Theorems · Theorem · number theory
NumberField.InfinitePlace.Completion.isometry_extensionEmbedding
∀ {K : Type u_1} [inst : Field K] (v : NumberField.InfinitePlace K),
Isometry ⇑(NumberField.InfinitePlace.Completion.extensionEmbedding v)The embedding v.Completion →+* ℂ is an isometry.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 185 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexstatement · cited by 5,565
- NumberField.InfinitePlacestatement and proof · cited by 604
- Isometrystatement · cited by 230
- NumberField.InfinitePlace.Completionstatement · cited by 69
- NumberField.InfinitePlace.Completion.extensionEmbeddingstatement · cited by 15
- Isometry.compproof · cited by 10
- Isometry.completion_extensionproof · cited by 4
- NumberField.InfinitePlace.Completion.isometry_toCompletionproof · cited by 3
- NumberField.InfinitePlace.isometry_embeddingproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_applyproof · cited by 2
- NumberField.InfinitePlace.Completion.liesOver_extensionEmbeddingproof · cited by 2
- NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbeddingproof · cited by 1
- NumberField.InfinitePlace.Completion.isometryEquivComplexOfIsComplexproof · cited by 0