Theorems · Theorem · group theory
Units.val_inj
∀ {α : Type u} [inst : Monoid α] {a b : αˣ}, ↑a = ↑b ↔ a = b- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 11 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_injectiveproof · cited by 17
Cited by20
Results whose statement or proof uses this declaration.
- Units.val_eq_oneproof · cited by 7
- HasEnoughRootsOfUnity.natCard_rootsOfUnityproof · cited by 5
- ClassGroup.mk_eq_mk_of_coe_idealproof · cited by 2
- pinGroup.star_memproof · cited by 2
- ClassGroup.equiv_mkproof · cited by 2
- RatFunc.uniformizingPolynomial_isUniformizerproof · cited by 1
- gaussSum_aux_of_mulShiftproof · cited by 1
- ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq_of_nonzeroproof · cited by 1
- ZMod.eq_unit_mul_divisorproof · cited by 1
- Set.subset_center_unitsproof · cited by 1
- HahnSeries.pow_addproof · cited by 0
- linearEquiv_det_rotationproof · cited by 0