Theorems · Definition · number theory
NumberField.InfinitePlace.embedding_of_isReal
{K : Type u_1} → [inst : Field K] → {w : NumberField.InfinitePlace K} → w.IsReal → K →+* ℝThe real embedding associated to a real infinite place.
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 172 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.
Cites6
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
- Fieldstatement and proof · cited by 7,404
- NumberField.InfinitePlacestatement and proof · cited by 604
- NumberField.InfinitePlace.IsRealstatement and proof · cited by 301
- NumberField.ComplexEmbedding.IsReal.embeddingproof · cited by 1
Cited by13
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbeddingproof · cited by 52
- NumberField.mixedEmbedding.normAtPlace_applyproof · cited by 8
- NumberField.InfinitePlace.embedding_of_isReal_applystatement · cited by 4
- NumberField.InfinitePlace.norm_embedding_of_isRealstatement and proof · cited by 2
- NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_applyproof · cited by 2
- NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_coestatement · cited by 2
- NumberField.mixedEmbedding.commMap_canonical_eq_mixedproof · cited by 2
- NumberField.InfinitePlace.isometry_embedding_of_isRealstatement and proof · cited by 2
- NumberField.mixedEmbedding.mixedEmbedding_apply_isRealstatement and proof · cited by 1
- NumberField.mixedEmbedding.convexBodyLT'_memproof · cited by 1
- NumberField.mixedEmbedding.convexBodyLT_memproof · cited by 1
- NumberField.InfiniteAdeleRing.mixedEmbedding_eq_algebraMap_compproof · cited by 0