Theorems · Theorem · group theory
Units.mk0_prod
∀ {ι : Type u_1} {G₀ : Type u_3} [inst : CommGroupWithZero G₀] (s : Finset ι) (f : ι → G₀) (h : ∏ i ∈ s, f i ≠ 0),
Units.mk0 (∏ i ∈ s, f i) h = ∏ i ∈ s.attach, Units.mk0 (f ↑i) ⋯- Cited by
- 2 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommGroupWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- Unitsstatement · cited by 2,804
- Finset.prodstatement and proof · cited by 2,356
- Finset.mapproof · cited by 747
- Finset.prod_congrproof · cited by 646
- Finset.consproof · cited by 221
- Units.mk0statement and proof · cited by 181
- Finset.attachstatement and proof · cited by 168
- CommGroupWithZerostatement and proof · cited by 94
- Finset.prod_mapproof · cited by 75
- Finset.prod_consproof · cited by 60
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.sub_one_pow_totient_lt_cyclotomic_evalproof · cited by 2
- Polynomial.cyclotomic_eval_lt_add_one_pow_totientproof · cited by 1