Theorems · Theorem · commutative algebra
AddSubmonoid.pow_eq_closure_pow_set
∀ {R : Type u_2} [inst : Semiring R] (s : AddSubmonoid R) (n : ℕ), s ^ n = AddSubmonoid.closure (↑s ^ n)- Defined in
- Mathlib.Algebra.Ring.Submonoid.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- SetLike.coestatement and proof · cited by 8,199
- AddSubmonoidstatement and proof · cited by 1,178
- AddSubmonoid.closurestatement · cited by 224
- Set.NPowstatement · cited by 51
- AddSubmonoid.closure_eqproof · cited by 10
- AddSubmonoid.monoidstatement · cited by 5
- AddSubmonoid.closure_powproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AddSubmonoid.pow_subset_powproof · cited by 1