Theorems · Theorem · group theory
IsUnit.mul_div_cancel
∀ {α : Type u} [inst : DivisionCommMonoid α] {a : α}, IsUnit a → ∀ (b : α), a * (b / a) = b- Defined in
- Mathlib.Algebra.Group.Units.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- DivisionCommMonoid
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.
- mul_commproof · cited by 2,262
- IsUnitstatement and proof · cited by 1,602
- DivisionCommMonoidstatement and proof · cited by 80
- IsUnit.div_mul_cancelproof · cited by 37
Cited by5
Results whose statement or proof uses this declaration.
- mul_div_cancel₀proof · cited by 77
- WeierstrassCurve.Projective.addXYZ_of_Z_ne_zeroproof · cited by 1
- WeierstrassCurve.Projective.dblXYZ_of_Z_ne_zeroproof · cited by 1
- WeierstrassCurve.Jacobian.addXYZ_of_Z_ne_zeroproof · cited by 1
- WeierstrassCurve.Jacobian.dblXYZ_of_Z_ne_zeroproof · cited by 1