UniformRing.lean`

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3 declarations, 0 contain sorry, 0 declared as axioms

Completion of topological rings

Imports (2)

Imported by 3 files

def UniformSpace.Completion.mapSemialgHom The semialgebra homomorphism Completion α →ₛₐ[f] Completion β induced from a continuous ring homomorphism f : α →+* β line 28 source
Source documentation
The semialgebra homomorphism Completion α →ₛₐ[f] Completion β induced from a continuous ring homomorphism f : α →+* β.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: CommRing, UniformSpace, IsTopologicalRing, IsUniformAddGroup, RingHom, Continuous, SemialgHom, UniformSpace.Completion
Proof uses: UniformSpace.Completion.mapRingHom, SemialgHom.mk, LinearMap.mk, AddHom.mk, OneHom.toFun
46 instances, coercions and auxiliary constants left out.

Tactic trace: 4 steps
Open to load the checked before-and-after goal states.
```
noncomputable def mapSemialgHom {α : Type*} [CommRing α] [UniformSpace α]
    [IsTopologicalRing α] [IsUniformAddGroup α] {β : Type*} [UniformSpace β] [CommRing β]
    [IsUniformAddGroup β] [IsTopologicalRing β] (f : α →+* β) (hf : Continuous f) :
    Completion α →ₛₐ[f] Completion β where
…
```
theorem UniformSpace.Completion.mapSemialgHom_apply line 40 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: CommRing, UniformSpace, IsTopologicalRing, IsUniformAddGroup, RingHom, Continuous, UniformSpace.Completion, Eq, SemialgHom, UniformSpace.Completion.mapSemialgHom, UniformSpace.Completion.map
Proof uses: rfl
30 instances, coercions and auxiliary constants left out.
theorem UniformSpace.Completion.mapSemialgHom_coe line 46 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: CommRing, UniformSpace, IsTopologicalRing, IsUniformAddGroup, RingHom, UniformContinuous, Eq, UniformSpace.Completion, SemialgHom, UniformSpace.Completion.mapSemialgHom, UniformContinuous.continuous
Proof uses: Eq.mpr, UniformSpace.Completion.map, id, congrArg, UniformSpace.Completion.mapSemialgHom_apply, UniformSpace.Completion.map_coe, Eq.refl
32 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.