Theorems · Theorem · general algebraic systems
Finsupp.coe_update
∀ {α : Type u_1} {M : Type u_5} [inst : Zero M] (f : α →₀ M) (a : α) (b : M) [inst_1 : DecidableEq α],
⇑(f.update a b) = Function.update (⇑f) a b- Defined in
- Mathlib.Data.Finsupp.Single
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ZeroDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Finsuppstatement and proof · cited by 5,255
- Function.updatestatement · cited by 502
- Finsupp.updatestatement · cited by 52
Cited by19
Results whose statement or proof uses this declaration.
- Finsupp.update_eq_erase_add_singleproof · cited by 4
- SkewMonoidAlgebra.coeff_update_applyproof · cited by 3
- Finsupp.optionElim_apply_noneproof · cited by 3
- MvPowerSeries.coeff_prodproof · cited by 3
- Polynomial.coeff_homogenizeproof · cited by 2
- Finsupp.update_eq_single_add_eraseproof · cited by 2
- Multiset.countPerms_filter_neproof · cited by 2
- Finset.mem_finsuppAntidiag_insertproof · cited by 1
- Polynomial.coeff_updateproof · cited by 1
- List.multinomial_consproof · cited by 1
- AList.insert_lookupFinsuppproof · cited by 1
- SkewPolynomial.coeff_updateproof · cited by 1