Theorems · Theorem · commutative algebra
ValuationSubring.valuation_le_one
∀ {K : Type u} [inst : Field K] (A : ValuationSubring K) (a : ↥A), A.valuation ↑a ≤ 1- Cited by
- 3 results in Mathlib
- Foundations
- Depth 79 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Valuationstatement · cited by 823
- ValuationSubringstatement and proof · cited by 187
- ValuationSubring.valuationstatement · cited by 29
- ValuationSubring.ValueGroupstatement · cited by 26
- ValuationRing.mem_integer_iffproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- ValuationSubring.valuation_le_one_iffproof · cited by 9
- ValuationSubring.valuation_lt_one_iffproof · cited by 4
- ValuationSubring.valuation_lt_one_or_eq_oneproof · cited by 0