analysis.normed.group.hom_completion
⟷
Mathlib.Analysis.Normed.Group.HomCompletion
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -289,7 +289,7 @@ theorem NormedAddGroupHom.ker_completion {f : NormedAddGroupHom G H} {C : ℝ}
_ < δ + C' * ‖f‖ * ‖hatg - g‖ := by linarith
_ ≤ δ + C' * ‖f‖ * δ := (add_le_add_left (mul_le_mul_of_nonneg_left hg.le hCf) δ)
_ = (1 + C' * ‖f‖) * δ := by ring
- _ = ε := mul_div_cancel' _ ineq.ne.symm
+ _ = ε := mul_div_cancel₀ _ ineq.ne.symm
· rw [← f.completion.is_closed_ker.closure_eq]
exact closure_mono f.ker_le_ker_completion
#align normed_add_group_hom.ker_completion NormedAddGroupHom.ker_completion
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -237,7 +237,7 @@ theorem NormedAddGroupHom.ker_le_ker_completion (f : NormedAddGroupHom G H) :
intro a h
replace h : ∃ y : f.ker, to_compl (y : G) = a; · simpa using h
rcases h with ⟨⟨g, g_in : g ∈ f.ker⟩, rfl⟩
- rw [f.mem_ker] at g_in
+ rw [f.mem_ker] at g_in
change f.completion (g : completion G) = 0
simp [NormedAddGroupHom.mem_ker, f.completion_coe g, g_in, completion.coe_zero]
#align normed_add_group_hom.ker_le_ker_completion NormedAddGroupHom.ker_le_ker_completion
@@ -301,7 +301,7 @@ section Extension
variable {G : Type _} [SeminormedAddCommGroup G]
-variable {H : Type _} [SeminormedAddCommGroup H] [SeparatedSpace H] [CompleteSpace H]
+variable {H : Type _} [SeminormedAddCommGroup H] [T0Space H] [CompleteSpace H]
#print NormedAddGroupHom.extension /-
/-- If `H` is complete, the extension of `f : normed_add_group_hom G H` to a
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -253,7 +253,7 @@ theorem NormedAddGroupHom.ker_completion {f : NormedAddGroupHom G H} {C : ℝ}
· intro hatg hatg_in
rw [SeminormedAddCommGroup.mem_closure_iff]
intro ε ε_pos
- have hCf : 0 ≤ C' * ‖f‖ := (zero_le_mul_left C'_pos).mpr (norm_nonneg f)
+ have hCf : 0 ≤ C' * ‖f‖ := (mul_nonneg_iff_of_pos_left C'_pos).mpr (norm_nonneg f)
have ineq : 0 < 1 + C' * ‖f‖ := by linarith
set δ := ε / (1 + C' * ‖f‖)
have δ_pos : δ > 0 := div_pos ε_pos ineq
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
-import Mathbin.Analysis.Normed.Group.Hom
-import Mathbin.Analysis.Normed.Group.Completion
+import Analysis.Normed.Group.Hom
+import Analysis.Normed.Group.Completion
#align_import analysis.normed.group.hom_completion from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f
@@ -70,7 +70,7 @@ def NormedAddGroupHom.completion (f : NormedAddGroupHom G H) :
NormedAddGroupHom (Completion G) (Completion H) :=
{ f.toAddMonoidHom.Completion f.Continuous with
bound' := by
- use ‖f‖
+ use‖f‖
intro y
apply completion.induction_on y
·
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-
-! This file was ported from Lean 3 source module analysis.normed.group.hom_completion
-! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Analysis.Normed.Group.Hom
import Mathbin.Analysis.Normed.Group.Completion
+#align_import analysis.normed.group.hom_completion from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
+
/-!
# Completion of normed group homs
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -67,6 +67,7 @@ variable {H : Type _} [SeminormedAddCommGroup H]
variable {K : Type _} [SeminormedAddCommGroup K]
+#print NormedAddGroupHom.completion /-
/-- The normed group hom induced between completions. -/
def NormedAddGroupHom.completion (f : NormedAddGroupHom G H) :
NormedAddGroupHom (Completion G) (Completion H) :=
@@ -86,24 +87,32 @@ def NormedAddGroupHom.completion (f : NormedAddGroupHom G H) :
simp only [completion.norm_coe]
exact f.le_op_norm x }
#align normed_add_group_hom.completion NormedAddGroupHom.completion
+-/
+#print NormedAddGroupHom.completion_def /-
theorem NormedAddGroupHom.completion_def (f : NormedAddGroupHom G H) (x : Completion G) :
f.Completion x = Completion.map f x :=
rfl
#align normed_add_group_hom.completion_def NormedAddGroupHom.completion_def
+-/
+#print NormedAddGroupHom.completion_coe_to_fun /-
@[simp]
theorem NormedAddGroupHom.completion_coe_to_fun (f : NormedAddGroupHom G H) :
(f.Completion : Completion G → Completion H) = Completion.map f := by ext x;
exact NormedAddGroupHom.completion_def f x
#align normed_add_group_hom.completion_coe_to_fun NormedAddGroupHom.completion_coe_to_fun
+-/
+#print NormedAddGroupHom.completion_coe /-
@[simp]
theorem NormedAddGroupHom.completion_coe (f : NormedAddGroupHom G H) (g : G) :
f.Completion g = f g :=
Completion.map_coe f.UniformContinuous _
#align normed_add_group_hom.completion_coe NormedAddGroupHom.completion_coe
+-/
+#print normedAddGroupHomCompletionHom /-
/-- Completion of normed group homs as a normed group hom. -/
@[simps]
def normedAddGroupHomCompletionHom :
@@ -117,7 +126,9 @@ def normedAddGroupHomCompletionHom :
apply to_add_monoid_hom_injective
exact f.to_add_monoid_hom.completion_add g.to_add_monoid_hom f.continuous g.continuous
#align normed_add_group_hom_completion_hom normedAddGroupHomCompletionHom
+-/
+#print NormedAddGroupHom.completion_id /-
@[simp]
theorem NormedAddGroupHom.completion_id :
(NormedAddGroupHom.id G).Completion = NormedAddGroupHom.id (Completion G) :=
@@ -126,7 +137,9 @@ theorem NormedAddGroupHom.completion_id :
rw [NormedAddGroupHom.completion_def, NormedAddGroupHom.coe_id, completion.map_id]
rfl
#align normed_add_group_hom.completion_id NormedAddGroupHom.completion_id
+-/
+#print NormedAddGroupHom.completion_comp /-
theorem NormedAddGroupHom.completion_comp (f : NormedAddGroupHom G H) (g : NormedAddGroupHom H K) :
g.Completion.comp f.Completion = (g.comp f).Completion :=
by
@@ -137,27 +150,37 @@ theorem NormedAddGroupHom.completion_comp (f : NormedAddGroupHom G H) (g : Norme
(NormedAddGroupHom.uniformContinuous _)]
rfl
#align normed_add_group_hom.completion_comp NormedAddGroupHom.completion_comp
+-/
+#print NormedAddGroupHom.completion_neg /-
theorem NormedAddGroupHom.completion_neg (f : NormedAddGroupHom G H) :
(-f).Completion = -f.Completion :=
map_neg (normedAddGroupHomCompletionHom : NormedAddGroupHom G H →+ _) f
#align normed_add_group_hom.completion_neg NormedAddGroupHom.completion_neg
+-/
+#print NormedAddGroupHom.completion_add /-
theorem NormedAddGroupHom.completion_add (f g : NormedAddGroupHom G H) :
(f + g).Completion = f.Completion + g.Completion :=
normedAddGroupHomCompletionHom.map_add f g
#align normed_add_group_hom.completion_add NormedAddGroupHom.completion_add
+-/
+#print NormedAddGroupHom.completion_sub /-
theorem NormedAddGroupHom.completion_sub (f g : NormedAddGroupHom G H) :
(f - g).Completion = f.Completion - g.Completion :=
map_sub (normedAddGroupHomCompletionHom : NormedAddGroupHom G H →+ _) f g
#align normed_add_group_hom.completion_sub NormedAddGroupHom.completion_sub
+-/
+#print NormedAddGroupHom.zero_completion /-
@[simp]
theorem NormedAddGroupHom.zero_completion : (0 : NormedAddGroupHom G H).Completion = 0 :=
normedAddGroupHomCompletionHom.map_zero
#align normed_add_group_hom.zero_completion NormedAddGroupHom.zero_completion
+-/
+#print NormedAddCommGroup.toCompl /-
/-- The map from a normed group to its completion, as a normed group hom. -/
def NormedAddCommGroup.toCompl : NormedAddGroupHom G (Completion G)
where
@@ -165,6 +188,7 @@ def NormedAddCommGroup.toCompl : NormedAddGroupHom G (Completion G)
map_add' := Completion.toCompl.map_add
bound' := ⟨1, by simp [le_refl]⟩
#align normed_add_comm_group.to_compl NormedAddCommGroup.toCompl
+-/
open NormedAddCommGroup
@@ -174,10 +198,13 @@ theorem NormedAddCommGroup.norm_toCompl (x : G) : ‖toCompl x‖ = ‖x‖ :=
#align normed_add_comm_group.norm_to_compl NormedAddCommGroup.norm_toCompl
-/
+#print NormedAddCommGroup.denseRange_toCompl /-
theorem NormedAddCommGroup.denseRange_toCompl : DenseRange (toCompl : G → Completion G) :=
Completion.denseInducing_coe.dense
#align normed_add_comm_group.dense_range_to_compl NormedAddCommGroup.denseRange_toCompl
+-/
+#print NormedAddGroupHom.completion_toCompl /-
@[simp]
theorem NormedAddGroupHom.completion_toCompl (f : NormedAddGroupHom G H) :
f.Completion.comp toCompl = toCompl.comp f :=
@@ -186,7 +213,9 @@ theorem NormedAddGroupHom.completion_toCompl (f : NormedAddGroupHom G H) :
change f.completion x = _
simpa
#align normed_add_group_hom.completion_to_compl NormedAddGroupHom.completion_toCompl
+-/
+#print NormedAddGroupHom.norm_completion /-
@[simp]
theorem NormedAddGroupHom.norm_completion (f : NormedAddGroupHom G H) : ‖f.Completion‖ = ‖f‖ :=
by
@@ -202,7 +231,9 @@ theorem NormedAddGroupHom.norm_completion (f : NormedAddGroupHom G H) : ‖f.Com
intro x
simpa using hN x
#align normed_add_group_hom.norm_completion NormedAddGroupHom.norm_completion
+-/
+#print NormedAddGroupHom.ker_le_ker_completion /-
theorem NormedAddGroupHom.ker_le_ker_completion (f : NormedAddGroupHom G H) :
(toCompl.comp <| incl f.ker).range ≤ f.Completion.ker :=
by
@@ -213,7 +244,9 @@ theorem NormedAddGroupHom.ker_le_ker_completion (f : NormedAddGroupHom G H) :
change f.completion (g : completion G) = 0
simp [NormedAddGroupHom.mem_ker, f.completion_coe g, g_in, completion.coe_zero]
#align normed_add_group_hom.ker_le_ker_completion NormedAddGroupHom.ker_le_ker_completion
+-/
+#print NormedAddGroupHom.ker_completion /-
theorem NormedAddGroupHom.ker_completion {f : NormedAddGroupHom G H} {C : ℝ}
(h : f.SurjectiveOnWith f.range C) :
(f.Completion.ker : Set <| Completion G) = closure (toCompl.comp <| incl f.ker).range :=
