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Theorems · Theorem · commutative algebra

IsIntegral.of_neg

∀ {R : Type u_1} {B : Type u_3} [inst : CommRing R] [inst_1 : Ring B] [inst_2 : Algebra R B] {x : B},
  IsIntegral R (-x) → IsIntegral R x
Defined in
Mathlib.RingTheory.IntegralClosure.Algebra.Basic
Cited by
1 results in Mathlib
Foundations
Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingRingAlgebra
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Around this declaration

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

IsIntegral.neg_iff · cited by 1IsIntegral.neg_iffCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraRing · cited by 7463Ringneg_neg · cited by 960neg_negIsIntegral · cited by 427IsIntegralIsIntegral.neg · cited by 4IsIntegral.negIsIntegral.of_negCITED BYCITES

Cites6

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

Cited by1

Results whose statement or proof uses this declaration.