Theorems · Theorem · group theory
IsIdempotentElem.eq
∀ {M : Type u_1} [inst : Mul M] {a : M}, IsIdempotentElem a → a * a = a- Defined in
- Mathlib.Algebra.Group.Idempotent
- Cited by
- 42 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- Mul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsIdempotentElemstatement and proof · cited by 217
Cited by42
Results whose statement or proof uses this declaration.
- IsIdempotentElem.one_subproof · cited by 20
- OrthogonalIdempotents.mul_eqproof · cited by 8
- IsIdempotentElem.pow_succ_eqproof · cited by 7
- BooleanRing.mul_selfproof · cited by 7
- IsIdempotentElem.mapproof · cited by 5
- Ideal.isIdempotentElem_iff_of_fgproof · cited by 5
- IsIdempotentElem.mul_one_sub_selfproof · cited by 4
- IsIdempotentElem.one_sub_mul_selfproof · cited by 4
- IsIdempotentElem.mul_of_commuteproof · cited by 3
- PrimeSpectrum.basicOpen_eq_zeroLocus_of_isIdempotentElemproof · cited by 3
- IsIdempotentElem.subproof · cited by 3
- exists_isIdempotentElem_mul_eq_zero_of_ker_isNilpotentproof · cited by 2