Theorems · Theorem · number theory
NumberField.InfinitePlace.conjugate_embedding_eq_of_isReal
∀ {K : Type u_1} [inst : Field K] {w : NumberField.InfinitePlace K},
w.IsReal → NumberField.ComplexEmbedding.conjugate w.embedding = w.embedding- Cited by
- 2 results in Mathlib
- Foundations
- Depth 171 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexstatement · cited by 5,565
- NumberField.InfinitePlacestatement and proof · cited by 604
- NumberField.InfinitePlace.IsRealstatement and proof · cited by 301
- NumberField.InfinitePlace.embeddingstatement · cited by 78
- NumberField.ComplexEmbedding.conjugatestatement · cited by 40
- NumberField.InfinitePlace.isReal_iffproof · cited by 13
- NumberField.ComplexEmbedding.isReal_iffproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.is_primitive_element_of_infinitePlace_ltproof · cited by 3
- NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mulproof · cited by 1