Theorems · Theorem · group theory
Units.mul_inv
∀ {α : Type u} [inst : Monoid α] (a : αˣ), ↑a * ↑a⁻¹ = 1- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 67 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- Monoid
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.
- Monoidstatement and proof · cited by 3,887
- Unitsstatement and proof · cited by 2,804
- Units.valstatement · cited by 1,966
- Units.val_invproof · cited by 8
Cited by67
Results whose statement or proof uses this declaration.
- Associated.symmproof · cited by 87
- Units.ne_zeroproof · cited by 68
- Units.val_inv_eq_inv_valproof · cited by 57
- IsUnit.val_inv_mulproof · cited by 35
- IsUnit.mul_val_invproof · cited by 29
- Units.mul_inv_cancel_rightproof · cited by 20
- map_ne_zeroproof · cited by 20
- Units.mul_inv_cancel_leftproof · cited by 10
- Units.mul_right_dvdproof · cited by 7
- invOf_unitsproof · cited by 7
- IsUnit.mul_inv_cancelproof · cited by 6
- Ring.mul_inverse_cancelproof · cited by 6