Theorems · Theorem · ring theory

TrivSqZeroExt.snd_pow_of_smul_comm

∀ {R : Type u} {M : Type v} [inst : Monoid R] [inst_1 : AddMonoid M] [inst_2 : DistribMulAction R M]
  [inst_3 : DistribMulAction Rᵐᵒᵖ M] [SMulCommClass R Rᵐᵒᵖ M] (x : TrivSqZeroExt R M) (n : ℕ),
  MulOpposite.op x.fst • x.snd = x.fst • x.snd → (x ^ n).snd = n • x.fst ^ n.pred • x.snd

Defined in

Mathlib.Algebra.TrivSqZeroExt.Basic

Cited by

3 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MonoidAddMonoidDistribMulActionDistribMulActionSMulCommClass