Theorems · Theorem · ring theory
SkewMonoidAlgebra.update_eq_erase_add_single
∀ {M : Type u_4} {α : Type u_5} [inst : AddCommMonoid M] (f : SkewMonoidAlgebra M α) (a : α) (b : M),
f.update a b = (SkewMonoidAlgebra.erase a) f + SkewMonoidAlgebra.single a b- Defined in
- Mathlib.Algebra.SkewMonoidAlgebra.Single
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- AddMonoidHomstatement · cited by 3,230
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- Finsupp.singleproof · cited by 943
- SkewMonoidAlgebrastatement and proof · cited by 216
- Function.update_selfproof · cited by 201
- Function.update_of_neproof · cited by 198
- Finsupp.single_eq_sameproof · cited by 171
- SkewMonoidAlgebra.coeffproof · cited by 110
- SkewMonoidAlgebra.singlestatement and proof · cited by 83
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.