Theorems · Theorem · number theory
NumberField.InfinitePlace.Completion.bijective_extensionEmbeddingOfIsReal
∀ {K : Type u_1} [inst : Field K] {v : NumberField.InfinitePlace K} (hv : v.IsReal),
Function.Bijective ⇑(NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal hv)If v is a real infinite place, then the embedding v.Completion →+* ℝ is bijective.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 188 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Function.Bijectivestatement · cited by 863
- NumberField.InfinitePlacestatement and proof · cited by 604
- NumberField.InfinitePlace.IsRealstatement and proof · cited by 301
- RingHom.injectiveproof · cited by 187
- NumberField.InfinitePlace.Completionstatement · cited by 69
- NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsRealstatement and proof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.Completion.ringEquivRealOfIsRealproof · cited by 4