Theorems · Theorem · group theory
IsUnit.div_eq_div_iff
∀ {α : Type u} [inst : DivisionCommMonoid α] {a b c d : α}, IsUnit b → IsUnit d → (a / b = c / d ↔ a * d = c * b)- Defined in
- Mathlib.Algebra.Group.Units.Basic
- Cited by
- 3 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_assocproof · cited by 1,667
- IsUnitstatement and proof · cited by 1,602
- mul_right_commproof · cited by 108
- DivisionCommMonoidstatement and proof · cited by 80
- IsUnit.div_mul_cancelproof · cited by 37
- IsUnit.mulproof · cited by 32
- IsUnit.mul_left_injproof · cited by 20
Cited by3
Results whose statement or proof uses this declaration.
- div_eq_div_iffproof · cited by 22
- IsUnit.mul_inv_eq_mul_inv_iffproof · cited by 1
- IsUnit.inv_mul_eq_inv_mul_iffproof · cited by 1