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Theorems · Theorem · general algebraic systems

pow_apply_eq_iterate

∀ {F : Type u_1} {α : Type u_2} [inst : FunLike F α α] [inst_1 : Monoid F] [IsOneApplyEqSelf F α] [IsMulApplyEqComp F α]
  (f : F) (n : ℕ) (x : α), (f ^ n) x = (⇑f)^[n] x
Defined in
Mathlib.Data.FunLike.IsApply
Cited by
1 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext, Quot.sound
Assumes
FunLikeMonoidIsOneApplyEqSelfIsMulApplyEqComp
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

FunLike.coe_pow_eq_iterate · cited by 2FunLike.coe_pow_eq_iterateDFunLike.coe · cited by 62936DFunLike.coeMonoid · cited by 3887MonoidFunLike · cited by 2560FunLikepow_zero · cited by 1094pow_zeroNat.iterate · cited by 740Nat.iteratepow_succ' · cited by 228pow_succ'one_apply_eq_self · cited by 34one_apply_eq_selfIsOneApplyEqSelf · cited by 12IsOneApplyEqSelfmul_apply_eq_comp · cited by 10mul_apply_eq_compIsMulApplyEqComp · cited by 7IsMulApplyEqComppow_apply_eq_iterateCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.