Theorems · Theorem · number theory
Finset.addEnergy_pos_iff
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Add α] {s t : Finset α}, 0 < s.addEnergy t ↔ s.Nonempty ∧ t.Nonempty- Defined in
- Mathlib.Combinatorics.Additive.Energy
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqAdd
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Finset.Nonemptystatement and proof · cited by 1,001
- lt_self_iff_falseproof · cited by 41
- Finset.addEnergystatement and proof · cited by 21
- Finset.not_nonempty_iff_eq_emptyproof · cited by 9
- Finset.addEnergy_posproof · cited by 2
- Finset.addEnergy_empty_leftproof · cited by 1
- Finset.addEnergy_empty_rightproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Finset.addEnergy_eq_zero_iffproof · cited by 1
- Finset.addEnergy_self_pos_iffproof · cited by 0