Theorems · Theorem · general topology
Filter.add_eq_zero_iff
∀ {α : Type u_2} [inst : SubtractionMonoid α] {f g : Filter α}, f + g = 0 ↔ ∃ a b, f = pure a ∧ g = pure b ∧ a + b = 0- Defined in
- Mathlib.Order.Filter.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Filter.NeBotproof · cited by 853
- SubtractionMonoidstatement and proof · cited by 208
- Filter.NeBot.nonempty_of_memproof · cited by 18
- Filter.le_pure_iffproof · cited by 11
- Filter.NeBot.le_pure_iffproof · cited by 9
- Set.add_eq_zero_iffproof · cited by 3
- Filter.pure_add_pureproof · cited by 2
- Filter.zero_mem_zeroproof · cited by 2
- Filter.zero_neBotproof · cited by 1
- Filter.pure_zeroproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Filter.isAddUnit_iffproof · cited by 0