Theorems · Theorem · commutative algebra
ValuationSubring.valuation_eq_one_iff
∀ {K : Type u} [inst : Field K] (A : ValuationSubring K) (a : ↥A), IsUnit a ↔ A.valuation ↑a = 1- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- one_mulproof · cited by 2,841
- le_reflproof · cited by 2,061
- IsUnitstatement and proof · cited by 1,602
- one_ne_zeroproof · cited by 885
- Valuationstatement · cited by 823
- div_oneproof · cited by 629
- inv_oneproof · cited by 301
- IsUnit.unitproof · cited by 252
- ValuationSubringstatement and proof · cited by 187
- map_inv₀proof · cited by 106
Cited by2
Results whose statement or proof uses this declaration.
- ValuationSubring.valuation_lt_one_iffproof · cited by 4
- ValuationSubring.ofPrime_valuation_eq_one_iff_mem_primeComplproof · cited by 0