Theorems · Theorem · combinatorics
Fin.sum_cons
∀ {M : Type u_2} [inst : AddCommMonoid M] {n : ℕ} (x : M) (f : Fin n → M), ∑ i, Fin.cons x f i = x + ∑ i, f i- Defined in
- Mathlib.Algebra.BigOperators.Fin
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement and proof · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- Fin.consstatement and proof · cited by 190
- Fin.cons_succproof · cited by 54
- Fin.cons_zeroproof · cited by 53
- Fin.sum_univ_succproof · cited by 36
Cited by2
Results whose statement or proof uses this declaration.
- List.Nat.mem_antidiagonalTupleproof · cited by 2
- Finsupp.sum_consproof · cited by 2