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Theorems · Theorem · group theory

AddSubmonoid.FG.finset_sup

∀ {M : Type u_1} [inst : AddMonoid M] {ι : Type u_3} (s : Finset ι) (P : ι → AddSubmonoid M),
  (∀ i ∈ s, (P i).FG) → (s.sup P).FG
Defined in
Mathlib.GroupTheory.Finiteness
Cited by
1 results in Mathlib
Foundations
Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddMonoid
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Around this declaration

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

AddSubmonoid.FG.biSup_finset · cited by 1FG.biSup_finsetFinset · cited by 13712FinsetAddMonoid · cited by 2864AddMonoidAddSubmonoid · cited by 1178AddSubmonoidFinset.sup · cited by 530Finset.supAddSubmonoid.FG · cited by 36AddSubmonoid.FGFinset.sup_induction · cited by 8Finset.sup_inductionAddSubmonoid.FG.sup · cited by 2FG.supAddSubmonoid.FG.bot · cited by 1FG.botFG.finset_supCITED BYCITES

Cites8

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Cited by1

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