Theorems · Theorem · ring theory
isIdempotentElem_one_sub_one_sub_pow_pow
∀ {R : Type u_1} [inst : Ring R] (x : R) (n : ℕ), (x - x ^ 2) ^ n = 0 → IsIdempotentElem (1 - (1 - x ^ n) ^ n)- Defined in
- Mathlib.RingTheory.Idempotents
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Finset.sumproof · cited by 5,195
- one_mulproof · cited by 2,841
- Finset.sum_congrproof · cited by 2,323
- Finset.rangeproof · cited by 1,341
- one_powproof · cited by 521
- sub_eq_zeroproof · cited by 407
- IsIdempotentElemstatement · cited by 217
- pow_twoproof · cited by 150
- sub_sub_cancelproof · cited by 105
- zero_dvd_iffproof · cited by 37
- Commute.mul_powproof · cited by 22
Cited by1
Results whose statement or proof uses this declaration.
- exists_isIdempotentElem_mul_eq_zero_of_ker_isNilpotent_auxproof · cited by 1