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Theorems · Theorem · group theory

AddSubgroup.FG.finset_sup

∀ {G : Type u_3} [inst : AddGroup G] {ι : Type u_5} (s : Finset ι) (P : ι → AddSubgroup G),
  (∀ i ∈ s, (P i).FG) → (s.sup P).FG
Defined in
Mathlib.GroupTheory.Finiteness
Cited by
1 results in Mathlib
Foundations
Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroup
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Around this declaration

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

AddSubgroup.FG.biSup_finset · cited by 1FG.biSup_finsetFinset · cited by 13712FinsetAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupFinset.sup · cited by 530Finset.supAddSubgroup.FG · cited by 21AddSubgroup.FGFinset.sup_induction · cited by 8Finset.sup_inductionAddSubgroup.FG.bot · cited by 1FG.botAddSubgroup.FG.sup · cited by 1FG.supFG.finset_supCITED BYCITES

Cites8

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Cited by1

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