Theorems · Theorem · group theory
Submonoid.subset_pointwise_smul_iff
∀ {α : Type u_1} {M : Type u_3} [inst : Monoid M] [inst_1 : Group α] [inst_2 : MulDistribMulAction α M] {a : α}
{S T : Submonoid M}, S ≤ a • T ↔ a⁻¹ • S ≤ T- Cited by
- 0 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, 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
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement and proof · cited by 3,086
- MulDistribMulActionstatement and proof · cited by 120
- Submonoid.pointwiseMulActionstatement · cited by 20
- Set.subset_smul_set_iffproof · cited by 13
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