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Theorems · Theorem · group theory

vadd_iterate

∀ {M : Type u_1} {α : Type u_5} [inst : AddMonoid M] [inst_1 : AddAction M α] (a : M) (n : ℕ),
  (fun x => a +ᵥ x)^[n] = fun x => n • a +ᵥ x
Defined in
Mathlib.Algebra.Group.Action.Defs
Cited by
2 results in Mathlib
Foundations
Depth 11 from the axioms · uses propext, Quot.sound
Assumes
AddMonoidAddAction
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Around this declaration

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

vadd_iterate_apply · cited by 2vadd_iterate_applyergodic_vadd_of_denseRange_nsmul · cited by 1ergodic_vadd_of_denseRang…AddMonoid · cited by 2864AddMonoidHVAdd.hVAdd · cited by 1820HVAdd.hVAddAddAction · cited by 820AddActionNat.iterate · cited by 740Nat.iteratevadd_iterateCITED BYCITES

Cites4

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

Cited by2

Results whose statement or proof uses this declaration.