Theorems · Theorem · group theory
IsIdempotentElem.coe_powers
∀ {M : Type u_1} [inst : Monoid M] {a : M}, IsIdempotentElem a → ↑(Submonoid.powers a) = {1, a}- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Monoidstatement and proof · cited by 3,887
- mul_oneproof · cited by 3,885
- Submonoidstatement and proof · cited by 3,086
- one_mulproof · cited by 2,841
- le_antisymmproof · cited by 2,068
- Submonoid.powersstatement and proof · cited by 408
- IsIdempotentElemstatement and proof · cited by 217
- OneMemClass.one_memproof · cited by 87
- Submonoid.powers_leproof · cited by 19
- Submonoid.mem_powersproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.exists_le_prime_notMem_of_isIdempotentElemproof · cited by 1