Theorems · Theorem · algebraic geometry
Multiset.trop_inf
∀ {R : Type u_1} [inst : LinearOrder R] [inst_1 : OrderTop R] (s : Multiset R),
Tropical.trop s.inf = (Multiset.map Tropical.trop s).sum- Defined in
- Mathlib.Algebra.Tropical.BigOperators
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- LinearOrderOrderTop
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Multisetstatement and proof · cited by 2,627
- Multiset.mapstatement and proof · cited by 876
- OrderTopstatement and proof · cited by 493
- Multiset.sumstatement and proof · cited by 388
- Multiset.map_consproof · cited by 93
- Tropicalstatement · cited by 74
- Multiset.sum_consproof · cited by 45
- Tropical.tropstatement and proof · cited by 35
- Multiset.inductionproof · cited by 31
- Multiset.infstatement and proof · cited by 19
- Multiset.inf_consproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Finset.trop_infproof · cited by 1