@@ -263,6 +296,7 @@ theorem NormedAddGroupHom.ker_completion {f : NormedAddGroupHom G H} {C : ℝ}
· rw [← f.completion.is_closed_ker.closure_eq]
exact closure_mono f.ker_le_ker_completion
#align normed_add_group_hom.ker_completion NormedAddGroupHom.ker_completion
+-/
end Completion
@@ -272,6 +306,7 @@ variable {G : Type _} [SeminormedAddCommGroup G]
variable {H : Type _} [SeminormedAddCommGroup H] [SeparatedSpace H] [CompleteSpace H]
+#print NormedAddGroupHom.extension /-
/-- If `H` is complete, the extension of `f : normed_add_group_hom G H` to a
`normed_add_group_hom (completion G) H`. -/
def NormedAddGroupHom.extension (f : NormedAddGroupHom G H) : NormedAddGroupHom (Completion G) H :=
@@ -284,22 +319,30 @@ def NormedAddGroupHom.extension (f : NormedAddGroupHom G H) : NormedAddGroupHom
· rw [completion.norm_coe, AddMonoidHom.toFun_eq_coe, AddMonoidHom.extension_coe]
exact le_op_norm f a }
#align normed_add_group_hom.extension NormedAddGroupHom.extension
+-/
+#print NormedAddGroupHom.extension_def /-
theorem NormedAddGroupHom.extension_def (f : NormedAddGroupHom G H) (v : G) :
f.extension v = Completion.extension f v :=
rfl
#align normed_add_group_hom.extension_def NormedAddGroupHom.extension_def
+-/
+#print NormedAddGroupHom.extension_coe /-
@[simp]
theorem NormedAddGroupHom.extension_coe (f : NormedAddGroupHom G H) (v : G) : f.extension v = f v :=
AddMonoidHom.extension_coe _ f.Continuous _
#align normed_add_group_hom.extension_coe NormedAddGroupHom.extension_coe
+-/
+#print NormedAddGroupHom.extension_coe_to_fun /-
theorem NormedAddGroupHom.extension_coe_to_fun (f : NormedAddGroupHom G H) :
(f.extension : Completion G → H) = Completion.extension f :=
rfl
#align normed_add_group_hom.extension_coe_to_fun NormedAddGroupHom.extension_coe_to_fun
+-/
+#print NormedAddGroupHom.extension_unique /-
theorem NormedAddGroupHom.extension_unique (f : NormedAddGroupHom G H)
{g : NormedAddGroupHom (Completion G) H} (hg : ∀ v, f v = g v) : f.extension = g :=
by
@@ -307,6 +350,7 @@ theorem NormedAddGroupHom.extension_unique (f : NormedAddGroupHom G H)
rw [NormedAddGroupHom.extension_coe_to_fun,
completion.extension_unique f.uniform_continuous g.uniform_continuous fun a => hg a]
#align normed_add_group_hom.extension_unique NormedAddGroupHom.extension_unique
+-/
end Extension
mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0
@@ -240,7 +240,6 @@ theorem NormedAddGroupHom.ker_completion {f : NormedAddGroupHom G H} {C : ℝ}
_ = ‖f.completion (g - hatg)‖ := by rw [map_sub]
_ ≤ ‖f.completion‖ * ‖(g : completion G) - hatg‖ := (f.completion.le_op_norm _)
_ = ‖f‖ * ‖hatg - g‖ := by rw [norm_sub_rev, f.norm_completion]
-
have : ‖(g' : completion G)‖ ≤ C' * ‖f‖ * ‖hatg - g‖
calc
‖(g' : completion G)‖ = ‖g'‖ := completion.norm_coe _
@@ -248,7 +247,6 @@ theorem NormedAddGroupHom.ker_completion {f : NormedAddGroupHom G H} {C : ℝ}
_ ≤ C' * ‖f‖ * ‖hatg - g‖ := by
rw [mul_assoc]
exact (mul_le_mul_left C'_pos).mpr this
-
refine' ⟨g - g', _, _⟩
· norm_cast
rw [NormedAddGroupHom.comp_range]
@@ -262,7 +260,6 @@ theorem NormedAddGroupHom.ker_completion {f : NormedAddGroupHom G H} {C : ℝ}
_ ≤ δ + C' * ‖f‖ * δ := (add_le_add_left (mul_le_mul_of_nonneg_left hg.le hCf) δ)
_ = (1 + C' * ‖f‖) * δ := by ring
_ = ε := mul_div_cancel' _ ineq.ne.symm
-
· rw [← f.completion.is_closed_ker.closure_eq]
exact closure_mono f.ker_le_ker_completion
#align normed_add_group_hom.ker_completion NormedAddGroupHom.ker_completion
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -209,7 +209,7 @@ theorem NormedAddGroupHom.ker_le_ker_completion (f : NormedAddGroupHom G H) :
intro a h
replace h : ∃ y : f.ker, to_compl (y : G) = a; · simpa using h
rcases h with ⟨⟨g, g_in : g ∈ f.ker⟩, rfl⟩
- rw [f.mem_ker] at g_in
+ rw [f.mem_ker] at g_in
change f.completion (g : completion G) = 0
simp [NormedAddGroupHom.mem_ker, f.completion_coe g, g_in, completion.coe_zero]
#align normed_add_group_hom.ker_le_ker_completion NormedAddGroupHom.ker_le_ker_completion
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -67,12 +67,6 @@ variable {H : Type _} [SeminormedAddCommGroup H]
variable {K : Type _} [SeminormedAddCommGroup K]
-/- warning: normed_add_group_hom.completion -> NormedAddGroupHom.completion is a dubious translation:
-lean 3 declaration is
- forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H], (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) -> (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2)))
-but is expected to have type
- forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H], (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) -> (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} H _inst_2)))
-Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion NormedAddGroupHom.completionₓ'. -/
/-- The normed group hom induced between completions. -/
def NormedAddGroupHom.completion (f : NormedAddGroupHom G H) :
NormedAddGroupHom (Completion G) (Completion H) :=
@@ -93,35 +87,23 @@ def NormedAddGroupHom.completion (f : NormedAddGroupHom G H) :
exact f.le_op_norm x }
#align normed_add_group_hom.completion NormedAddGroupHom.completion
-/- warning: normed_add_group_hom.completion_def -> NormedAddGroupHom.completion_def is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion_def NormedAddGroupHom.completion_defₓ'. -/
theorem NormedAddGroupHom.completion_def (f : NormedAddGroupHom G H) (x : Completion G) :
f.Completion x = Completion.map f x :=
rfl
#align normed_add_group_hom.completion_def NormedAddGroupHom.completion_def
-/- warning: normed_add_group_hom.completion_coe_to_fun -> NormedAddGroupHom.completion_coe_to_fun is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion_coe_to_fun NormedAddGroupHom.completion_coe_to_funₓ'. -/
@[simp]
theorem NormedAddGroupHom.completion_coe_to_fun (f : NormedAddGroupHom G H) :
(f.Completion : Completion G → Completion H) = Completion.map f := by ext x;
exact NormedAddGroupHom.completion_def f x
#align normed_add_group_hom.completion_coe_to_fun NormedAddGroupHom.completion_coe_to_fun
-/- warning: normed_add_group_hom.completion_coe -> NormedAddGroupHom.completion_coe is a dubious translation:
-<too large>
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@[simp]
theorem NormedAddGroupHom.completion_coe (f : NormedAddGroupHom G H) (g : G) :
f.Completion g = f g :=
Completion.map_coe f.UniformContinuous _
#align normed_add_group_hom.completion_coe NormedAddGroupHom.completion_coe
-/- warning: normed_add_group_hom_completion_hom -> normedAddGroupHomCompletionHom is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align normed_add_group_hom_completion_hom normedAddGroupHomCompletionHomₓ'. -/
/-- Completion of normed group homs as a normed group hom. -/
@[simps]
def normedAddGroupHomCompletionHom :
@@ -136,12 +118,6 @@ def normedAddGroupHomCompletionHom :
exact f.to_add_monoid_hom.completion_add g.to_add_monoid_hom f.continuous g.continuous
#align normed_add_group_hom_completion_hom normedAddGroupHomCompletionHom
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@[simp]
theorem NormedAddGroupHom.completion_id :
(NormedAddGroupHom.id G).Completion = NormedAddGroupHom.id (Completion G) :=
@@ -151,12 +127,6 @@ theorem NormedAddGroupHom.completion_id :
rfl
#align normed_add_group_hom.completion_id NormedAddGroupHom.completion_id
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theorem NormedAddGroupHom.completion_comp (f : NormedAddGroupHom G H) (g : NormedAddGroupHom H K) :
g.Completion.comp f.Completion = (g.comp f).Completion :=
by
@@ -168,50 +138,26 @@ theorem NormedAddGroupHom.completion_comp (f : NormedAddGroupHom G H) (g : Norme
rfl
#align normed_add_group_hom.completion_comp NormedAddGroupHom.completion_comp
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theorem NormedAddGroupHom.completion_neg (f : NormedAddGroupHom G H) :
(-f).Completion = -f.Completion :=
map_neg (normedAddGroupHomCompletionHom : NormedAddGroupHom G H →+ _) f
#align normed_add_group_hom.completion_neg NormedAddGroupHom.completion_neg
-/- warning: normed_add_group_hom.completion_add -> NormedAddGroupHom.completion_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion_add NormedAddGroupHom.completion_addₓ'. -/
theorem NormedAddGroupHom.completion_add (f g : NormedAddGroupHom G H) :
(f + g).Completion = f.Completion + g.Completion :=
normedAddGroupHomCompletionHom.map_add f g
#align normed_add_group_hom.completion_add NormedAddGroupHom.completion_add
-/- warning: normed_add_group_hom.completion_sub -> NormedAddGroupHom.completion_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion_sub NormedAddGroupHom.completion_subₓ'. -/
theorem NormedAddGroupHom.completion_sub (f g : NormedAddGroupHom G H) :
(f - g).Completion = f.Completion - g.Completion :=
map_sub (normedAddGroupHomCompletionHom : NormedAddGroupHom G H →+ _) f g
#align normed_add_group_hom.completion_sub NormedAddGroupHom.completion_sub
-/- warning: normed_add_group_hom.zero_completion -> NormedAddGroupHom.zero_completion is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.zero_completion NormedAddGroupHom.zero_completionₓ'. -/
@[simp]
theorem NormedAddGroupHom.zero_completion : (0 : NormedAddGroupHom G H).Completion = 0 :=
normedAddGroupHomCompletionHom.map_zero
#align normed_add_group_hom.zero_completion NormedAddGroupHom.zero_completion
