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Theorems · Theorem · commutative algebra

MonoidHom.map_sub_swap

∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : Monoid M] [IsMulTorsionFree M] (f : R →* M) (x y : R),
  f (x - y) = f (y - x)
Defined in
Mathlib.Algebra.Ring.Torsion
Cited by
1 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext
Assumes
RingMonoidIsMulTorsionFree
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Around this declaration

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

Valuation.map_sub_swap · cited by 7Valuation.map_sub_swapDFunLike.coe · cited by 62936DFunLike.coeRing · cited by 7463RingMonoid · cited by 3887MonoidMonoidHom · cited by 3629MonoidHomneg_sub · cited by 272neg_subIsMulTorsionFree · cited by 44IsMulTorsionFreeMonoidHom.map_neg · cited by 2MonoidHom.map_negMonoidHom.map_sub_swapCITED BYCITES

Cites7

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Cited by1

Results whose statement or proof uses this declaration.