Theorems · Theorem · group theory
IsUnit.eq_div_iff
∀ {α : Type u} [inst : DivisionMonoid α] {a b c : α}, IsUnit c → (a = b / c ↔ a * c = b)- Defined in
- Mathlib.Algebra.Group.Units.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- 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.
- IsUnitstatement and proof · cited by 1,602
- div_eq_mul_invproof · cited by 715
- DivisionMonoidstatement and proof · cited by 201
- IsUnit.eq_mul_inv_iff_mul_eqproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- eq_div_iffproof · cited by 38
- eq_div_iff_mul_eqproof · cited by 19
- IsUnit.eq_div_of_mul_eqproof · cited by 1