Theorems · Theorem · general topology
Filter.pure_prod
∀ {α : Type u_1} {β : Type u_2} {a : α} {f : Filter β}, pure a ×ˢ f = Filter.map (Prod.mk a) f- Defined in
- Mathlib.Order.Filter.Prod
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- SProd.sprodstatement · cited by 1,750
- Filter.mapstatement and proof · cited by 819
- Filter.seqproof · cited by 15
- Filter.map_pureproof · cited by 9
- Filter.prod_eqproof · cited by 3
- Filter.pure_seq_eq_mapproof · cited by 1
Cited by10
Results whose statement or proof uses this declaration.
- Filter.map₂_pure_leftproof · cited by 8
- Real.continuousAt_rpow_of_posproof · cited by 1
- continuousWithinAt_prod_of_discrete_leftproof · cited by 1
- SummationFilter.conditional_filter_eq_map_Iicproof · cited by 1
- ENat.continuousAt_subproof · cited by 1
- isOpenMap_prod_of_discrete_leftproof · cited by 0
- Filter.map_pure_prodproof · cited by 0
- Filter.zero_prodproof · cited by 0
- Filter.one_prodproof · cited by 0
- WithZeroTopology.orderClosedTopologyproof · cited by 0