Theorems · Theorem · group theory
Finset.sum_pair
∀ {ι : Type u_1} {M : Type u_4} [inst : AddCommMonoid M] {f : ι → M} [inst_1 : DecidableEq ι] {a b : ι},
a ≠ b → ∑ x ∈ {a, b}, f x = f a + f b- Cited by
- 11 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement · cited by 5,195
- Finset.sum_singletonproof · cited by 251
- Finset.sum_insertproof · cited by 196
- Finset.notMem_singletonproof · cited by 13
Cited by11
Results whose statement or proof uses this declaration.
- Finset.sum_eq_add_of_memproof · cited by 1
- LinearIndepOn.pair_iffproof · cited by 1
- Nat.binomial_eqproof · cited by 1
- BoxIntegral.Prepartition.sum_split_boxesproof · cited by 1
- RootPairing.Base.root_ne_neg_of_neproof · cited by 1
- Finset.centerMass_pairproof · cited by 0
- lt_hasSumproof · cited by 0
- Nat.binomial_specproof · cited by 0
- Finset.sum_Icc_of_even_eq_rangeproof · cited by 0
- Affine.Simplex.incenter_mem_interiorproof · cited by 0
- convex_iff_sum_memproof · cited by 0