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Theorems · Theorem · group theory

add_left_iterate_apply_zero

∀ {M : Type u_4} [inst : AddMonoid M] {n : ℕ} (a : M), (fun x => a + x)^[n] 0 = n • a
Defined in
Mathlib.Algebra.Group.Basic
Cited by
3 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext, Quot.sound
Assumes
AddMonoid
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

addOrderOf_nsmul_eq_zero · cited by 11addOrderOf_nsmul_eq_zeroisPeriodicPt_add_iff_nsmul_eq_zero · cited by 10isPeriodicPt_add_iff_nsmu…nsmul_injOn_Iio_addOrderOf · cited by 1nsmul_injOn_Iio_addOrderOfAddMonoid · cited by 2864AddMonoidadd_zero · cited by 2707add_zeroNat.iterate · cited by 740Nat.iterateadd_left_iterate · cited by 10add_left_iterateadd_left_iterate_apply_zeroCITED BYCITES

Cites4

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

Cited by3

Results whose statement or proof uses this declaration.