Theorems · Theorem · general topology
Filter.isUnit_iff
∀ {α : Type u_2} [inst : DivisionMonoid α] {f : Filter α}, IsUnit f ↔ ∃ a, f = pure a ∧ IsUnit a- Defined in
- Mathlib.Order.Filter.Pointwise
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionMonoid
Around this declaration
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- DivisionMonoidstatement and proof · cited by 201
- Units.mul_invproof · cited by 67
- Units.inv_mulproof · cited by 46
- Filter.pure_injectiveproof · cited by 6
- Filter.monoidstatement · cited by 4
- IsUnit.filterproof · cited by 2
- Filter.pure_mul_pureproof · cited by 2
- Filter.mul_eq_one_iffproof · cited by 1
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