smul_left_of_isCompact · cited by 5IsClosed.smul_left_of_isC…smul_set_closure_subset · cited by 2smul_set_closure_subsetIsLinearTopology.hasBasis_subbimodule · cited by 2IsLinearTopology.hasBasis…AddSubmonoid.smul_subset_smul · cited by 2AddSubmonoid.smul_subset_…UniformFun.continuousSMul_induced_of_range_bounded · cited by 1UniformFun.continuousSMul…IsClosed.smul_right_of_isCompact · cited by 0IsClosed.smul_right_of_is…Set · cited by 53352SetSet.smul · cited by 110Set.smulSet.image2_subset_iff · cited by 30Set.image2_subset_iffSet.smul_subset_iffCITED BYCITES

Cites3

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

Cited by6

Results whose statement or proof uses this declaration.