Theorems · Theorem · general topology
Filter.prod_pure
∀ {α : Type u_1} {β : Type u_2} {f : Filter α} {b : β}, f ×ˢ pure b = Filter.map (fun a => (a, b)) f- Defined in
- Mathlib.Order.Filter.Prod
- Cited by
- 30 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.
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
- SProd.sprodstatement · cited by 1,750
- Filter.mapstatement and proof · cited by 819
- Filter.map_mapproof · cited by 80
- Filter.prod_eqproof · cited by 3
- Filter.seq_pureproof · cited by 1
Cited by30
Results whose statement or proof uses this declaration.
- Filter.map₂_pure_rightproof · cited by 9
- hasFDerivWithinAt_interproof · cited by 7
- CauchyFilter.isUniformInducing_pureCauchyproof · cited by 6
- hasFDerivWithinAt_inter'proof · cited by 5
- hasFDerivWithinAt_iff_isLittleOTVSproof · cited by 4
- HasFDerivAtFilter.tendsto_nhdsproof · cited by 4
- hasFDerivWithinAt_iff_tendstoproof · cited by 3
- hasFDerivAt_iff_isLittleOTVSproof · cited by 3
- hasGradientAtFilter_iff_isLittleOproof · cited by 2
- hasDerivAtFilter_iff_tendsto_slopeproof · cited by 2
- HasFDerivWithinAt.isBigOTVS_subproof · cited by 2
- HasFDerivWithinAt.iterateproof · cited by 2