Theorems · Theorem · group theory
sq
∀ {M : Type u_2} [inst : Monoid M] (a : M), a ^ 2 = a * aAlias of pow_two.
Note that most of the lemmas about powers of two refer to it as sq.
- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 280 results in Mathlib
- Foundations
- Depth 12 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.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by280
Results whose statement or proof uses this declaration.
- sq_nonnegproof · cited by 106
- Real.sq_sqrtproof · cited by 53
- sq_absproof · cited by 49
- Complex.I_sqproof · cited by 40
- Real.sqrt_sqproof · cited by 36
- mul_self_nonnegproof · cited by 35
- neg_sqproof · cited by 31
- Real.sin_pi_div_twoproof · cited by 29
- Int.units_mul_selfproof · cited by 27
- Real.sqrt_eq_rpowproof · cited by 25
- Complex.normSq_eq_norm_sqproof · cited by 14
- Real.sqrt_sq_eq_absproof · cited by 13
Showing the 200 most cited of 280.