Theorems · Theorem · group theory
pow_two
∀ {M : Type u_2} [inst : Monoid M] (a : M), a ^ 2 = a * aNote that most of the lemmas about powers of two refer to it as sq.
- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 150 results in Mathlib
- Foundations
- Depth 11 from the axioms, rests on 52 definitions · uses no axioms
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by150
Results whose statement or proof uses this declaration.
- sqproof · cited by 280
- one_le_mabsproof · cited by 11
- real_inner_self_eq_norm_sqproof · cited by 7
- inner_self_eq_norm_sqproof · cited by 7
- IsRadical.squarefreeproof · cited by 6
- Algebra.Generators.Cotangent.exactproof · cited by 6
- InnerProductGeometry.angle_add_eq_arcsin_of_inner_eq_zeroproof · cited by 5
- EuclideanGeometry.dist_orthogonalProjection_eq_infDistproof · cited by 5
- MulArchimedeanClass.min_le_mk_mulproof · cited by 4
- ProbabilityTheory.variance_eq_subproof · cited by 4
- isSquare_iff_exists_sqproof · cited by 4
- Algebra.discr_eq_det_embeddingsMatrixReindex_pow_twoproof · cited by 4