Theorems · Theorem · commutative algebra

RingHom.StableUnderCompositionWithLocalizationAwayTarget.and

∀ {P Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop},
  (RingHom.StableUnderCompositionWithLocalizationAwayTarget fun {R S} [CommRing R] [CommRing S] => P) →
    (RingHom.StableUnderCompositionWithLocalizationAwayTarget fun {R S} [CommRing R] [CommRing S] => Q) →
      RingHom.StableUnderCompositionWithLocalizationAwayTarget fun {R S} [CommRing R] [CommRing S] f => P f ∧ Q f

Defined in: Mathlib.RingTheory.LocalProperties.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CommRingstatement and proof · cited by 17,173
Algebraproof · cited by 11,388
RingHomstatement and proof · cited by 10,189
IsLocalization.Awayproof · cited by 218
RingHom.StableUnderCompositionWithLocalizationAwayTargetstatement and proof · cited by 6

Cited by1

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RingHom.PropertyIsLocal.andproof · cited by 2