R : Type u_1
inst✝ : CommRing R
I : Ideal R
x : R
this : TopologicalSpace R := adicTopology I
⊢ HasBasis (𝓝 x) (fun _n => True) fun n => (fun y => x + y) '' ↑(I ^ n)
R : Type u_1
inst✝ : CommRing R
I : Ideal R
x : R
⊢ HasBasis (𝓝 x) (fun _n => True) fun n => (fun y => x + y) '' ↑(I ^ n)
letI := I.adicTopology
R : Type u_1
inst✝ : CommRing R
I : Ideal R
x : R
this✝ : TopologicalSpace R := adicTopology I
this : HasBasis (Filter.map (fun y => x + y) (𝓝 0)) (fun _n => True) fun i => (fun y => x + y) '' ↑(I ^ i)
⊢ HasBasis (𝓝 x) (fun _n => True) fun n => (fun y => x + y) '' ↑(I ^ n)
R : Type u_1
inst✝ : CommRing R
I : Ideal R
x : R
this : TopologicalSpace R := adicTopology I
⊢ HasBasis (𝓝 x) (fun _n => True) fun n => (fun y => x + y) '' ↑(I ^ n)
have := I.hasBasis_nhds_zero_adic.map fun y => x + y
no goals
R : Type u_1
inst✝ : CommRing R
I : Ideal R
x : R
this✝ : TopologicalSpace R := adicTopology I
this : HasBasis (Filter.map (fun y => x + y) (𝓝 0)) (fun _n => True) fun i => (fun y => x + y) '' ↑(I ^ i)
⊢ HasBasis (𝓝 x) (fun _n => True) fun n => (fun y => x + y) '' ↑(I ^ n)
rwa [map_add_left_nhds_zero x] at this