Theorems · Theorem · algebraic geometry
untrop_sum_eq_sInf_image
∀ {R : Type u_1} {S : Type u_2} [inst : ConditionallyCompleteLinearOrder R] (s : Finset S)
(f : S → Tropical (WithTop R)), Tropical.untrop (∑ i ∈ s, f i) = sInf (Tropical.untrop ∘ f '' ↑s)- Defined in
- Mathlib.Algebra.Tropical.BigOperators
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Top.topproof · cited by 9,680
- SetLike.coestatement · cited by 8,199
- Set.imagestatement and proof · cited by 5,609
- Finset.sumstatement and proof · cited by 5,195
- WithTopstatement and proof · cited by 3,754
- Finset.Nonemptyproof · cited by 1,001
- InfSet.sInfstatement and proof · cited by 935
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- Finset.infproof · cited by 219
- Finset.coe_emptyproof · cited by 109
- Finset.eq_empty_or_nonemptyproof · cited by 104
Cited by1
Results whose statement or proof uses this declaration.
- untrop_sumproof · cited by 0