Theorems · Theorem · number theory
Algebra.coe_norm_int
∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (x : NumberField.RingOfIntegers K),
↑((Algebra.norm ℤ) x) = (Algebra.norm ℚ) ↑x- Defined in
- Mathlib.NumberTheory.NumberField.Norm
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 187 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- MonoidHomstatement · cited by 3,629
- nonZeroDivisorsproof · cited by 895
- NumberFieldstatement and proof · cited by 653
- NumberField.RingOfIntegersstatement and proof · cited by 413
- Algebra.normstatement · cited by 155
- NumberField.RingOfIntegers.valstatement · cited by 74
- Algebra.norm_localizationproof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.one_le_of_lt_oneproof · cited by 2
- NumberField.abs_discr_ge'proof · cited by 2
- NumberField.mixedEmbedding.fundamentalCone.intNorm_coeproof · cited by 1
- NumberField.Units.dirichletUnitTheorem.seq_norm_leproof · cited by 1
- NumberField.FinitePlace.prod_eq_inv_abs_normproof · cited by 1