Theorems · Theorem · number theory

NumberField.ComplexEmbedding.IsUnmixed.isReal_iff_isReal

∀ (K : Type u_3) {L : Type u_4} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] {φ : L →+* ℂ},
  NumberField.ComplexEmbedding.IsUnmixed K φ →
    (NumberField.ComplexEmbedding.IsReal (φ.comp (algebraMap K L)) ↔ NumberField.ComplexEmbedding.IsReal φ)

Defined in: Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings
Cited by: 0 results in Mathlib
Foundations: Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra

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Algebrastatement and proof · cited by 11,388
RingHomstatement and proof · cited by 10,189
Fieldstatement and proof · cited by 7,404
Complexstatement and proof · cited by 5,565
Algebra.algebraMapstatement and proof · cited by 4,706
RingHom.compstatement and proof · cited by 899
NumberField.ComplexEmbedding.IsRealstatement and proof · cited by 38
NumberField.ComplexEmbedding.IsUnmixedstatement and proof · cited by 5

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