Theorems · Theorem · group theory
sq_eq_one
∀ {M : Type u_1} [inst : Monoid M] [IsMulTorsionFree M] {a : M}, a ^ 2 = 1 ↔ a = 1See sq_eq_one_iff for a version that holds in rings.
- Defined in
- Mathlib.Algebra.Group.Torsion
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidIsMulTorsionFree
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.
- Monoidstatement and proof · cited by 3,887
- IsMulTorsionFreestatement and proof · cited by 44
- pow_eq_one_iff_leftproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- self_eq_invproof · cited by 2