Theorems · Theorem · order theory
Finset.prod_lt_prod
∀ {ι : Type u_1} {R : Type u_2} [inst : CommMonoidWithZero R] [inst_1 : PartialOrder R] [ZeroLEOneClass R]
[PosMulStrictMono R] [Nontrivial R] {f g : ι → R} {s : Finset ι},
(∀ i ∈ s, 0 < f i) → (∀ i ∈ s, f i ≤ g i) → (∃ i ∈ s, f i < g i) → ∏ i ∈ s, f i < ∏ i ∈ s, g i- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- PartialOrderstatement and proof · cited by 6,410
- LE.le.transproof · cited by 3,151
- Nontrivialstatement and proof · cited by 2,416
- Finset.prodstatement and proof · cited by 2,356
- LT.lt.leproof · cited by 2,189
- le_of_ltproof · cited by 1,175
- CommMonoidWithZerostatement and proof · cited by 913
- Finset.eraseproof · cited by 455
- ZeroLEOneClassstatement and proof · cited by 304
- PosMulStrictMonostatement and proof · cited by 151
- Finset.prod_insertproof · cited by 109
Cited by1
Results whose statement or proof uses this declaration.
- Finset.prod_lt_prod_of_nonemptyproof · cited by 2