Theorems · Theorem · group theory

Set.image_pow

∀ {F : Type u_1} {α : Type u_2} {β : Type u_3} [inst : Monoid α] [inst_1 : Monoid β] [inst_2 : FunLike F α β]
  [MonoidHomClass F α β] (f : F) (s : Set α) (n : ℕ), ⇑f '' s ^ n = (⇑f '' s) ^ n

Defined in: Mathlib.Algebra.Group.Pointwise.Set.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Monoid Monoid FunLike MonoidHomClass

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Cites12

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
Set.imagestatement and proof · cited by 5,609
Monoidstatement and proof · cited by 3,887
FunLikestatement and proof · cited by 2,560
pow_zeroproof · cited by 1,094
map_oneproof · cited by 861
MonoidHomClassstatement and proof · cited by 244
Set.NPowstatement · cited by 51
Set.monoidstatement · cited by 19
Set.image_oneproof · cited by 5
Set.image_pow_of_ne_zeroproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

Finsupp.image_pow_eq_finsuppProd_imageproof · cited by 1