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Theorems · Theorem · combinatorics

Fin.sum_univ_two

∀ {M : Type u_2} [inst : AddCommMonoid M] (f : Fin 2 → M), ∑ i, f i = f 0 + f 1
Defined in
Mathlib.Algebra.BigOperators.Fin
Cited by
49 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.

groupHomology.comp_d₂₁_eq · cited by 10groupHomology.comp_d₂₁_eqgroupCohomology.comp_d₁₂_eq · cited by 10groupCohomology.comp_d₁₂_…Fin.sum_univ_three · cited by 7Fin.sum_univ_threeComplex.hasSum_cos' · cited by 3Complex.hasSum_cos'Complex.hasSum_sin' · cited by 3Complex.hasSum_sin'Affine.Simplex.closedInterior_eq_affineSegment · cited by 2Simplex.closedInterior_eq…iteratedDerivWithin_vcomp_three · cited by 2iteratedDerivWithin_vcomp…CompleteOrthogonalIdempotents.pair_iff'ₛ · cited by 2CompleteOrthogonalIdempot…MeasureTheory.integral_divergence_prod_Icc_of_hasFDerivAt_off_countable_of_le · cited by 2MeasureTheory.integral_di…RootPairing.EmbeddedG2.allRoots_eq_map_allCoeffs · cited by 2EmbeddedG2.allRoots_eq_ma…InnerProductSpace.laplacian_eq_iteratedFDeriv_complexPlane · cited by 2InnerProductSpace.laplaci…Matrix.toLin_finTwoProd_apply · cited by 2Matrix.toLin_finTwoProd_a…Height.mulHeight₁_add_le · cited by 2Height.mulHeight₁_add_lesameRay_or_sameRay_neg_iff_not_linearIndependent · cited by 2sameRay_or_sameRay_neg_if…Matrix.sub_scalar_sq_eq_discr · cited by 2Matrix.sub_scalar_sq_eq_d…AddCommMonoid · cited by 12281AddCommMonoidFinset.sum · cited by 5195Finset.sumFinset.univ · cited by 3473Finset.univFinset.sum_congr · cited by 2323Finset.sum_congrFinset.sum_singleton · cited by 251Finset.sum_singletonFinset.univ_unique · cited by 94Finset.univ_uniqueFin.sum_univ_succ · cited by 36Fin.sum_univ_succFin.sum_univ_twoCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by49

Results whose statement or proof uses this declaration.