Theorems · Theorem · number theory

NumberField.InfinitePlace.IsUnramified.isUnmixed_conjugate

∀ {k : Type u_1} [inst : Field k] {K : Type u_2} [inst_1 : Field K] [inst_2 : Algebra k K]
  {w : NumberField.InfinitePlace K},
  NumberField.InfinitePlace.IsUnramified k w →
    NumberField.ComplexEmbedding.IsUnmixed k (NumberField.ComplexEmbedding.conjugate w.embedding)

Defined in: Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification
Cited by: 1 results in Mathlib
Foundations: Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra

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Cites16

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

Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
Algebra.algebraMapproof · cited by 4,706
RingHom.compproof · cited by 899
NumberField.InfinitePlacestatement and proof · cited by 604
NumberField.InfinitePlace.IsRealproof · cited by 301
NumberField.InfinitePlace.embeddingstatement and proof · cited by 78
NumberField.InfinitePlace.comapproof · cited by 55
NumberField.ComplexEmbedding.conjugatestatement and proof · cited by 40
NumberField.ComplexEmbedding.IsRealproof · cited by 38
NumberField.InfinitePlace.IsUnramifiedstatement and proof · cited by 35
NumberField.InfinitePlace.mk_embeddingproof · cited by 25

Cited by1

Results whose statement or proof uses this declaration.

NumberField.InfinitePlace.isUnramified_mk_iff_isUnmixedproof · cited by 1