Theorems · Theorem · group theory
IsUnit.mul_inv_cancel
∀ {α : Type u} [inst : DivisionMonoid α] {a : α}, IsUnit a → a * a⁻¹ = 1- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- DivisionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- DivisionMonoidstatement and proof · cited by 201
- Units.mul_invproof · cited by 67
- Units.val_inv_eq_inv_valproof · cited by 57
Cited by7
Results whose statement or proof uses this declaration.
- IsUnit.unit'proof · cited by 14
- IsUnit.div_selfproof · cited by 3
- IsUnit.eq_on_invproof · cited by 2
- Real.qaryEntropy_strictMonoOnproof · cited by 1
- IsUnit.div_div_cancel_leftproof · cited by 1
- Commute.inv_mul_eq_inv_mul_iff_of_isUnitproof · cited by 1
- IsUnit.mul_one_div_cancelproof · cited by 1