-/- warning: normed_add_comm_group.to_compl -> NormedAddCommGroup.toCompl is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align normed_add_comm_group.to_compl NormedAddCommGroup.toComplₓ'. -/
/-- The map from a normed group to its completion, as a normed group hom. -/
def NormedAddCommGroup.toCompl : NormedAddGroupHom G (Completion G)
where
@@ -228,22 +174,10 @@ theorem NormedAddCommGroup.norm_toCompl (x : G) : ‖toCompl x‖ = ‖x‖ :=
#align normed_add_comm_group.norm_to_compl NormedAddCommGroup.norm_toCompl
-/
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-Case conversion may be inaccurate. Consider using '#align normed_add_comm_group.dense_range_to_compl NormedAddCommGroup.denseRange_toComplₓ'. -/
theorem NormedAddCommGroup.denseRange_toCompl : DenseRange (toCompl : G → Completion G) :=
Completion.denseInducing_coe.dense
#align normed_add_comm_group.dense_range_to_compl NormedAddCommGroup.denseRange_toCompl
-/- warning: normed_add_group_hom.completion_to_compl -> NormedAddGroupHom.completion_toCompl is a dubious translation:
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@[simp]
theorem NormedAddGroupHom.completion_toCompl (f : NormedAddGroupHom G H) :
f.Completion.comp toCompl = toCompl.comp f :=
@@ -253,12 +187,6 @@ theorem NormedAddGroupHom.completion_toCompl (f : NormedAddGroupHom G H) :
simpa
#align normed_add_group_hom.completion_to_compl NormedAddGroupHom.completion_toCompl
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-Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.norm_completion NormedAddGroupHom.norm_completionₓ'. -/
@[simp]
theorem NormedAddGroupHom.norm_completion (f : NormedAddGroupHom G H) : ‖f.Completion‖ = ‖f‖ :=
by
@@ -275,9 +203,6 @@ theorem NormedAddGroupHom.norm_completion (f : NormedAddGroupHom G H) : ‖f.Com
simpa using hN x
#align normed_add_group_hom.norm_completion NormedAddGroupHom.norm_completion
-/- warning: normed_add_group_hom.ker_le_ker_completion -> NormedAddGroupHom.ker_le_ker_completion is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.ker_le_ker_completion NormedAddGroupHom.ker_le_ker_completionₓ'. -/
theorem NormedAddGroupHom.ker_le_ker_completion (f : NormedAddGroupHom G H) :
(toCompl.comp <| incl f.ker).range ≤ f.Completion.ker :=
by
@@ -289,9 +214,6 @@ theorem NormedAddGroupHom.ker_le_ker_completion (f : NormedAddGroupHom G H) :
simp [NormedAddGroupHom.mem_ker, f.completion_coe g, g_in, completion.coe_zero]
#align normed_add_group_hom.ker_le_ker_completion NormedAddGroupHom.ker_le_ker_completion
-/- warning: normed_add_group_hom.ker_completion -> NormedAddGroupHom.ker_completion is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.ker_completion NormedAddGroupHom.ker_completionₓ'. -/
theorem NormedAddGroupHom.ker_completion {f : NormedAddGroupHom G H} {C : ℝ}
(h : f.SurjectiveOnWith f.range C) :
(f.Completion.ker : Set <| Completion G) = closure (toCompl.comp <| incl f.ker).range :=
@@ -353,12 +275,6 @@ variable {G : Type _} [SeminormedAddCommGroup G]
variable {H : Type _} [SeminormedAddCommGroup H] [SeparatedSpace H] [CompleteSpace H]
-/- warning: normed_add_group_hom.extension -> NormedAddGroupHom.extension is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.extension NormedAddGroupHom.extensionₓ'. -/
/-- If `H` is complete, the extension of `f : normed_add_group_hom G H` to a
`normed_add_group_hom (completion G) H`. -/
def NormedAddGroupHom.extension (f : NormedAddGroupHom G H) : NormedAddGroupHom (Completion G) H :=
@@ -372,33 +288,21 @@ def NormedAddGroupHom.extension (f : NormedAddGroupHom G H) : NormedAddGroupHom
exact le_op_norm f a }
#align normed_add_group_hom.extension NormedAddGroupHom.extension
-/- warning: normed_add_group_hom.extension_def -> NormedAddGroupHom.extension_def is a dubious translation:
-<too large>
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theorem NormedAddGroupHom.extension_def (f : NormedAddGroupHom G H) (v : G) :
f.extension v = Completion.extension f v :=
rfl
#align normed_add_group_hom.extension_def NormedAddGroupHom.extension_def
-/- warning: normed_add_group_hom.extension_coe -> NormedAddGroupHom.extension_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.extension_coe NormedAddGroupHom.extension_coeₓ'. -/
@[simp]
theorem NormedAddGroupHom.extension_coe (f : NormedAddGroupHom G H) (v : G) : f.extension v = f v :=
AddMonoidHom.extension_coe _ f.Continuous _
#align normed_add_group_hom.extension_coe NormedAddGroupHom.extension_coe
-/- warning: normed_add_group_hom.extension_coe_to_fun -> NormedAddGroupHom.extension_coe_to_fun is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.extension_coe_to_fun NormedAddGroupHom.extension_coe_to_funₓ'. -/
theorem NormedAddGroupHom.extension_coe_to_fun (f : NormedAddGroupHom G H) :
(f.extension : Completion G → H) = Completion.extension f :=
rfl
#align normed_add_group_hom.extension_coe_to_fun NormedAddGroupHom.extension_coe_to_fun
-/- warning: normed_add_group_hom.extension_unique -> NormedAddGroupHom.extension_unique is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.extension_unique NormedAddGroupHom.extension_uniqueₓ'. -/
theorem NormedAddGroupHom.extension_unique (f : NormedAddGroupHom G H)
{g : NormedAddGroupHom (Completion G) H} (hg : ∀ v, f v = g v) : f.extension = g :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -106,9 +106,7 @@ theorem NormedAddGroupHom.completion_def (f : NormedAddGroupHom G H) (x : Comple
Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion_coe_to_fun NormedAddGroupHom.completion_coe_to_funₓ'. -/
@[simp]
theorem NormedAddGroupHom.completion_coe_to_fun (f : NormedAddGroupHom G H) :
- (f.Completion : Completion G → Completion H) = Completion.map f :=
- by
- ext x
+ (f.Completion : Completion G → Completion H) = Completion.map f := by ext x;
exact NormedAddGroupHom.completion_def f x
#align normed_add_group_hom.completion_coe_to_fun NormedAddGroupHom.completion_coe_to_fun
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -94,10 +94,7 @@ def NormedAddGroupHom.completion (f : NormedAddGroupHom G H) :
#align normed_add_group_hom.completion NormedAddGroupHom.completion
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_inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (fun (_x : UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) => UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (AddHomClass.toFunLike.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G 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_inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))))) (AddMonoid.toAddZeroClass.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (SubNegMonoid.toAddMonoid.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (AddGroup.toSubNegMonoid.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) 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(PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))))) (NormedAddGroupHom.completion.{u2, u1} G _inst_1 H _inst_2 f) x) (UniformSpace.Completion.map.{u2, u1} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1)) H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) G (fun (_x : G) => H) (AddHomClass.toFunLike.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) G H (AddZeroClass.toAdd.{u2} G (AddMonoid.toAddZeroClass.{u2} G (SubNegMonoid.toAddMonoid.{u2} G (AddGroup.toSubNegMonoid.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1)))))) (AddZeroClass.toAdd.{u1} H (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2)))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) G H (AddMonoid.toAddZeroClass.{u2} G (SubNegMonoid.toAddMonoid.{u2} G (AddGroup.toSubNegMonoid.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))))) (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2))))) (NormedAddGroupHom.toAddMonoidHomClass.{u2, u1} G H _inst_1 _inst_2))) f) x)
+<too large>
Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion_def NormedAddGroupHom.completion_defₓ'. -/
theorem NormedAddGroupHom.completion_def (f : NormedAddGroupHom G H) (x : Completion G) :
f.Completion x = Completion.map f x :=
@@ -105,10 +102,7 @@ theorem NormedAddGroupHom.completion_def (f : NormedAddGroupHom G H) (x : Comple
#align normed_add_group_hom.completion_def NormedAddGroupHom.completion_def
/- warning: normed_add_group_hom.completion_coe_to_fun -> NormedAddGroupHom.completion_coe_to_fun is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion_coe_to_fun NormedAddGroupHom.completion_coe_to_funₓ'. -/
@[simp]
theorem NormedAddGroupHom.completion_coe_to_fun (f : NormedAddGroupHom G H) :
@@ -119,10 +113,7 @@ theorem NormedAddGroupHom.completion_coe_to_fun (f : NormedAddGroupHom G H) :
#align normed_add_group_hom.completion_coe_to_fun NormedAddGroupHom.completion_coe_to_fun
/- warning: normed_add_group_hom.completion_coe -> NormedAddGroupHom.completion_coe is a dubious translation:
