Theorems · Theorem · commutative algebra
DualNumber.commute_eps_left
∀ {R : Type u_1} [inst : Semiring R] (x : DualNumber R), Commute DualNumber.eps xε commutes with every element of the algebra.
- Defined in
- Mathlib.Algebra.DualNumber
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- MulOppositestatement and proof · cited by 1,135
- zero_smulproof · cited by 716
- Commutestatement · cited by 639
- TrivSqZeroExt.fstproof · cited by 96
- TrivSqZeroExt.sndproof · cited by 83
Cited by3
Results whose statement or proof uses this declaration.
- DualNumber.commute_eps_rightproof · cited by 1
- DualNumber.ideal_trichotomyproof · cited by 1
- DualNumber.lift_inlAlgHom_epsstatement · cited by 0