Theorems · Theorem · group theory
AddSubgroup.injective_noncommPiCoprod_of_iSupIndep
∀ {G : Type u_1} [inst : AddGroup G] {ι : Type u_2} {H : ι → AddSubgroup G} [inst_1 : Fintype ι]
{hcomm : Pairwise fun i j => ∀ (x y : G), x ∈ H i → y ∈ H j → AddCommute x y},
iSupIndep H → Function.Injective ⇑(AddSubgroup.noncommPiCoprod hcomm)- Defined in
- Mathlib.GroupTheory.NoncommPiCoprod
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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- DFunLike.coestatement · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement · cited by 3,230
- Pairwisestatement and proof · cited by 516
- Subtype.coe_injectiveproof · cited by 205
- AddCommutestatement and proof · cited by 185
- iSupIndepstatement and proof · cited by 100
- AddSubgroup.subtypeproof · cited by 82
- AddSubgroup.range_subtypeproof · cited by 16
- AddSubgroup.noncommPiCoprodstatement · cited by 5
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