Theorems · Theorem · order theory
FiniteMulArchimedeanClass.subsemigroup_eq_subgroup
∀ {M : Type u_1} [inst : CommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedMonoid M]
{s : UpperSet (FiniteMulArchimedeanClass M)},
↑(MulArchimedeanClass.subsemigroup (FiniteMulArchimedeanClass.toUpperSetMulArchimedeanClass s)) =
↑(FiniteMulArchimedeanClass.subgroup s)- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
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- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Top.topstatement · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- SetLike.coestatement · cited by 8,199
- Subgroupstatement · cited by 3,593
- CommGroupstatement and proof · cited by 990
- OrderEmbeddingstatement · cited by 619
- IsOrderedMonoidstatement and proof · cited by 577
- Subsemigroupstatement · cited by 323
- UpperSetstatement and proof · cited by 245
- MulArchimedeanClassstatement · cited by 81
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