Theorems · Definition · number theory
NumberField.mixedEmbedding.fundamentalCone.completeFamily
(K : Type u_1) → [inst : Field K] → [NumberField K] → NumberField.InfinitePlace K → NumberField.mixedEmbedding.realSpace K
A family of elements in the realSpace K formed of the image of the fundamental units
and the vector (mult w)_w. This family is in fact a basis of realSpace K, see completeBasis.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 325 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- Equiv.symmproof · cited by 3,681
- Units.valproof · cited by 1,966
- OpenPartialHomeomorph.toFun'proof · cited by 745
- NumberFieldstatement and proof · cited by 653
- NumberField.InfinitePlacestatement and proof · cited by 604
- OpenPartialHomeomorph.symmproof · cited by 460
- NumberField.RingOfIntegersproof · cited by 413
- NumberField.InfinitePlace.multproof · cited by 107
- NumberField.mixedEmbedding.realSpacestatement · cited by 87
Cited by5
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.fundamentalCone.linearIndependent_completeFamilystatement and proof · cited by 2
- NumberField.mixedEmbedding.fundamentalCone.sum_eq_zero_of_mem_span_completeFamilystatement and proof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_nestatement and proof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.completeFamily.congr_simpstatement and proof · cited by 0
- NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_eqstatement and proof · cited by 0