Theorems · Theorem · number theory
NumberField.RingOfIntegers.isIntegral
∀ {K : Type u_1} [inst : Field K] (x : NumberField.RingOfIntegers K), IsIntegral ℤ x- Defined in
- Mathlib.NumberTheory.NumberField.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 153 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHomproof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- Polynomial.Monicproof · cited by 461
- IsIntegralstatement · cited by 427
- NumberField.RingOfIntegersstatement and proof · cited by 413
- Polynomial.eval₂proof · cited by 267
- IsScalarTower.algebraMap_eqproof · cited by 110
- Polynomial.hom_eval₂proof · cited by 16
- NumberField.RingOfIntegers.isIntegral_coeproof · cited by 9
Cited by8
Results whose statement or proof uses this declaration.
- NumberField.Ideal.primesOverSpanEquivMonicFactorsModproof · cited by 10
- NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply_eq_spanproof · cited by 2
- RingOfIntegers.ZModXQuotSpanEquivQuotSpanproof · cited by 2
- IsCyclotomicExtension.Rat.inertiaDeg_eq_of_not_dvdproof · cited by 1
- IsCyclotomicExtension.Rat.ramificationIdx_eq_of_not_dvdproof · cited by 1
- NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_applystatement · cited by 0
- RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_applyproof · cited by 0