Theorems · Theorem · group theory
Finset.prod_eq_zero
∀ {ι : Type u_1} {M₀ : Type u_4} [inst : CommMonoidWithZero M₀] {f : ι → M₀} {s : Finset ι} {i : ι},
i ∈ s → f i = 0 → ∏ j ∈ s, f j = 0- Cited by
- 44 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidWithZero
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 and proof · cited by 13,712
- Finset.prodstatement and proof · cited by 2,356
- MulZeroClass.mul_zeroproof · cited by 2,091
- CommMonoidWithZerostatement and proof · cited by 913
- Finset.eraseproof · cited by 455
- Finset.prod_erase_mulproof · cited by 20
Cited by44
Results whose statement or proof uses this declaration.
- Matrix.det_diagonalproof · cited by 27
- Matrix.det_fromBlocks_zero₂₁proof · cited by 10
- MvPowerSeries.constantCoeff_subst_eq_zeroproof · cited by 7
- Matrix.adjugate_transposeproof · cited by 5
- Real.geom_mean_le_arith_mean_weightedproof · cited by 5
- prod_indicator_applyproof · cited by 4
- Real.geom_mean_eq_arith_mean_weighted_iff_of_pos'proof · cited by 4
- Matrix.det_blockDiagonalproof · cited by 4
- MultilinearMap.bound_of_shell_of_norm_map_coord_zeroproof · cited by 3
- MulSemiringAction.eval_charpolyproof · cited by 3
- PrimeSpectrum.exists_comap_evalRingHom_eqproof · cited by 3
- MeasureTheory.Measure.pi_eval_preimage_nullproof · cited by 3