Theorems · Theorem · number theory

NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_apply

∀ {K : Type u_1} [inst : Field K] {v : NumberField.InfinitePlace K} (hv : v.IsReal) (x : v.Completion),
  ↑((NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal hv) x) =
    (NumberField.InfinitePlace.Completion.extensionEmbedding v) x

Defined in: Mathlib.NumberTheory.NumberField.Completion.InfinitePlace
Cited by: 2 results in Mathlib
Foundations: Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites26

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Realstatement · cited by 25,697
RingHomstatement · cited by 10,189
Fieldstatement and proof · cited by 7,404
Complexstatement · cited by 5,565
Complex.ofRealstatement and proof · cited by 1,654
NumberField.InfinitePlacestatement and proof · cited by 604
Continuous.compproof · cited by 371
NumberField.InfinitePlace.IsRealstatement and proof · cited by 301
Complex.continuous_ofRealproof · cited by 107
WithAbsproof · cited by 102
NumberField.InfinitePlace.embeddingproof · cited by 78

Cited by2

Results whose statement or proof uses this declaration.

NumberField.InfinitePlace.IsUnramified.finrank_eq_oneproof · cited by 3
NumberField.InfinitePlace.IsRamified.finrank_eq_twoproof · cited by 3