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(UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2)))))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (AddMonoid.toAddZeroClass.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))))))) (NormedAddGroupHom.toAddMonoidHomClass.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))))) (NormedAddGroupHom.completion.{u2, u1} G _inst_1 H _inst_2 f) (UniformSpace.Completion.coe'.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1)) g)) (UniformSpace.Completion.coe'.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) G (fun (_x : G) => H) (AddHomClass.toFunLike.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) G H (AddZeroClass.toAdd.{u2} G (AddMonoid.toAddZeroClass.{u2} G (SubNegMonoid.toAddMonoid.{u2} G (AddGroup.toSubNegMonoid.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1)))))) (AddZeroClass.toAdd.{u1} H (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2)))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) G H (AddMonoid.toAddZeroClass.{u2} G (SubNegMonoid.toAddMonoid.{u2} G (AddGroup.toSubNegMonoid.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))))) (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2))))) (NormedAddGroupHom.toAddMonoidHomClass.{u2, u1} G H _inst_1 _inst_2))) f g))
+<too large>
Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion_coe NormedAddGroupHom.completion_coeₓ'. -/
@[simp]
theorem NormedAddGroupHom.completion_coe (f : NormedAddGroupHom G H) (g : G) :
@@ -131,10 +122,7 @@ theorem NormedAddGroupHom.completion_coe (f : NormedAddGroupHom G H) (g : G) :
#align normed_add_group_hom.completion_coe NormedAddGroupHom.completion_coe
/- warning: normed_add_group_hom_completion_hom -> normedAddGroupHomCompletionHom is a dubious translation:
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(UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.toNormedAddCommGroup.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H 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+<too large>
Case conversion may be inaccurate. Consider using '#align normed_add_group_hom_completion_hom normedAddGroupHomCompletionHomₓ'. -/
/-- Completion of normed group homs as a normed group hom. -/
@[simps]
@@ -194,10 +182,7 @@ theorem NormedAddGroupHom.completion_neg (f : NormedAddGroupHom G H) :
#align normed_add_group_hom.completion_neg NormedAddGroupHom.completion_neg
/- warning: normed_add_group_hom.completion_add -> NormedAddGroupHom.completion_add is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion_add NormedAddGroupHom.completion_addₓ'. -/
theorem NormedAddGroupHom.completion_add (f g : NormedAddGroupHom G H) :
(f + g).Completion = f.Completion + g.Completion :=
@@ -205,10 +190,7 @@ theorem NormedAddGroupHom.completion_add (f g : NormedAddGroupHom G H) :
#align normed_add_group_hom.completion_add NormedAddGroupHom.completion_add
/- warning: normed_add_group_hom.completion_sub -> NormedAddGroupHom.completion_sub is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion_sub NormedAddGroupHom.completion_subₓ'. -/
theorem NormedAddGroupHom.completion_sub (f g : NormedAddGroupHom G H) :
(f - g).Completion = f.Completion - g.Completion :=
@@ -296,10 +278,7 @@ theorem NormedAddGroupHom.norm_completion (f : NormedAddGroupHom G H) : ‖f.Com
#align normed_add_group_hom.norm_completion NormedAddGroupHom.norm_completion
/- warning: normed_add_group_hom.ker_le_ker_completion -> NormedAddGroupHom.ker_le_ker_completion is a dubious translation:
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_inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (AddSubgroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (AddSubgroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))) (AddSubgroup.instCompleteLatticeAddSubgroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))))))) (NormedAddGroupHom.range.{u2, u2} (Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (AddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))) G (AddSubgroup.instSetLikeAddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1)))) x (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f))) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddSubgroup.seminormedAddCommGroup.{u2} G _inst_1 (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddGroupHom.comp.{u2, u2, u2} (Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (AddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))) G (AddSubgroup.instSetLikeAddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1)))) x (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f))) G (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddSubgroup.seminormedAddCommGroup.{u2} G _inst_1 (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f)) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toCompl.{u2} G _inst_1) (NormedAddGroupHom.incl.{u2} G _inst_1 (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f)))) (NormedAddGroupHom.ker.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2)) (NormedAddGroupHom.completion.{u2, u1} G _inst_1 H _inst_2 f))
+<too large>
Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.ker_le_ker_completion NormedAddGroupHom.ker_le_ker_completionₓ'. -/
theorem NormedAddGroupHom.ker_le_ker_completion (f : NormedAddGroupHom G H) :
(toCompl.comp <| incl f.ker).range ≤ f.Completion.ker :=
@@ -313,10 +292,7 @@ theorem NormedAddGroupHom.ker_le_ker_completion (f : NormedAddGroupHom G H) :
#align normed_add_group_hom.ker_le_ker_completion NormedAddGroupHom.ker_le_ker_completion
/- warning: normed_add_group_hom.ker_completion -> NormedAddGroupHom.ker_completion is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.ker_completion NormedAddGroupHom.ker_completionₓ'. -/
theorem NormedAddGroupHom.ker_completion {f : NormedAddGroupHom G H} {C : ℝ}
(h : f.SurjectiveOnWith f.range C) :
@@ -399,10 +375,7 @@ def NormedAddGroupHom.extension (f : NormedAddGroupHom G H) : NormedAddGroupHom
#align normed_add_group_hom.extension NormedAddGroupHom.extension
/- warning: normed_add_group_hom.extension_def -> NormedAddGroupHom.extension_def is a dubious translation:
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(PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddMonoid.toAddZeroClass.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SubNegMonoid.toAddMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddGroup.toSubNegMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)))))))) (AddZeroClass.toAdd.{u1} H (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2)))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) _inst_2) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (AddMonoid.toAddZeroClass.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SubNegMonoid.toAddMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddGroup.toSubNegMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))))) (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2))))) (NormedAddGroupHom.toAddMonoidHomClass.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) _inst_2))) (NormedAddGroupHom.extension.{u2, u1} G _inst_1 H _inst_2 _inst_3 _inst_4 f) (UniformSpace.Completion.coe'.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1)) v)) (UniformSpace.Completion.extension.{u2, u1} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1)) H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) G (fun (_x : G) => H) (AddHomClass.toFunLike.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) G H (AddZeroClass.toAdd.{u2} G (AddMonoid.toAddZeroClass.{u2} G (SubNegMonoid.toAddMonoid.{u2} G (AddGroup.toSubNegMonoid.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1)))))) (AddZeroClass.toAdd.{u1} H (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2)))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) G H (AddMonoid.toAddZeroClass.{u2} G (SubNegMonoid.toAddMonoid.{u2} G (AddGroup.toSubNegMonoid.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))))) (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2))))) (NormedAddGroupHom.toAddMonoidHomClass.{u2, u1} G H _inst_1 _inst_2))) f) (UniformSpace.Completion.coe'.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1)) v))
+<too large>
Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.extension_def NormedAddGroupHom.extension_defₓ'. -/
theorem NormedAddGroupHom.extension_def (f : NormedAddGroupHom G H) (v : G) :
f.extension v = Completion.extension f v :=
@@ -410,10 +383,7 @@ theorem NormedAddGroupHom.extension_def (f : NormedAddGroupHom G H) (v : G) :
#align normed_add_group_hom.extension_def NormedAddGroupHom.extension_def
/- warning: normed_add_group_hom.extension_coe -> NormedAddGroupHom.extension_coe is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.extension_coe NormedAddGroupHom.extension_coeₓ'. -/
@[simp]
theorem NormedAddGroupHom.extension_coe (f : NormedAddGroupHom G H) (v : G) : f.extension v = f v :=
@@ -421,10 +391,7 @@ theorem NormedAddGroupHom.extension_coe (f : NormedAddGroupHom G H) (v : G) : f.
#align normed_add_group_hom.extension_coe NormedAddGroupHom.extension_coe
/- warning: normed_add_group_hom.extension_coe_to_fun -> NormedAddGroupHom.extension_coe_to_fun is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.extension_coe_to_fun NormedAddGroupHom.extension_coe_to_funₓ'. -/
theorem NormedAddGroupHom.extension_coe_to_fun (f : NormedAddGroupHom G H) :
(f.extension : Completion G → H) = Completion.extension f :=
@@ -432,10 +399,7 @@ theorem NormedAddGroupHom.extension_coe_to_fun (f : NormedAddGroupHom G H) :
#align normed_add_group_hom.extension_coe_to_fun NormedAddGroupHom.extension_coe_to_fun
/- warning: normed_add_group_hom.extension_unique -> NormedAddGroupHom.extension_unique is a dubious translation:
