Mathlib Map

Theorems · Theorem · ring theory

RingHom.map_neg

∀ {α : Type u_2} {β : Type u_3} [inst : NonAssocRing α] [inst_1 : NonAssocRing β] (f : α →+* β) (x : α), f (-x) = -f x

Ring homomorphisms preserve additive inverse.

Defined in
Mathlib.Algebra.Ring.Hom.Defs
Cited by
10 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext
Assumes
NonAssocRingNonAssocRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Polynomial.map_neg · cited by 5Polynomial.map_negspectralNorm_unique · cited by 3spectralNorm_uniqueMatrix.SpecialLinearGroup.coe_int_neg · cited by 2SpecialLinearGroup.coe_in…MvPolynomial.eval₂_neg · cited by 1MvPolynomial.eval₂_negGaussianInt.toComplex_neg · cited by 0GaussianInt.toComplex_negFreeCommRing.lift_comp_of · cited by 0FreeCommRing.lift_comp_ofPowerSeries.coe_neg · cited by 0PowerSeries.coe_negSkewPolynomial.C_neg · cited by 0SkewPolynomial.C_negPolynomial.coe_neg · cited by 0Polynomial.coe_negZMod.cast_neg · cited by 0ZMod.cast_negDFunLike.coe · cited by 62936DFunLike.coeRingHom · cited by 10189RingHomNonAssocRing · cited by 483NonAssocRingmap_neg · cited by 378map_negRingHom.map_negCITED BYCITES

Cites4

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

Cited by10

Results whose statement or proof uses this declaration.