Theorems · Theorem · number theory
NumberField.mixedEmbedding.fundamentalCone.expMapBasis_pos
∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (x : NumberField.mixedEmbedding.realSpace K)
(w : NumberField.InfinitePlace K), 0 < ↑NumberField.mixedEmbedding.fundamentalCone.expMapBasis x w- Cited by
- 7 results in Mathlib
- Foundations
- Depth 331 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- PartialEquiv.sourceproof · cited by 964
- PartialHomeomorph.toPartialEquivproof · cited by 917
- OpenPartialHomeomorph.toPartialHomeomorphproof · cited by 851
- PartialEquiv.toFunproof · cited by 821
- OpenPartialHomeomorph.toFun'statement · cited by 745
- NumberFieldstatement and proof · cited by 653
- NumberField.InfinitePlacestatement and proof · cited by 604
- PartialEquiv.symmproof · cited by 453
- ContinuousLinearEquiv.symmproof · cited by 368
- NumberField.mixedEmbedding.realSpacestatement and proof · cited by 87
Cited by7
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasisproof · cited by 3
- NumberField.mixedEmbedding.fundamentalCone.volume_normLeOneproof · cited by 2
- NumberField.mixedEmbedding.fundamentalCone.expMapBasis_nonnegproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.nonneg_of_mem_compactSetproof · cited by 1