Theorems · Theorem · group theory
IsUnit.exists_right_inv
∀ {M : Type u_1} [inst : Monoid M] {a : M}, IsUnit a → ∃ b, a * b = 1- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- Units.casesOnproof · cited by 15
Cited by11
Results whose statement or proof uses this declaration.
- isUnit_iff_exists_invproof · cited by 21
- Polynomial.Monic.eq_one_of_isUnitproof · cited by 6
- Polynomial.natDegree_eq_zero_of_isUnitproof · cited by 5
- IsUnit.smul_uniformityproof · cited by 2
- IsLocalHom.isFieldproof · cited by 2
- Polynomial.coeff_isUnit_isNilpotent_of_isUnitproof · cited by 2
- AlgebraicGeometry.RingedSpace.isUnit_res_of_isUnit_germproof · cited by 1
- AlgebraicGeometry.RingedSpace.isUnit_of_isUnit_germproof · cited by 1
- RingPreordering.hasIdealSupport_of_isUnit_twoproof · cited by 0
- AffineSubspace.shift_eq_map_homothetyproof · cited by 0
- divisor_closure_eq_closureproof · cited by 0