Theorems · Theorem
Multiplicative.toAdd_image_nsmul
∀ {M : Type u_1} [inst : AddMonoid M] (n : ℕ) (s : Set (Multiplicative M)),
⇑Multiplicative.toAdd '' s ^ n = n • ⇑Multiplicative.toAdd '' s- Defined in
- Mathlib.Algebra.Group.TypeTags.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- Set.imagestatement and proof · cited by 5,609
- AddMonoidstatement and proof · cited by 2,864
- pow_zeroproof · cited by 1,094
- Multiplicativestatement and proof · cited by 875
- pow_succproof · cited by 374
- Multiplicative.toAddstatement and proof · cited by 161
- zero_nsmulproof · cited by 137
- succ_nsmulproof · cited by 65
- Set.NPowstatement · cited by 51
Cited by1
Results whose statement or proof uses this declaration.
- Finsupp.image_pow_eq_finsuppProd_imageproof · cited by 1