Theorems · Theorem · commutative algebra
normUnit_mul_normUnit
∀ {α : Type u_1} [inst : MonoidWithZero α] [inst_1 : NormalizationMonoid α] (a : α), normUnit (a * ↑(normUnit a)) = 1- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- Unitsstatement and proof · cited by 2,804
- Nontrivialproof · cited by 2,416
- Units.valstatement and proof · cited by 1,966
- MulZeroClass.zero_mulproof · cited by 1,625
- eq_or_neproof · cited by 1,117
- MonoidWithZerostatement and proof · cited by 456
- NormalizationMonoidstatement and proof · cited by 165
- inv_mul_cancelproof · cited by 107
- NormalizationMonoid.normUnitstatement and proof · cited by 33
- NormalizationMonoid.normUnit_mul_unitsproof · cited by 3
- NormalizationMonoid.normUnit_zeroproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- normalize_idemproof · cited by 4