Theorems · Theorem · group theory
Finsupp.update_eq_sub_add_single
∀ {ι : Type u_1} {G : Type u_6} [inst : AddGroup G] (f : ι →₀ G) (a : ι) (b : G),
f.update a b = (f - fun₀ | a => f a) + fun₀ | a => b- Defined in
- Mathlib.Algebra.Group.Finsupp
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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Cites7
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
- Finsuppstatement and proof · cited by 5,255
- AddGroupstatement and proof · cited by 4,410
- Finsupp.singlestatement and proof · cited by 943
- Finsupp.updatestatement · cited by 52
- Finsupp.update_eq_erase_add_singleproof · cited by 4
- Finsupp.erase_eq_sub_singleproof · cited by 1
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