Theorems · Theorem · group theory
AddSubmonoid.pointwise_smul_le_pointwise_smul_iff
∀ {G : Type u_2} {A : Type u_4} [inst : AddMonoid A] [inst_1 : Group G] [inst_2 : DistribMulAction G A] {a : G}
{S T : AddSubmonoid A}, a • S ≤ a • T ↔ S ≤ T- Cited by
- 0 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement and proof · cited by 1,178
- DistribMulActionstatement and proof · cited by 584
- AddSubmonoid.pointwiseMulActionstatement · cited by 23
- Set.smul_set_subset_smul_set_iffproof · cited by 10
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