Mathlib Map

Theorems · Theorem · group theory

Submonoid.FG.biSup_finset

∀ {M : Type u_1} [inst : Monoid M] {ι : Type u_3} (s : Finset ι) (P : ι → Submonoid M),
  (∀ i ∈ s, (P i).FG) → (⨆ i ∈ s, P i).FG
Defined in
Mathlib.GroupTheory.Finiteness
Cited by
1 results in Mathlib
Foundations
Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Monoid
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Submonoid.FG.biSup · cited by 1FG.biSupFinset · cited by 13712FinsetMonoid · cited by 3887MonoidSubmonoid · cited by 3086SubmonoidiSup · cited by 2415iSupFinset.sup_eq_iSup · cited by 30Finset.sup_eq_iSupSubmonoid.FG · cited by 24Submonoid.FGSubmonoid.FG.finset_sup · cited by 1FG.finset_supFG.biSup_finsetCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.