Theorems · Theorem · group theory
IsUnit.unit_spec
∀ {M : Type u_1} [inst : Monoid M] {a : M} (h : IsUnit a), ↑h.unit = a- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses Classical.choice
- 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
- Units.valstatement · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- IsUnit.unitstatement · cited by 252
Cited by25
Results whose statement or proof uses this declaration.
- ZMod.isUnit_iff_coprimeproof · cited by 7
- HasEnoughRootsOfUnity.natCard_rootsOfUnityproof · cited by 5
- MonoidWithZeroHom.mem_valueGroup_iff_of_commproof · cited by 3
- Valuation.exists_pow_Uniformizerproof · cited by 3
- ZLattice.covolume_div_covolume_eq_relIndexproof · cited by 2
- Module.Basis.det_invproof · cited by 2
- ZMod.isCyclic_units_of_prime_powproof · cited by 2
- Matrix.nonsing_inv_applyproof · cited by 2
- RatFunc.uniformizingPolynomial_isUniformizerproof · cited by 1
- spectrum.units_smul_resolventproof · cited by 1
- ZLattice.covolume_eq_det_invproof · cited by 1
- MulChar.exists_apply_ne_one_of_hasEnoughRootsOfUnityproof · cited by 1