Theorems · Definition · number theory
NumberField.InfinitePlace.Completion.equiv
{K : Type u_1} → [inst : Field K] → (v : NumberField.InfinitePlace K) → v.Completion ≃+* (↑v).CompletionCompletion.toCompletion as a ring isomorphism onto the underlying completion.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 183 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- RingHomstatement · cited by 10,189
- Equivproof · cited by 8,337
- Fieldstatement and proof · cited by 7,404
- Complexstatement · cited by 5,565
- RingEquivstatement · cited by 1,147
- NumberField.InfinitePlacestatement and proof · cited by 604
- AbsoluteValuestatement · cited by 363
- WithAbsstatement · cited by 102
- NumberField.placestatement · cited by 71
- NumberField.InfinitePlace.Completionstatement and proof · cited by 69
- AbsoluteValue.Completionstatement and proof · cited by 24
Cited by5
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.Completion.extensionEmbeddingproof · cited by 15
- NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsRealproof · cited by 9
- NumberField.LiesOver.completionMapproof · cited by 4
- NumberField.InfinitePlace.Completion.WithAbs.ratCast_equivproof · cited by 1
- NumberField.InfinitePlace.Completion.equiv_applystatement and proof · cited by 0