Theorems · Theorem · commutative algebra
Finsupp.le_weight_of_ne_zero
∀ {σ : Type u_1} {M : Type u_2} [inst : AddCommMonoid M] [inst_1 : PartialOrder M] [IsOrderedAddMonoid M] {w : σ → M},
(∀ (s : σ), 0 ≤ w s) → ∀ {s : σ} {f : σ →₀ ℕ}, f s ≠ 0 → w s ≤ (Finsupp.weight w) f- Defined in
- Mathlib.Data.Finsupp.Weight
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- Finsuppstatement and proof · cited by 5,255
- AddMonoidHomstatement · cited by 3,230
- Finset.sum_congrproof · cited by 2,323
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Finsupp.supportproof · cited by 828
- Finset.sum_nonnegproof · cited by 91
- Finsupp.weightstatement · cited by 90
- Finsupp.mem_support_iffproof · cited by 89
- le_add_of_nonneg_rightproof · cited by 69
Cited by1
Results whose statement or proof uses this declaration.
- Finsupp.le_weight_of_ne_zero'proof · cited by 1