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(SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SubNegMonoid.toAddMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddGroup.toSubNegMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)))))))) (AddZeroClass.toAdd.{u1} H (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2)))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) _inst_2) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (AddMonoid.toAddZeroClass.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SubNegMonoid.toAddMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddGroup.toSubNegMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))))) (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2))))) (NormedAddGroupHom.toAddMonoidHomClass.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) _inst_2))) g (UniformSpace.Completion.coe'.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1)) v))) -> (Eq.{max (succ u2) (succ u1)} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) _inst_2) (NormedAddGroupHom.extension.{u2, u1} G _inst_1 H _inst_2 _inst_3 _inst_4 f) g)
+<too large>
Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.extension_unique NormedAddGroupHom.extension_uniqueₓ'. -/
theorem NormedAddGroupHom.extension_unique (f : NormedAddGroupHom G H)
{g : NormedAddGroupHom (Completion G) H} (hg : ∀ v, f v = g v) : f.extension = g :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -297,7 +297,7 @@ theorem NormedAddGroupHom.norm_completion (f : NormedAddGroupHom G H) : ‖f.Com
/- warning: normed_add_group_hom.ker_le_ker_completion -> NormedAddGroupHom.ker_le_ker_completion is a dubious translation:
lean 3 declaration is
- forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H] (f : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2), LE.le.{u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) (Preorder.toLE.{u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) (AddSubgroup.completeLattice.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))))))) (NormedAddGroupHom.range.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1))) G (AddSubgroup.setLike.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1)))) (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (AddSubgroup.seminormedAddCommGroup.{u1} G _inst_1 (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddGroupHom.comp.{u1, u1, u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1))) G (AddSubgroup.setLike.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1)))) (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (AddSubgroup.seminormedAddCommGroup.{u1} G _inst_1 (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toCompl.{u1} G _inst_1) (NormedAddGroupHom.incl.{u1} G _inst_1 (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)))) (NormedAddGroupHom.ker.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2)) (NormedAddGroupHom.completion.{u1, u2} G _inst_1 H _inst_2 f))
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H] (f : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2), LE.le.{u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) (AddSubgroup.completeLattice.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))))))) (NormedAddGroupHom.range.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1))) G (AddSubgroup.setLike.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1)))) (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (AddSubgroup.seminormedAddCommGroup.{u1} G _inst_1 (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddGroupHom.comp.{u1, u1, u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1))) G (AddSubgroup.setLike.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1)))) (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (AddSubgroup.seminormedAddCommGroup.{u1} G _inst_1 (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toCompl.{u1} G _inst_1) (NormedAddGroupHom.incl.{u1} G _inst_1 (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)))) (NormedAddGroupHom.ker.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2)) (NormedAddGroupHom.completion.{u1, u2} G _inst_1 H _inst_2 f))
but is expected to have type
forall {G : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} G] {H : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} H] (f : NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2), LE.le.{u2} (AddSubgroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))) (Preorder.toLE.{u2} (AddSubgroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (AddSubgroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (AddSubgroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))) (AddSubgroup.instCompleteLatticeAddSubgroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))))))) (NormedAddGroupHom.range.{u2, u2} (Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (AddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))) G (AddSubgroup.instSetLikeAddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1)))) x (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f))) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddSubgroup.seminormedAddCommGroup.{u2} G _inst_1 (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddGroupHom.comp.{u2, u2, u2} (Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (AddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))) G (AddSubgroup.instSetLikeAddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1)))) x (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f))) G (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddSubgroup.seminormedAddCommGroup.{u2} G _inst_1 (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f)) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toCompl.{u2} G _inst_1) (NormedAddGroupHom.incl.{u2} G _inst_1 (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f)))) (NormedAddGroupHom.ker.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2)) (NormedAddGroupHom.completion.{u2, u1} G _inst_1 H _inst_2 f))
Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.ker_le_ker_completion NormedAddGroupHom.ker_le_ker_completionₓ'. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/da3fc4a33ff6bc75f077f691dc94c217b8d41559
@@ -297,7 +297,7 @@ theorem NormedAddGroupHom.norm_completion (f : NormedAddGroupHom G H) : ‖f.Com
/- warning: normed_add_group_hom.ker_le_ker_completion -> NormedAddGroupHom.ker_le_ker_completion is a dubious translation:
lean 3 declaration is
- forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H] (f : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2), LE.le.{u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) (Preorder.toLE.{u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) (SetLike.partialOrder.{u1, u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G 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_inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)))))))) (NormedAddGroupHom.range.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1))) G (AddSubgroup.setLike.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1)))) (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (AddSubgroup.seminormedAddCommGroup.{u1} G _inst_1 (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddGroupHom.comp.{u1, u1, u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1))) G (AddSubgroup.setLike.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1)))) (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (AddSubgroup.seminormedAddCommGroup.{u1} G _inst_1 (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toCompl.{u1} G _inst_1) (NormedAddGroupHom.incl.{u1} G _inst_1 (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)))) (NormedAddGroupHom.ker.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2)) (NormedAddGroupHom.completion.{u1, u2} G _inst_1 H _inst_2 f))
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H] (f : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2), LE.le.{u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) (Preorder.toLE.{u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) (AddSubgroup.completeLattice.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))))))) (NormedAddGroupHom.range.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1))) G (AddSubgroup.setLike.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1)))) (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (AddSubgroup.seminormedAddCommGroup.{u1} G _inst_1 (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddGroupHom.comp.{u1, u1, u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1))) G (AddSubgroup.setLike.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1)))) (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (AddSubgroup.seminormedAddCommGroup.{u1} G _inst_1 (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toCompl.{u1} G _inst_1) (NormedAddGroupHom.incl.{u1} G _inst_1 (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)))) (NormedAddGroupHom.ker.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2)) (NormedAddGroupHom.completion.{u1, u2} G _inst_1 H _inst_2 f))
but is expected to have type
