Theorems · Theorem · group theory
Set.add_eq_zero_iff
∀ {α : Type u_2} [inst : SubtractionMonoid α] {s t : Set α}, s + t = 0 ↔ ∃ a b, s = {a} ∧ t = {b} ∧ a + b = 0- Cited by
- 3 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SubtractionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Nonemptyproof · cited by 2,627
- Set.addstatement · cited by 338
- SubtractionMonoidstatement and proof · cited by 208
- Eq.subsetproof · cited by 124
- Set.zerostatement · cited by 87
- Set.mem_image2_of_memproof · cited by 40
- eq_neg_of_add_eq_zero_leftproof · cited by 21
- Set.eq_singleton_iff_unique_memproof · cited by 20
- Set.Nonempty.of_image2_leftproof · cited by 12
- Set.Nonempty.of_image2_rightproof · cited by 12
- neg_eq_of_add_eq_zero_rightproof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- Set.isAddUnit_iffproof · cited by 2
- Finset.add_eq_zero_iffproof · cited by 1
- Filter.add_eq_zero_iffproof · cited by 1