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Theorems · Theorem · order theory

List.prod_pos

∀ {R : Type u_1} [inst : CommMonoidWithZero R] [inst_1 : PartialOrder R] [ZeroLEOneClass R] [PosMulStrictMono R]
  [NeZero 1] {s : List R}, (∀ a ∈ s, 0 < a) → 0 < s.prod
Defined in
Mathlib.Algebra.Order.BigOperators.GroupWithZero.List
Cited by
2 results in Mathlib
Foundations
Depth 9 from the axioms · uses propext, Quot.sound
Assumes
CommMonoidWithZeroPartialOrderZeroLEOneClassPosMulStrictMonoNeZero
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Multiset.prod_pos · cited by 1Multiset.prod_posList.prod_map_lt_prod_map · cited by 1List.prod_map_lt_prod_mapPartialOrder · cited by 6410PartialOrderCommMonoidWithZero · cited by 913CommMonoidWithZeromul_pos · cited by 374mul_posZeroLEOneClass · cited by 304ZeroLEOneClassPosMulStrictMono · cited by 151PosMulStrictMonoList.prod_posCITED BYCITES

Cites5

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Cited by2

Results whose statement or proof uses this declaration.