forall {G : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} G] {H : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} H] (f : NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2), LE.le.{u2} (AddSubgroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))) (Preorder.toLE.{u2} (AddSubgroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (AddSubgroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (AddSubgroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))) (AddSubgroup.instCompleteLatticeAddSubgroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))))))) (NormedAddGroupHom.range.{u2, u2} (Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (AddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))) G (AddSubgroup.instSetLikeAddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1)))) x (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f))) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddSubgroup.seminormedAddCommGroup.{u2} G _inst_1 (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddGroupHom.comp.{u2, u2, u2} (Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (AddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))) G (AddSubgroup.instSetLikeAddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1)))) x (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f))) G (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddSubgroup.seminormedAddCommGroup.{u2} G _inst_1 (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f)) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toCompl.{u2} G _inst_1) (NormedAddGroupHom.incl.{u2} G _inst_1 (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f)))) (NormedAddGroupHom.ker.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2)) (NormedAddGroupHom.completion.{u2, u1} G _inst_1 H _inst_2 f))
Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.ker_le_ker_completion NormedAddGroupHom.ker_le_ker_completionₓ'. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
! This file was ported from Lean 3 source module analysis.normed.group.hom_completion
-! leanprover-community/mathlib commit 17ef379e997badd73e5eabb4d38f11919ab3c4b3
+! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.Analysis.Normed.Group.Completion
/-!
# Completion of normed group homs
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
Given two (semi) normed groups `G` and `H` and a normed group hom `f : normed_add_group_hom G H`,
we build and study a normed group hom
`f.completion : normed_add_group_hom (completion G) (completion H)` such that the diagram
mathlib commit https://github.com/leanprover-community/mathlib/commit/f24cc2891c0e328f0ee8c57387103aa462c44b5e
@@ -64,6 +64,12 @@ variable {H : Type _} [SeminormedAddCommGroup H]
variable {K : Type _} [SeminormedAddCommGroup K]
+/- warning: normed_add_group_hom.completion -> NormedAddGroupHom.completion is a dubious translation:
+lean 3 declaration is
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H], (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) -> (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2)))
+but is expected to have type
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H], (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) -> (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} H _inst_2)))
+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion NormedAddGroupHom.completionₓ'. -/
/-- The normed group hom induced between completions. -/
def NormedAddGroupHom.completion (f : NormedAddGroupHom G H) :
NormedAddGroupHom (Completion G) (Completion H) :=
@@ -84,11 +90,23 @@ def NormedAddGroupHom.completion (f : NormedAddGroupHom G H) :
exact f.le_op_norm x }
#align normed_add_group_hom.completion NormedAddGroupHom.completion
+/- warning: normed_add_group_hom.completion_def -> NormedAddGroupHom.completion_def is a dubious translation:
+lean 3 declaration is
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H] (f : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (x : UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))), Eq.{succ u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (fun (_x : NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) => (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) -> (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2)))) (NormedAddGroupHom.hasCoeToFun.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.completion.{u1, u2} G _inst_1 H _inst_2 f) x) (UniformSpace.Completion.map.{u1, u2} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1)) H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (fun (_x : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) => G -> H) (NormedAddGroupHom.hasCoeToFun.{u1, u2} G H _inst_1 _inst_2) f) x)
+but is expected to have type
+ forall {G : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} G] {H : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} H] (f : NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) (x : UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))), Eq.{succ u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (fun (_x : UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) => UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (AddHomClass.toFunLike.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G 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(AddZeroClass.toAdd.{u1} H (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2)))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) G H (AddMonoid.toAddZeroClass.{u2} G (SubNegMonoid.toAddMonoid.{u2} G (AddGroup.toSubNegMonoid.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))))) (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2))))) (NormedAddGroupHom.toAddMonoidHomClass.{u2, u1} G H _inst_1 _inst_2))) f) x)
+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion_def NormedAddGroupHom.completion_defₓ'. -/
theorem NormedAddGroupHom.completion_def (f : NormedAddGroupHom G H) (x : Completion G) :
f.Completion x = Completion.map f x :=
rfl
#align normed_add_group_hom.completion_def NormedAddGroupHom.completion_def
+/- warning: normed_add_group_hom.completion_coe_to_fun -> NormedAddGroupHom.completion_coe_to_fun is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (fun (_x : UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) => UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (AddHomClass.toFunLike.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (AddZeroClass.toAdd.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddMonoid.toAddZeroClass.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SubNegMonoid.toAddMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddGroup.toSubNegMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)))))))) (AddZeroClass.toAdd.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (AddMonoid.toAddZeroClass.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (SubNegMonoid.toAddMonoid.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (AddGroup.toSubNegMonoid.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2)))))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (AddMonoid.toAddZeroClass.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SubNegMonoid.toAddMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddGroup.toSubNegMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))))) (AddMonoid.toAddZeroClass.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (SubNegMonoid.toAddMonoid.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (AddGroup.toSubNegMonoid.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))))))) (NormedAddGroupHom.toAddMonoidHomClass.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))))) (NormedAddGroupHom.completion.{u2, u1} G _inst_1 H _inst_2 f)) (UniformSpace.Completion.map.{u2, u1} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1)) H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) G (fun (_x : G) => H) (AddHomClass.toFunLike.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) G H (AddZeroClass.toAdd.{u2} G (AddMonoid.toAddZeroClass.{u2} G (SubNegMonoid.toAddMonoid.{u2} G (AddGroup.toSubNegMonoid.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1)))))) (AddZeroClass.toAdd.{u1} H (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2)))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) G H (AddMonoid.toAddZeroClass.{u2} G (SubNegMonoid.toAddMonoid.{u2} G (AddGroup.toSubNegMonoid.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))))) (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2))))) (NormedAddGroupHom.toAddMonoidHomClass.{u2, u1} G H _inst_1 _inst_2))) f))
+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion_coe_to_fun NormedAddGroupHom.completion_coe_to_funₓ'. -/
@[simp]
theorem NormedAddGroupHom.completion_coe_to_fun (f : NormedAddGroupHom G H) :
(f.Completion : Completion G → Completion H) = Completion.map f :=
@@ -97,12 +115,24 @@ theorem NormedAddGroupHom.completion_coe_to_fun (f : NormedAddGroupHom G H) :
exact NormedAddGroupHom.completion_def f x
#align normed_add_group_hom.completion_coe_to_fun NormedAddGroupHom.completion_coe_to_fun
+/- warning: normed_add_group_hom.completion_coe -> NormedAddGroupHom.completion_coe is a dubious translation:
+lean 3 declaration is
