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Theorems · Theorem · general algebraic systems

FunLike.coe_pow_eq_iterate

∀ {F' : Type u_4} {α : Type u_5} [inst : FunLike F' α α] [inst_1 : Monoid F'] [IsMulApplyEqComp F' α]
  [IsOneApplyEqSelf F' α] (f : F') (n : ℕ), ⇑(f ^ n) = (⇑f)^[n]
Defined in
Mathlib.Data.FunLike.IsApply
Cited by
2 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Quot.sound
Assumes
FunLikeMonoidIsMulApplyEqCompIsOneApplyEqSelf
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ContinuousLinearMap.toLinearMap_pow · cited by 4ContinuousLinearMap.toLin…ContinuousLinearMap.coe_pow' · cited by 0ContinuousLinearMap.coe_p…DFunLike.coe · cited by 62936DFunLike.coeMonoid · cited by 3887MonoidFunLike · cited by 2560FunLikeNat.iterate · cited by 740Nat.iterateIsOneApplyEqSelf · cited by 12IsOneApplyEqSelfIsMulApplyEqComp · cited by 7IsMulApplyEqComppow_apply_eq_iterate · cited by 1pow_apply_eq_iterateFunLike.coe_pow_eq_iterateCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.