Theorems · Theorem · group theory
mul_left_iterate
∀ {M : Type u_4} [inst : Monoid M] (a : M) (n : ℕ), (fun x => a * x)^[n] = fun x => a ^ n * x- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Nat.iteratestatement · cited by 740
Cited by11
Results whose statement or proof uses this declaration.
- mul_left_iterate_apply_oneproof · cited by 3
- orderOf_pow'proof · cited by 3
- Ordinal.nfp_mul_oneproof · cited by 2
- WittVector.exists_eq_pow_p_mulproof · cited by 2
- IsOfFinOrder.orderOf_powproof · cited by 2
- Ordinal.nfp_mul_zeroproof · cited by 1
- LinearEquiv.isOfFinOrder_of_finite_of_span_eq_top_of_mapsToproof · cited by 1
- CommMonoid.torsion.isMulTorsionproof · cited by 1
- Equiv.pow_mulLeftproof · cited by 1
- ONote.fastGrowing_twoproof · cited by 1
- mul_left_iterate_applyproof · cited by 0