Theorems · Theorem · number theory
Int.ModEq.multisetSum_map_zero
∀ {α : Type u_1} {n : ℤ} {f : α → ℤ} {s : Multiset α}, (∀ x ∈ s, f x ≡ 0 [ZMOD n]) → (Multiset.map f s).sum ≡ 0 [ZMOD n]- Defined in
- Mathlib.Algebra.BigOperators.ModEq
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Multisetstatement and proof · cited by 2,627
- Multiset.mapstatement and proof · cited by 876
- Multiset.sumstatement and proof · cited by 388
- Multiset.cardproof · cited by 375
- Int.ModEqstatement and proof · cited by 147
- nsmul_zeroproof · cited by 73
- Multiset.map_const'proof · cited by 39
- Multiset.sum_replicateproof · cited by 30
- Int.ModEq.multisetSum_mapproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Int.ModEq.multisetSum_zeroproof · cited by 0
- Int.ModEq.sum_zeroproof · cited by 0