Theorems · Theorem · group theory
Units.val_eq_one
∀ {α : Type u} [inst : Monoid α] {a : αˣ}, ↑a = 1 ↔ a = 1- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- 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
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- Units.val_oneproof · cited by 39
- Units.val_injproof · cited by 20
Cited by7
Results whose statement or proof uses this declaration.
- MulChar.pow_card_eq_oneproof · cited by 2
- Polynomial.normUnit_Xproof · cited by 2
- MulChar.exists_apply_ne_one_of_hasEnoughRootsOfUnityproof · cited by 1
- PowerSeries.invOneSubPow_eq_inv_one_sub_powproof · cited by 1
- Polynomial.orderOf_root_cyclotomic_dvdproof · cited by 0
- LaurentPolynomial.smeval_oneproof · cited by 0