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Theorems · Theorem · group theory

vadd_iterate_apply

∀ {M : Type u_1} {α : Type u_5} [inst : AddMonoid M] [inst_1 : AddAction M α] (a : M) (n : ℕ) (x : α),
  (fun x => a +ᵥ x)^[n] x = n • a +ᵥ x
Defined in
Mathlib.Algebra.Group.Action.Defs
Cited by
2 results in Mathlib
Foundations
Depth 12 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.

AddAction.isPeriodicPt_vadd_iff · cited by 4AddAction.isPeriodicPt_va…AddAction.nsmul_period_vadd · cited by 2AddAction.nsmul_period_va…AddMonoid · cited by 2864AddMonoidHVAdd.hVAdd · cited by 1820HVAdd.hVAddAddAction · cited by 820AddActionNat.iterate · cited by 740Nat.iteratevadd_iterate · cited by 2vadd_iteratevadd_iterate_applyCITED BYCITES

Cites5

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Cited by2

Results whose statement or proof uses this declaration.