Theorems · Theorem · order theory
Finset.prod_mono_set_of_one_le
∀ {ι : Type u_1} {R : Type u_2} [inst : CommMonoidWithZero R] [inst_1 : Preorder R] [ZeroLEOneClass R] [PosMulMono R]
{f : ι → R}, (∀ (x : ι), 1 ≤ f x) → Monotone fun s => ∏ x ∈ s, f x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- Preorderstatement and proof · cited by 7,952
- LE.le.transproof · cited by 3,151
- Finset.prodstatement · cited by 2,356
- Monotonestatement · cited by 1,397
- CommMonoidWithZerostatement and proof · cited by 913
- zero_le_oneproof · cited by 316
- ZeroLEOneClassstatement and proof · cited by 304
- PosMulMonostatement and proof · cited by 165
- Finset.prod_le_prod_of_subset_of_one_leproof · cited by 2
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