Theorems · Theorem · group theory
Finset.add_eq_zero_iff
∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : SubtractionMonoid α] {s t : Finset α},
s + t = 0 ↔ ∃ a b, s = {a} ∧ t = {b} ∧ a + b = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqSubtractionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- SetLike.coeproof · cited by 8,199
- SubtractionMonoidstatement and proof · cited by 208
- Finset.coe_singletonproof · cited by 145
- Finset.addstatement · cited by 133
- Finset.zerostatement · cited by 74
- Finset.coe_injproof · cited by 41
- Finset.coe_addproof · cited by 19
- Finset.coe_zeroproof · cited by 6
- Set.add_eq_zero_iffproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Finset.isAddUnit_iffproof · cited by 1