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Theorems · Definition · group theory

AddSubgroup.prodEquiv

{G : Type u_1} →
  [inst : AddGroup G] →
    {N : Type u_5} → [inst_1 : AddGroup N] → (H : AddSubgroup G) → (K : AddSubgroup N) → ↥(H.prod K) ≃+ ↥H × ↥K

Product of additive subgroups is isomorphic to their product as additive groups

Defined in
Mathlib.Algebra.Group.Subgroup.Basic
Cited by
1 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Quot.sound
Assumes
AddGroupAddGroup
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddGroup.isAddCyclic_prod_iff · cited by 0AddGroup.isAddCyclic_prod…Equiv · cited by 8337EquivSetLike.coe · cited by 8199SetLike.coeSet.Elem · cited by 7166Set.ElemAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupSProd.sprod · cited by 1750SProd.sprodAddEquiv · cited by 1087AddEquivAddSubgroup.prod · cited by 34AddSubgroup.prodEquiv.Set.prod · cited by 9Set.prodAddSubgroup.prodEquivCITED BYCITES

Cites9

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Cited by1

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