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Theorems · Theorem · group theory

Set.smul_subset_smul_left

∀ {α : Type u_2} {β : Type u_3} [inst : SMul α β] {s : Set α} {t₁ t₂ : Set β}, t₁ ⊆ t₂ → s • t₁ ⊆ s • t₂
Defined in
Mathlib.Algebra.Group.Pointwise.Set.Scalar
Cited by
4 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
SMul
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Around this declaration

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

subset_mul_closure_one · cited by 4subset_mul_closure_onesubset_interior_smul_right · cited by 2subset_interior_smul_rightIsLinearTopology.hasBasis_subbimodule · cited by 2IsLinearTopology.hasBasis…Seminorm.ball_smul_ball · cited by 1Seminorm.ball_smul_ballSet · cited by 53352SetSet.smul · cited by 110Set.smulSet.image2_subset_left · cited by 12Set.image2_subset_leftSet.smul_subset_smul_leftCITED BYCITES

Cites3

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Cited by4

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