Theorems · Theorem · number theory
NumberField.RingOfIntegers.isIntegral_coe
∀ {K : Type u_1} [inst : Field K] (x : NumberField.RingOfIntegers K),
IsIntegral ℤ ((algebraMap (NumberField.RingOfIntegers K) K) x)- Defined in
- Mathlib.NumberTheory.NumberField.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 149 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement · cited by 4,706
- IsIntegralstatement · cited by 427
- NumberField.RingOfIntegersstatement and proof · cited by 413
Cited by9
Results whose statement or proof uses this declaration.
- NumberField.RingOfIntegers.isIntegralproof · cited by 6
- NumberField.hermiteTheorem.natDegree_le_rankOfDiscrBddproof · cited by 2
- NumberField.Units.mem_torsionproof · cited by 2
- NumberField.IsCMField.RingOfIntegers.complexConj_eq_self_iffproof · cited by 2
- NumberField.finite_setOfPred_prod_infinitePlace_iSup_leproof · cited by 2
- NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplexproof · cited by 1
- NumberField.hermiteTheorem.finite_of_discr_bdd_of_isRealproof · cited by 1
- NumberField.exists_nat_le_mulHeight₁proof · cited by 1
- RingOfIntegers.dvd_normproof · cited by 1