Theorems · Theorem · algebraic geometry
Finset.trop_inf
∀ {R : Type u_1} {S : Type u_2} [inst : LinearOrder R] [inst_1 : OrderTop R] (s : Finset S) (f : S → R),
Tropical.trop (s.inf f) = ∑ i ∈ s, Tropical.trop (f i)- Defined in
- Mathlib.Algebra.Tropical.BigOperators
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
- Assumes
- LinearOrderOrderTop
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- LinearOrderstatement and proof · cited by 8,572
- Finset.sumstatement and proof · cited by 5,195
- Multiset.mapproof · cited by 876
- OrderTopstatement and proof · cited by 493
- Finset.valproof · cited by 438
- Multiset.sumproof · cited by 388
- Multiset.map_congrproof · cited by 232
- Finset.infstatement and proof · cited by 219
- Multiset.map_mapproof · cited by 151
- Tropicalstatement and proof · cited by 74
- Tropical.tropstatement and proof · cited by 35
Cited by1
Results whose statement or proof uses this declaration.
- trop_sInf_imageproof · cited by 1