Theorems · Theorem · group theory
Finset.prod_const_one
∀ {ι : Type u_1} {M : Type u_3} {s : Finset ι} [inst : CommMonoid M], ∏ _x ∈ s, 1 = 1- Cited by
- 100 results in Mathlib
- Foundations
- Depth 23 from the axioms, rests on 192 definitions · uses propext, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Multiset.prodproof · cited by 528
- one_powproof · cited by 521
- Finset.valproof · cited by 438
- Multiset.cardproof · cited by 375
- Multiset.prod_replicateproof · cited by 40
- Multiset.map_const'proof · cited by 39
Cited by100
Results whose statement or proof uses this declaration.
- Matrix.det_oneproof · cited by 35
- FormalMultilinearSeries.coeff_ofScalarsproof · cited by 23
- Finset.prod_eq_oneproof · cited by 22
- iteratedDerivWithin_succproof · cited by 11
- Polynomial.resultant_commproof · cited by 11
- Finset.prod_eq_singleproof · cited by 7
- hasProd_oneproof · cited by 7
- Finset.one_le_prod'proof · cited by 6
- Finset.prod_disjiUnionproof · cited by 6
- Nat.uniformBell_eqproof · cited by 5
- Finset.prod_le_oneproof · cited by 4
- Finset.prod_booleproof · cited by 4