Theorems · Theorem · group theory
AddSubgroup.pointwise_smul_le_iff
∀ {G : Type u_2} {A : Type u_4} [inst : Group G] [inst_1 : AddGroup A] [inst_2 : DistribMulAction G A]
{S T : AddSubgroup A} {a : G}, a • S ≤ T ↔ S ≤ a⁻¹ • T- Defined in
- Mathlib.Algebra.GroupWithZero.Subgroup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
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Cites6
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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- DistribMulActionstatement and proof · cited by 584
- AddSubgroup.pointwiseMulActionstatement · cited by 24
- Set.smul_set_subset_iff_subset_inv_smul_setproof · cited by 9
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