Theorems · Theorem · group theory
Units.val_one
∀ {α : Type u} [inst : Monoid α], ↑1 = 1- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 39 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.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by40
Results whose statement or proof uses this declaration.
- Units.coeHomproof · cited by 44
- Associated.of_eqproof · cited by 7
- Units.val_eq_oneproof · cited by 7
- ZMod.val_coe_unit_coprimeproof · cited by 6
- Int.units_sqproof · cited by 5
- HasEnoughRootsOfUnity.natCard_rootsOfUnityproof · cited by 5
- Int.normalize_of_nonnegproof · cited by 4
- Complex.norm_eq_one_of_mem_rootsOfUnityproof · cited by 3
- Function.Antiperiodic.add_zsmul_eqproof · cited by 3
- Submodule.fg_unitproof · cited by 3
- NumberField.Units.even_torsionOrderproof · cited by 3
- Ideal.rootsOfUnityMapQuot_injectiveproof · cited by 2