Theorems · Theorem · group theory
Submonoid.fg_of_divisive
∀ {M : Type u_5} [inst : CommMonoid M] [inst_1 : PartialOrder M] [WellQuasiOrderedLE M] [IsOrderedCancelMonoid M]
[CanonicallyOrderedMul M] {P : Submonoid M}, (∀ x ∈ P, ∀ (y : M), x * y ∈ P → y ∈ P) → P.FGIn a canonically ordered and well-quasi-ordered monoid, any divisive submonoid is finitely generated.
- Defined in
- Mathlib.GroupTheory.Finiteness
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- PartialOrderstatement and proof · cited by 6,410
- Set.ofPredproof · cited by 6,101
- LE.le.transproof · cited by 3,151
- Submonoidstatement and proof · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- LT.lt.leproof · cited by 2,189
- LT.lt.neproof · cited by 872
- LT.lt.not_geproof · cited by 305
- MulMemClass.mul_memproof · cited by 173
- Submonoid.closureproof · cited by 167
- Minimalproof · cited by 150
Cited by2
Results whose statement or proof uses this declaration.
- Submonoid.fg_eqLocusMproof · cited by 0
- CommMonoid.fg_of_wellQuasiOrderedLEproof · cited by 0