Theorems · Theorem · commutative algebra
ValuationSubring.smul_mem_pointwise_smul_iff
∀ {K : Type u} [inst : Field K] {G : Type u_1} [inst_1 : Group G] [inst_2 : MulSemiringAction G K] {g : G}
{S : ValuationSubring K} {x : K}, g • x ∈ g • S ↔ x ∈ S- Cited by
- 0 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldGroupMulSemiringAction
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Groupstatement and proof · cited by 6,238
- MulSemiringActionstatement and proof · cited by 423
- ValuationSubringstatement and proof · cited by 187
- Set.smul_mem_smul_set_iffproof · cited by 14
- ValuationSubring.pointwiseHasSMulstatement · cited by 10
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