Theorems · Theorem · commutative algebra
Valuation.IsUniformizer.not_isUnit
∀ {Γ : Type u_1} [inst : LinearOrderedCommGroupWithZero Γ] {R : Type u_2} [inst_1 : CommRing R] {v : Valuation R Γ}
[hv : v.IsRankOneDiscrete] {π : ↥v.integer}, v.IsUniformizer ↑π → ¬IsUnit π- Cited by
- 2 results in Mathlib
- Foundations
- Depth 73 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.
- CommRingstatement and proof · cited by 17,173
- IsUnitstatement and proof · cited by 1,602
- Valuationstatement and proof · cited by 823
- ne_of_gtproof · cited by 637
- Subringstatement · cited by 602
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Valuation.integerstatement and proof · cited by 68
- Valuation.IsRankOneDiscretestatement and proof · cited by 53
- Valuation.IsUniformizerstatement and proof · cited by 22
- Valuation.integer.integersproof · cited by 17
- Valuation.IsUniformizer.val_lt_oneproof · cited by 2
- Valuation.Integers.one_of_isUnitproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Valuation.Uniformizer.is_generatorproof · cited by 4
- Valuation.valuationSubring_not_isFieldproof · cited by 1