Theorems · Theorem · general topology
Filter.vadd_pure
∀ {α : Type u_2} {β : Type u_3} [inst : VAdd α β] {f : Filter α} {b : β}, f +ᵥ pure b = Filter.map (fun x => x +ᵥ b) f- Defined in
- Mathlib.Order.Filter.Pointwise
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- VAdd
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- HVAdd.hVAddstatement · cited by 1,820
- Filter.mapstatement · cited by 819
- VAddstatement and proof · cited by 616
- Filter.map₂_pure_rightproof · cited by 9
Cited by12
Results whose statement or proof uses this declaration.
- AffineSpace.asymptoticNhds_vadd_pureproof · cited by 5
- AffineSpace.asymptoticNhds_le_coboundedproof · cited by 2
- AffineSpace.nhds_bind_asymptoticNhdsproof · cited by 2
- AffineSpace.asymptoticNhds_zeroproof · cited by 1
- AffineSpace.cobounded_eq_iSup_sphere_asymptoticNhdsproof · cited by 1
- AffineSpace.vadd_asymptoticNhdsproof · cited by 1
- StarConvex.smul_vadd_mem_of_isClosed_of_mem_asymptoticConeproof · cited by 1
- asymptoticCone_affineSubspaceproof · cited by 1
- Filter.Tendsto.asymptoticNhds_vadd_constproof · cited by 1
- AffineSpace.asymptoticNhds_bind_nhdsproof · cited by 1
- Filter.pure_vadd_pureproof · cited by 0
- Convex.smul_vadd_mem_of_mem_nhds_of_mem_asymptoticConeproof · cited by 0