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Theorems · Theorem · number theory

NumberField.mixedEmbedding.negAt_symm

∀ {K : Type u_1} [inst : Field K] {s : Set { w // w.IsReal }},
  (NumberField.mixedEmbedding.negAt s).symm = NumberField.mixedEmbedding.negAt s

negAt is its own inverse.

Defined in
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
Cited by
2 results in Mathlib
Foundations
Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Field
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Around this declaration

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

NumberField.mixedEmbedding.volume_negAt_plusPart · cited by 1mixedEmbedding.volume_neg…NumberField.mixedEmbedding.negAt_preimage · cited by 1mixedEmbedding.negAt_prei…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetReal · cited by 25697RealRingHom.id · cited by 18349RingHom.idField · cited by 7404FieldComplex · cited by 5565ComplexContinuousLinearEquiv · cited by 743ContinuousLinearEquivNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceContinuousLinearEquiv.symm · cited by 368ContinuousLinearEquiv.symmNumberField.InfinitePlace.IsReal · cited by 301InfinitePlace.IsRealNumberField.InfinitePlace.IsComplex · cited by 272InfinitePlace.IsComplexNumberField.mixedEmbedding.mixedSpace · cited by 239mixedEmbedding.mixedSpaceContinuousLinearEquiv.refl · cited by 24ContinuousLinearEquiv.reflNumberField.mixedEmbedding.negAt · cited by 20mixedEmbedding.negAtContinuousLinearEquiv.ext · cited by 14ContinuousLinearEquiv.extmixedEmbedding.negAt_symmCITED BYCITES

Cites19

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

Cited by2

Results whose statement or proof uses this declaration.