Theorems · Theorem · group theory
Set.smul_mem_smul_set
∀ {α : Type u_2} {β : Type u_3} [inst : SMul α β] {s : Set β} {a : α} {b : β}, b ∈ s → a • b ∈ a • s- Cited by
- 39 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- SMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.smulSetstatement · cited by 608
- Set.mem_image_of_memproof · cited by 371
Cited by39
Results whose statement or proof uses this declaration.
- gauge_smul_of_nonnegproof · cited by 7
- Submodule.smul_mem_pointwise_smulproof · cited by 6
- gauge_add_leproof · cited by 4
- MulAction.isPreprimitive_of_is_two_pretransitiveproof · cited by 3
- Convex.combo_interior_closure_mem_interiorproof · cited by 3
- MulAction.stabilizer_mul_selfproof · cited by 3
- Bornology.IsVonNBounded.smul_tendsto_zeroproof · cited by 3
- Convex.combo_closure_interior_mem_interiorproof · cited by 2
- Ideal.smul_mem_pointwise_smulproof · cited by 2
- Subgroup.smul_mem_pointwise_smulproof · cited by 2
- UniformConvergenceCLM.isVonNBounded_image2_applyproof · cited by 2