Theorems · Theorem · group theory
IsIdempotentElem.pow_succ_eq
∀ {M : Type u_1} [inst : Monoid M] {a : M} (n : ℕ), IsIdempotentElem a → a ^ (n + 1) = a- Defined in
- Mathlib.Algebra.Group.Idempotent
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- pow_oneproof · cited by 894
- pow_succproof · cited by 374
- IsIdempotentElemstatement and proof · cited by 217
- IsIdempotentElem.eqproof · cited by 42
Cited by7
Results whose statement or proof uses this declaration.
- Algebra.FormallyUnramified.bijective_of_isAlgClosed_of_isLocalRingproof · cited by 1
- IsIdempotentElem.pow_eqproof · cited by 1
- exists_isIdempotentElem_mul_eq_zero_of_ker_isNilpotent_auxproof · cited by 1
- Ideal.isIdempotentElem_iff_eq_bot_or_top_of_isLocalRingproof · cited by 1
- IsIdempotentElem.eq_zero_of_isNilpotentproof · cited by 1
- IsLocalization.Away.algebraMap_surjective_of_isIdempotentElemproof · cited by 1
- IsStarProjection.pow_succ_eqproof · cited by 0