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H] (f : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (g : G), Eq.{succ u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (fun (_x : NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) => (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) -> (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2)))) (NormedAddGroupHom.hasCoeToFun.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.completion.{u1, u2} G _inst_1 H _inst_2 f) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (HasLiftT.mk.{succ u1, succ u1} G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (CoeTCₓ.coe.{succ u1, succ u1} G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.hasCoeT.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))))) g)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) H (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (HasLiftT.mk.{succ u2, succ u2} H (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (CoeTCₓ.coe.{succ u2, succ u2} H (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.hasCoeT.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (fun (_x : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) => G -> H) (NormedAddGroupHom.hasCoeToFun.{u1, u2} G H _inst_1 _inst_2) f g))
+but is expected to have type
+ forall {G : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} G] {H : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} H] (f : NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) (g : G), Eq.{succ u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (fun (_x : UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) => UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (AddHomClass.toFunLike.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (AddZeroClass.toAdd.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddMonoid.toAddZeroClass.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SubNegMonoid.toAddMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddGroup.toSubNegMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)))))))) (AddZeroClass.toAdd.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (AddMonoid.toAddZeroClass.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (SubNegMonoid.toAddMonoid.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (AddGroup.toSubNegMonoid.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2)))))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (AddMonoid.toAddZeroClass.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SubNegMonoid.toAddMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddGroup.toSubNegMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))))) (AddMonoid.toAddZeroClass.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (SubNegMonoid.toAddMonoid.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (AddGroup.toSubNegMonoid.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))))))) (NormedAddGroupHom.toAddMonoidHomClass.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))))) (NormedAddGroupHom.completion.{u2, u1} G _inst_1 H _inst_2 f) (UniformSpace.Completion.coe'.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1)) g)) (UniformSpace.Completion.coe'.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) G (fun (_x : G) => H) (AddHomClass.toFunLike.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) G H (AddZeroClass.toAdd.{u2} G (AddMonoid.toAddZeroClass.{u2} G (SubNegMonoid.toAddMonoid.{u2} G (AddGroup.toSubNegMonoid.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1)))))) (AddZeroClass.toAdd.{u1} H (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2)))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) G H (AddMonoid.toAddZeroClass.{u2} G (SubNegMonoid.toAddMonoid.{u2} G (AddGroup.toSubNegMonoid.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))))) (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2))))) (NormedAddGroupHom.toAddMonoidHomClass.{u2, u1} G H _inst_1 _inst_2))) f g))
+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion_coe NormedAddGroupHom.completion_coeₓ'. -/
@[simp]
theorem NormedAddGroupHom.completion_coe (f : NormedAddGroupHom G H) (g : G) :
f.Completion g = f g :=
Completion.map_coe f.UniformContinuous _
#align normed_add_group_hom.completion_coe NormedAddGroupHom.completion_coe
+/- warning: normed_add_group_hom_completion_hom -> normedAddGroupHomCompletionHom is a dubious translation:
+lean 3 declaration is
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H], AddMonoidHom.{max u1 u2, max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (AddMonoid.toAddZeroClass.{max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (SubNegMonoid.toAddMonoid.{max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (AddGroup.toSubNegMonoid.{max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (SeminormedAddGroup.toAddGroup.{max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (SeminormedAddCommGroup.toSeminormedAddGroup.{max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (NormedAddGroupHom.toSeminormedAddCommGroup.{u1, u2} G H _inst_1 _inst_2)))))) (AddMonoid.toAddZeroClass.{max u1 u2} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (SubNegMonoid.toAddMonoid.{max u1 u2} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (AddGroup.toSubNegMonoid.{max u1 u2} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroup.toAddGroup.{max u1 u2} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddCommGroup.toNormedAddGroup.{max u1 u2} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.toNormedAddCommGroup.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2)))))))
+but is expected to have type
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H], AddMonoidHom.{max u2 u1, max u2 u1} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} H _inst_2))) (AddMonoid.toAddZeroClass.{max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (SubNegMonoid.toAddMonoid.{max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (AddGroup.toSubNegMonoid.{max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (SeminormedAddGroup.toAddGroup.{max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (SeminormedAddCommGroup.toSeminormedAddGroup.{max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (NormedAddGroupHom.toSeminormedAddCommGroup.{u1, u2} G H _inst_1 _inst_2)))))) (AddMonoid.toAddZeroClass.{max u1 u2} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} H _inst_2))) (SubNegMonoid.toAddMonoid.{max u1 u2} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} H _inst_2))) (AddGroup.toSubNegMonoid.{max u1 u2} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} H _inst_2))) (NormedAddGroup.toAddGroup.{max u1 u2} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toNormedAddGroup.{max u1 u2} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} H _inst_2))) (NormedAddGroupHom.toNormedAddCommGroup.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} H _inst_2)))))))
+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom_completion_hom normedAddGroupHomCompletionHomₓ'. -/
/-- Completion of normed group homs as a normed group hom. -/
@[simps]
def normedAddGroupHomCompletionHom :
@@ -117,6 +147,12 @@ def normedAddGroupHomCompletionHom :
exact f.to_add_monoid_hom.completion_add g.to_add_monoid_hom f.continuous g.continuous
#align normed_add_group_hom_completion_hom normedAddGroupHomCompletionHom
+/- warning: normed_add_group_hom.completion_id -> NormedAddGroupHom.completion_id is a dubious translation:
+lean 3 declaration is
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G], Eq.{succ u1} (NormedAddGroupHom.{u1, u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))) (NormedAddGroupHom.completion.{u1, u1} G _inst_1 G _inst_1 (NormedAddGroupHom.id.{u1} G _inst_1)) (NormedAddGroupHom.id.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)))
+but is expected to have type
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G], Eq.{succ u1} (NormedAddGroupHom.{u1, u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1))) (NormedAddGroupHom.completion.{u1, u1} G _inst_1 G _inst_1 (NormedAddGroupHom.id.{u1} G _inst_1)) (NormedAddGroupHom.id.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1)))
+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion_id NormedAddGroupHom.completion_idₓ'. -/
@[simp]
theorem NormedAddGroupHom.completion_id :
(NormedAddGroupHom.id G).Completion = NormedAddGroupHom.id (Completion G) :=
@@ -126,6 +162,12 @@ theorem NormedAddGroupHom.completion_id :
rfl
#align normed_add_group_hom.completion_id NormedAddGroupHom.completion_id
+/- warning: normed_add_group_hom.completion_comp -> NormedAddGroupHom.completion_comp is a dubious translation:
+lean 3 declaration is
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H] {K : Type.{u3}} [_inst_3 : SeminormedAddCommGroup.{u3} K] (f : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (g : NormedAddGroupHom.{u2, u3} H K _inst_2 _inst_3), Eq.{max (succ u1) (succ u3)} (NormedAddGroupHom.{u1, u3} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u3} K (PseudoMetricSpace.toUniformSpace.{u3} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} K _inst_3))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (UniformSpace.Completion.{u3} K (PseudoMetricSpace.toUniformSpace.{u3} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} K _inst_3))) (UniformSpace.Completion.normedAddCommGroup.{u3} K _inst_3))) (NormedAddGroupHom.comp.{u1, u2, u3} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.{u3} K (PseudoMetricSpace.toUniformSpace.{u3} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} K _inst_3))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (UniformSpace.Completion.{u3} K (PseudoMetricSpace.toUniformSpace.{u3} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} K _inst_3))) (UniformSpace.Completion.normedAddCommGroup.{u3} K _inst_3)) (NormedAddGroupHom.completion.{u2, u3} H _inst_2 K _inst_3 g) (NormedAddGroupHom.completion.{u1, u2} G _inst_1 H _inst_2 f)) (NormedAddGroupHom.completion.{u1, u3} G _inst_1 K _inst_3 (NormedAddGroupHom.comp.{u1, u2, u3} G H K _inst_1 _inst_2 _inst_3 g f))
