Theorems · Theorem · group theory
Multiplicative.mem_toSubgroup
∀ {A : Type u_2} [inst : AddGroup A] (S : AddSubgroup A) (a : Multiplicative A),
a ∈ AddSubgroup.toSubgroup S ↔ Multiplicative.toAdd a ∈ S- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Equivstatement · cited by 8,337
- AddGroupstatement and proof · cited by 4,410
- Subgroupstatement · cited by 3,593
- AddSubgroupstatement and proof · cited by 3,232
- Multiplicativestatement and proof · cited by 875
- OrderIsostatement · cited by 874
- Multiplicative.toAddstatement · cited by 161
- AddSubgroup.toSubgroupstatement · cited by 15
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