Theorems · Theorem · group theory
finsum_eq_zero_of_forall_eq_zero
∀ {α : Type u_1} {M : Type u_5} [inst : AddCommMonoid M] {f : α → M}, (∀ (x : α), f x = 0) → ∑ᶠ (i : α), f i = 0- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 75 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.
Cites3
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
- finsumstatement and proof · cited by 286
- finsum_zeroproof · cited by 18
Cited by7
Results whose statement or proof uses this declaration.
- MvPowerSeries.constantCoeff_subst_eq_zeroproof · cited by 7
- MvPowerSeries.coeff_expand_of_not_dvdproof · cited by 5
- MvPowerSeries.le_weightedOrder_substproof · cited by 3
- PowerSeries.coeff_subst_X_powproof · cited by 2
- IsOpen.exists_contMDiff_support_eqproof · cited by 1
- HahnSeries.SummableFamily.powerSeriesFamily_hsum_zeroproof · cited by 1
- PowerSeries.toMvPowerSeries_coeff_eq_zeroproof · cited by 1