Theorems · Definition · general topology
Filter.addMonoid
{α : Type u_2} → [AddMonoid α] → AddMonoid (Filter α)Filter α is an AddMonoid under pointwise operations if α is.
- Defined in
- Mathlib.Order.Filter.Pointwise
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- AddMonoidstatement and proof · cited by 2,864
- AddZeroClassproof · cited by 1,237
- AddSemigroupproof · cited by 136
- Filter.addZeroClassproof · cited by 2
- Filter.addSemigroupproof · cited by 0
Cited by6
Results whose statement or proof uses this declaration.
- IsAddUnit.filterstatement · cited by 2
- Filter.isAddUnit_iffstatement · cited by 0
- Filter.isAddUnit_purestatement · cited by 0
- Filter.distribMulActionFilterstatement · cited by 0
- Filter.subtractionMonoidproof · cited by 0
- Filter.addActionstatement · cited by 0