Theorems · Theorem · combinatorics
Finset.piecewise_singleton
∀ {ι : Type u_1} {π : ι → Sort u_2} (f g : (i : ι) → π i) [inst : DecidableEq ι] (i : ι),
{i}.piecewise f g = Function.update g i (f i)- Defined in
- Mathlib.Data.Finset.Piecewise
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Function.updatestatement and proof · cited by 502
- Finset.piecewisestatement and proof · cited by 64
- Finset.piecewise_emptyproof · cited by 7
- Finset.piecewise_insertproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Finset.piecewise_erase_univproof · cited by 2
- Finset.update_eq_piecewiseproof · cited by 2
- MultilinearMap.map_add_eq_map_add_linearDeriv_addproof · cited by 1