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Theorems · Theorem · commutative algebra

IsFractionRing.num.congr_simp

∀ (A : Type u_1) [inst : CommRing A] [inst_1 : IsDomain A] [inst_2 : UniqueFactorizationMonoid A] {K : Type u_2}
  [inst_3 : Field K] [inst_4 : Algebra A K] [inst_5 : IsFractionRing A K] (x x_1 : K),
  x = x_1 → IsFractionRing.num A x = IsFractionRing.num A x_1
Defined in
Mathlib.RingTheory.Localization.NumDen
Cited by
1 results in Mathlib
Foundations
Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingIsDomainUniqueFactorizationMonoidFieldAlgebraIsFractionRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

num_dvd_of_is_root · cited by 1num_dvd_of_is_rootCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraField · cited by 7404FieldIsDomain · cited by 2196IsDomainIsFractionRing · cited by 738IsFractionRingUniqueFactorizationMonoid · cited by 279UniqueFactorizationMonoidIsFractionRing.num · cited by 22IsFractionRing.numnum.congr_simpCITED BYCITES

Cites7

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Cited by1

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