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[Merged by Bors] - feat: inv lemmas for uniform convergence, missing to_fun attributes #35384

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[Merged by Bors] - feat: inv lemmas for uniform convergence, missing to_fun attributes #35384

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60 changes: 52 additions & 8 deletions Mathlib/Topology/Algebra/IsUniformGroup/Basic.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -144,48 +144,92 @@ section UniformConvergence

variable {ι : Type*} {l : Filter ι} {l' : Filter β} {f f' : ι → β → α} {g g' : β → α} {s : Set β}

@[to_additive]
@[to_additive (attr := to_fun)]
theorem TendstoUniformlyOnFilter.mul (hf : TendstoUniformlyOnFilter f g l l')
(hf' : TendstoUniformlyOnFilter f' g' l l') : TendstoUniformlyOnFilter (f * f') (g * g') l l' :=
fun u hu =>
((uniformContinuous_mul.comp_tendstoUniformlyOnFilter (hf.prodMk hf')) u hu).diag_of_prod_left

@[to_additive]
attribute [to_additive existing] TendstoUniformlyOnFilter.fun_mul

@[to_additive (attr := to_fun)]
theorem TendstoUniformlyOnFilter.div (hf : TendstoUniformlyOnFilter f g l l')
(hf' : TendstoUniformlyOnFilter f' g' l l') : TendstoUniformlyOnFilter (f / f') (g / g') l l' :=
fun u hu =>
((uniformContinuous_div.comp_tendstoUniformlyOnFilter (hf.prodMk hf')) u hu).diag_of_prod_left

@[to_additive]
attribute [to_additive existing] TendstoUniformlyOnFilter.fun_div

@[to_additive (attr := to_fun)]
theorem TendstoUniformlyOnFilter.inv (hf : TendstoUniformlyOnFilter f g l l') :
TendstoUniformlyOnFilter (f⁻¹) (g⁻¹) l l' :=
fun u hu ↦ uniformContinuous_inv.comp_tendstoUniformlyOnFilter hf u hu

attribute [to_additive existing] TendstoUniformlyOnFilter.fun_inv

@[to_additive (attr := to_fun)]
theorem TendstoUniformlyOn.mul (hf : TendstoUniformlyOn f g l s)
(hf' : TendstoUniformlyOn f' g' l s) : TendstoUniformlyOn (f * f') (g * g') l s := fun u hu =>
((uniformContinuous_mul.comp_tendstoUniformlyOn (hf.prodMk hf')) u hu).diag_of_prod

@[to_additive]
attribute [to_additive existing] TendstoUniformlyOn.fun_mul

@[to_additive (attr := to_fun)]
theorem TendstoUniformlyOn.div (hf : TendstoUniformlyOn f g l s)
(hf' : TendstoUniformlyOn f' g' l s) : TendstoUniformlyOn (f / f') (g / g') l s := fun u hu =>
((uniformContinuous_div.comp_tendstoUniformlyOn (hf.prodMk hf')) u hu).diag_of_prod

@[to_additive]
attribute [to_additive existing] TendstoUniformlyOn.fun_div

@[to_additive (attr := to_fun)]
theorem TendstoUniformlyOn.inv (hf : TendstoUniformlyOn f g l s) :
TendstoUniformlyOn (f⁻¹) (g⁻¹) l s :=
fun u hu ↦ uniformContinuous_inv.comp_tendstoUniformlyOn hf u hu

attribute [to_additive existing] TendstoUniformlyOn.fun_inv

@[to_additive (attr := to_fun)]
theorem TendstoUniformly.mul (hf : TendstoUniformly f g l) (hf' : TendstoUniformly f' g' l) :
TendstoUniformly (f * f') (g * g') l := fun u hu =>
((uniformContinuous_mul.comp_tendstoUniformly (hf.prodMk hf')) u hu).diag_of_prod

@[to_additive]
attribute [to_additive existing] TendstoUniformly.fun_mul

@[to_additive (attr := to_fun)]
theorem TendstoUniformly.div (hf : TendstoUniformly f g l) (hf' : TendstoUniformly f' g' l) :
TendstoUniformly (f / f') (g / g') l := fun u hu =>
((uniformContinuous_div.comp_tendstoUniformly (hf.prodMk hf')) u hu).diag_of_prod

@[to_additive]
attribute [to_additive existing] TendstoUniformly.fun_div

@[to_additive (attr := to_fun)]
theorem TendstoUniformly.inv (hf : TendstoUniformly f g l) :
TendstoUniformly (f⁻¹) (g⁻¹) l :=
fun u hu ↦ uniformContinuous_inv.comp_tendstoUniformly hf u hu

attribute [to_additive existing] TendstoUniformly.fun_inv

@[to_additive (attr := to_fun)]
theorem UniformCauchySeqOn.mul (hf : UniformCauchySeqOn f l s) (hf' : UniformCauchySeqOn f' l s) :
UniformCauchySeqOn (f * f') l s := fun u hu => by
simpa using (uniformContinuous_mul.comp_uniformCauchySeqOn (hf.prod' hf')) u hu

@[to_additive]
attribute [to_additive existing] UniformCauchySeqOn.fun_mul

@[to_additive (attr := to_fun)]
theorem UniformCauchySeqOn.div (hf : UniformCauchySeqOn f l s) (hf' : UniformCauchySeqOn f' l s) :
UniformCauchySeqOn (f / f') l s := fun u hu => by
simpa using (uniformContinuous_div.comp_uniformCauchySeqOn (hf.prod' hf')) u hu

attribute [to_additive existing] UniformCauchySeqOn.fun_div

@[to_additive (attr := to_fun)]
theorem UniformCauchySeqOn.inv (hf : UniformCauchySeqOn f l s) :
UniformCauchySeqOn (f⁻¹) l s :=
fun u hu ↦ by simpa using (uniformContinuous_inv.comp_uniformCauchySeqOn hf u hu)

attribute [to_additive existing] UniformCauchySeqOn.fun_inv

end UniformConvergence

section LocalUniformConvergence
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