Theorems · Theorem · group theory
finsum_mem_pair
∀ {α : Type u_1} {M : Type u_5} [inst : AddCommMonoid M] {f : α → M} {a b : α},
a ≠ b → ∑ᶠ (i : α) (_ : i ∈ {a, b}), f i = f a + f bThe sum of f i over i ∈ {a, b}, a ≠ b, is equal to f a + f b.
- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- AddCommMonoidstatement and proof · cited by 12,281
- finsumstatement · cited by 286
- Set.finite_singletonproof · cited by 70
- finsum_mem_singletonproof · cited by 3
- finsum_mem_insertproof · cited by 2
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