Theorems · Theorem · order theory
Finset.abs_prod
∀ {ι : Type u_1} {R : Type u_2} [inst : CommRing R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] (s : Finset ι)
(f : ι → R), |∏ x ∈ s, f x| = ∏ x ∈ s, |f x|- Cited by
- 9 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Finsetstatement and proof · cited by 13,712
- LinearOrderstatement and proof · cited by 8,572
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Finset.prodstatement · cited by 2,356
- absstatement · cited by 1,814
- map_prodproof · cited by 108
- absHomproof · cited by 5
Cited by9
Results whose statement or proof uses this declaration.
- Orientation.abs_volumeForm_apply_leproof · cited by 2
- Real.smul_map_diagonal_volume_piproof · cited by 1
- lintegral_comp_pi_polarCoord_symmproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasisproof · cited by 1
- BoxIntegral.hasIntegral_GP_pderivproof · cited by 1
- NumberField.mixedEmbedding.integral_comp_polarCoordReal_symmproof · cited by 1
- integral_comp_pi_polarCoord_symmproof · cited by 1
- Orientation.abs_volumeForm_apply_of_pairwise_orthogonalproof · cited by 1
- NumberField.mixedEmbedding.lintegral_comp_polarCoordReal_symmproof · cited by 1