Theorems · Theorem · group theory
Finsupp.update_eq_single_add_erase
∀ {ι : Type u_1} {M : Type u_3} [inst : AddZeroClass M] (f : ι →₀ M) (a : ι) (b : M),
f.update a b = (fun₀ | a => b) + Finsupp.erase a f- Defined in
- Mathlib.Algebra.Group.Finsupp
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsuppstatement and proof · cited by 5,255
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- AddZeroClassstatement and proof · cited by 1,237
- eq_or_neproof · cited by 1,117
- Finsupp.singlestatement · cited by 943
- Finsupp.extproof · cited by 399
- Function.update_selfproof · cited by 201
- Function.update_of_neproof · cited by 198
- Finsupp.single_eq_sameproof · cited by 171
- Finsupp.single_eq_of_neproof · cited by 61
Cited by2
Results whose statement or proof uses this declaration.
- Finsupp.single_add_eraseproof · cited by 6
- Finsupp.update_eq_single_addproof · cited by 0