Theorems · Theorem · commutative algebra
ValuationSubring.nonunits_le_nonunits
∀ {K : Type u} [inst : Field K] {A B : ValuationSubring K}, B.nonunits ≤ A.nonunits ↔ A ≤ B- Cited by
- 0 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- not_ltproof · cited by 306
- ValuationSubringstatement and proof · cited by 187
- NonUnitalSubringstatement · cited by 185
- ValuationSubring.valuationproof · cited by 29
- ValuationSubring.nonunitsstatement and proof · cited by 14
- ValuationSubring.valuation_le_one_iffproof · cited by 9
- Valuation.one_lt_val_iffproof · cited by 4
- ValuationSubring.monotone_mapOfLEproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- ValuationSubring.nonunitsOrderEmbeddingproof · cited by 0