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Theorems · Theorem · group theory

AddSubmonoid.closure_addIrreducible

∀ {M : Type u_1} [inst : AddCancelCommMonoid M] [Subsingleton (AddUnits M)] [AddMonoid.FG M],
  AddSubmonoid.closure {p | AddIrreducible p} = ⊤

A finitely generated cancellative additive monoid with a single unit is generated by its (finitely many) irreducible elements.

Defined in
Mathlib.Algebra.AffineMonoid.Irreducible
Cited by
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Foundations
Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCancelCommMonoidSubsingletonAddMonoid.FG

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