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Theorems · Theorem · group theory

Fintype.sum_subsingleton

∀ {M : Type u_4} {ι : Type u_7} [inst : Fintype ι] [inst_1 : AddCommMonoid M] [Subsingleton ι] (f : ι → M) (a : ι),
  ∑ x, f x = f a
Defined in
Mathlib.Algebra.BigOperators.Group.Finset.Basic
Cited by
2 results in Mathlib
Foundations
Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FintypeAddCommMonoidSubsingleton
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Finset.sum_pow_of_commute · cited by 1Finset.sum_pow_of_commuteMvPolynomial.msymm_zero · cited by 0MvPolynomial.msymm_zeroAddCommMonoid · cited by 12281AddCommMonoidFintype · cited by 7736FintypeFinset.sum · cited by 5195Finset.sumFinset.univ · cited by 3473Finset.univUnique · cited by 400UniqueuniqueOfSubsingleton · cited by 9uniqueOfSubsingletonFintype.sum_unique · cited by 6Fintype.sum_uniqueFintype.sum_subsingletonCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.