Theorems · Theorem · group theory
div_eq_one
∀ {G : Type u_3} [inst : Group G] {a b : G}, a / b = 1 ↔ a = b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- Group
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.
- Groupstatement and proof · cited by 6,238
- div_self'proof · cited by 25
- eq_of_div_eq_oneproof · cited by 6
Cited by11
Results whose statement or proof uses this declaration.
- Subgroup.cyclic_of_minproof · cited by 2
- sdiv_left_cancelproof · cited by 2
- modularCyclotomicCharacter.pow_dvd_aux_pow_sub_aux_powproof · cited by 2
- isMulTorsionFree_iff_not_isOfFinOrderproof · cited by 2
- norm_div_eq_zero_iffproof · cited by 2
- eq_of_mabs_div_eq_oneproof · cited by 1
- div_ne_oneproof · cited by 0
- MeasureTheory.div_ae_eq_oneproof · cited by 0
- eq_of_norm_div_le_zeroproof · cited by 0
- div_eq_one_of_eqproof · cited by 0
- eq_iff_eq_of_div_eq_divproof · cited by 0