Theorems · Theorem · number theory
NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem
∀ {K : Type u_1} [inst : Field K] {s : Set { w // w.IsReal }} (x : NumberField.mixedEmbedding.mixedSpace K)
{w : { w // w.IsReal }}, w ∉ s → ((NumberField.mixedEmbedding.negAt s) x).1 w = x.1 w- Cited by
- 5 results in Mathlib
- Foundations
- Depth 167 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.
Cites14
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
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- RingHom.idstatement and proof · cited by 18,349
- Fieldstatement and proof · cited by 7,404
- Complexstatement · cited by 5,565
- ContinuousLinearEquivstatement and proof · cited by 743
- NumberField.InfinitePlacestatement and proof · cited by 604
- NumberField.InfinitePlace.IsRealstatement and proof · cited by 301
- NumberField.InfinitePlace.IsComplexstatement · cited by 272
- NumberField.mixedEmbedding.mixedSpacestatement and proof · cited by 239
- ContinuousLinearEquiv.reflproof · cited by 24
Cited by5
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.pos_of_notMem_negAt_plusPartproof · cited by 2
- NumberField.mixedEmbedding.negAt_apply_norm_isRealproof · cited by 2
- NumberField.mixedEmbedding.negAt_symmproof · cited by 2
- NumberField.mixedEmbedding.mem_negAt_plusPart_of_memproof · cited by 1
- NumberField.mixedEmbedding.negAt_signSet_apply_isRealproof · cited by 0