Theorems · Theorem · group theory
IsUnit.div_eq_iff
∀ {α : Type u} [inst : DivisionMonoid α] {a b c : α}, IsUnit b → (a / b = c ↔ a = c * b)- Defined in
- Mathlib.Algebra.Group.Units.Basic
- Cited by
- 4 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.mul_inv_eq_iff_eq_mulproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- div_eq_iffproof · cited by 37
- div_eq_iff_mul_eqproof · cited by 5
- IsUnit.div_eq_of_eq_mulproof · cited by 1
- groupCohomology.exists_div_of_norm_eq_oneproof · cited by 1