Theorems · Theorem · group theory
Submonoid.FG.prod
∀ {M : Type u_1} {N : Type u_2} [inst : Monoid M] [inst_1 : Monoid N] {P : Submonoid M} {Q : Submonoid N},
P.FG → Q.FG → (P.prod Q).FGThe product of two finitely generated submonoids is finitely generated.
- Defined in
- Mathlib.GroupTheory.Finiteness
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Bot.botproof · cited by 4,720
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement and proof · cited by 3,086
- SProd.sprodproof · cited by 1,750
- Submonoid.closureproof · cited by 167
- Finset.coe_singletonproof · cited by 145
- Finset.coe_unionproof · cited by 78
- Submonoid.prodstatement and proof · cited by 27
- Submonoid.FGstatement and proof · cited by 24
- Finset.coe_productproof · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.FG.prodproof · cited by 0