Theorems · Theorem · group theory
eq_of_div_eq_one
∀ {α : Type u_1} [inst : DivisionMonoid α] {a b : α}, a / b = 1 → a = b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- DivisionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- div_eq_mul_invproof · cited by 715
- DivisionMonoidstatement and proof · cited by 201
- inv_injectiveproof · cited by 17
- inv_eq_of_mul_eq_one_rightproof · cited by 15
Cited by6
Results whose statement or proof uses this declaration.
- div_eq_oneproof · cited by 11
- real_inner_div_norm_mul_norm_eq_one_iffproof · cited by 2
- div_ne_one_of_neproof · cited by 1
- norm_inner_div_norm_mul_norm_eq_one_iffproof · cited by 1
- IsUnit.div_eq_one_iff_eqproof · cited by 1
- IsFractionRing.associated_den_num_invproof · cited by 1