Theorems · Theorem · commutative algebra
ValuationSubring.toSubring_injective
∀ {K : Type u} [inst : Field K], Function.Injective ValuationSubring.toSubring- Cited by
- 1 results in Mathlib
- Foundations
- Depth 48 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Subringstatement and proof · cited by 602
- ValuationSubringstatement and proof · cited by 187
- Subsemigroup.carrierproof · cited by 160
- Submonoid.toSubsemigroupproof · cited by 159
- Subsemiring.toSubmonoidproof · cited by 153
- Subring.toSubsemiringproof · cited by 71
- ValuationSubring.toSubringstatement and proof · cited by 32
- ValuationSubring.casesOnproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- ValuationSubring.toLocalSubring_injectiveproof · cited by 0
- ValuationSubring.pointwiseMulActionproof · cited by 0