+but is expected to have type
+ forall {G : Type.{u3}} [_inst_1 : SeminormedAddCommGroup.{u3} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H] {K : Type.{u1}} [_inst_3 : SeminormedAddCommGroup.{u1} K] (f : NormedAddGroupHom.{u3, u2} G H _inst_1 _inst_2) (g : NormedAddGroupHom.{u2, u1} H K _inst_2 _inst_3), Eq.{max (succ u3) (succ u1)} (NormedAddGroupHom.{u3, u1} (UniformSpace.Completion.{u3} G (PseudoMetricSpace.toUniformSpace.{u3} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} G _inst_1))) (UniformSpace.Completion.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K _inst_3))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (UniformSpace.Completion.{u3} G (PseudoMetricSpace.toUniformSpace.{u3} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u3} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K _inst_3))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} K _inst_3))) (NormedAddGroupHom.comp.{u3, u2, u1} (UniformSpace.Completion.{u3} G (PseudoMetricSpace.toUniformSpace.{u3} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K _inst_3))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} (UniformSpace.Completion.{u3} G (PseudoMetricSpace.toUniformSpace.{u3} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u3} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} H _inst_2)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} K _inst_3))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} K _inst_3)) (NormedAddGroupHom.completion.{u2, u1} H _inst_2 K _inst_3 g) (NormedAddGroupHom.completion.{u3, u2} G _inst_1 H _inst_2 f)) (NormedAddGroupHom.completion.{u3, u1} G _inst_1 K _inst_3 (NormedAddGroupHom.comp.{u3, u2, u1} G H K _inst_1 _inst_2 _inst_3 g f))
+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion_comp NormedAddGroupHom.completion_compₓ'. -/
theorem NormedAddGroupHom.completion_comp (f : NormedAddGroupHom G H) (g : NormedAddGroupHom H K) :
g.Completion.comp f.Completion = (g.comp f).Completion :=
by
@@ -137,26 +179,56 @@ theorem NormedAddGroupHom.completion_comp (f : NormedAddGroupHom G H) (g : Norme
rfl
#align normed_add_group_hom.completion_comp NormedAddGroupHom.completion_comp
+/- warning: normed_add_group_hom.completion_neg -> NormedAddGroupHom.completion_neg is a dubious translation:
+lean 3 declaration is
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H] (f : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2), Eq.{max (succ u1) (succ u2)} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.completion.{u1, u2} G _inst_1 H _inst_2 (Neg.neg.{max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (NormedAddGroupHom.hasNeg.{u1, u2} G H _inst_1 _inst_2) f)) (Neg.neg.{max u1 u2} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.hasNeg.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.completion.{u1, u2} G _inst_1 H _inst_2 f))
+but is expected to have type
+ forall {G : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} G] {H : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} H] (f : NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2), Eq.{max (succ u2) (succ u1)} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (NormedAddGroupHom.completion.{u2, u1} G _inst_1 H _inst_2 (Neg.neg.{max u2 u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) (NormedAddGroupHom.neg.{u2, u1} G H _inst_1 _inst_2) f)) (Neg.neg.{max u2 u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (NormedAddGroupHom.neg.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (NormedAddGroupHom.completion.{u2, u1} G _inst_1 H _inst_2 f))
+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion_neg NormedAddGroupHom.completion_negₓ'. -/
theorem NormedAddGroupHom.completion_neg (f : NormedAddGroupHom G H) :
(-f).Completion = -f.Completion :=
map_neg (normedAddGroupHomCompletionHom : NormedAddGroupHom G H →+ _) f
#align normed_add_group_hom.completion_neg NormedAddGroupHom.completion_neg
+/- warning: normed_add_group_hom.completion_add -> NormedAddGroupHom.completion_add is a dubious translation:
+lean 3 declaration is
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H] (f : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (g : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2), Eq.{max (succ u1) (succ u2)} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.completion.{u1, u2} G _inst_1 H _inst_2 (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (instHAdd.{max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (NormedAddGroupHom.hasAdd.{u1, u2} G H _inst_1 _inst_2)) f g)) (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (instHAdd.{max u1 u2} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.hasAdd.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2)))) (NormedAddGroupHom.completion.{u1, u2} G _inst_1 H _inst_2 f) (NormedAddGroupHom.completion.{u1, u2} G _inst_1 H _inst_2 g))
+but is expected to have type
+ forall {G : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} G] {H : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} H] (f : NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) (g : NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2), Eq.{max (succ u2) (succ u1)} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (NormedAddGroupHom.completion.{u2, u1} G _inst_1 H _inst_2 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) (instHAdd.{max u2 u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) (NormedAddGroupHom.add.{u2, u1} G H _inst_1 _inst_2)) f g)) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (instHAdd.{max u2 u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (NormedAddGroupHom.add.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2)))) (NormedAddGroupHom.completion.{u2, u1} G _inst_1 H _inst_2 f) (NormedAddGroupHom.completion.{u2, u1} G _inst_1 H _inst_2 g))
+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion_add NormedAddGroupHom.completion_addₓ'. -/
theorem NormedAddGroupHom.completion_add (f g : NormedAddGroupHom G H) :
(f + g).Completion = f.Completion + g.Completion :=
normedAddGroupHomCompletionHom.map_add f g
#align normed_add_group_hom.completion_add NormedAddGroupHom.completion_add
+/- warning: normed_add_group_hom.completion_sub -> NormedAddGroupHom.completion_sub is a dubious translation:
+lean 3 declaration is
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H] (f : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (g : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2), Eq.{max (succ u1) (succ u2)} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.completion.{u1, u2} G _inst_1 H _inst_2 (HSub.hSub.{max u1 u2, max u1 u2, max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (instHSub.{max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (NormedAddGroupHom.hasSub.{u1, u2} G H _inst_1 _inst_2)) f g)) (HSub.hSub.{max u1 u2, max u1 u2, max u1 u2} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (instHSub.{max u1 u2} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.hasSub.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2)))) (NormedAddGroupHom.completion.{u1, u2} G _inst_1 H _inst_2 f) (NormedAddGroupHom.completion.{u1, u2} G _inst_1 H _inst_2 g))
+but is expected to have type
+ forall {G : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} G] {H : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} H] (f : NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) (g : NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2), Eq.{max (succ u2) (succ u1)} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (NormedAddGroupHom.completion.{u2, u1} G _inst_1 H _inst_2 (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) (instHSub.{max u2 u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) (NormedAddGroupHom.sub.{u2, u1} G H _inst_1 _inst_2)) f g)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (instHSub.{max u2 u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (NormedAddGroupHom.sub.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2)))) (NormedAddGroupHom.completion.{u2, u1} G _inst_1 H _inst_2 f) (NormedAddGroupHom.completion.{u2, u1} G _inst_1 H _inst_2 g))
+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion_sub NormedAddGroupHom.completion_subₓ'. -/
theorem NormedAddGroupHom.completion_sub (f g : NormedAddGroupHom G H) :
(f - g).Completion = f.Completion - g.Completion :=
map_sub (normedAddGroupHomCompletionHom : NormedAddGroupHom G H →+ _) f g
#align normed_add_group_hom.completion_sub NormedAddGroupHom.completion_sub
+/- warning: normed_add_group_hom.zero_completion -> NormedAddGroupHom.zero_completion is a dubious translation:
+lean 3 declaration is
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H], Eq.{max (succ u1) (succ u2)} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.completion.{u1, u2} G _inst_1 H _inst_2 (OfNat.ofNat.{max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) 0 (OfNat.mk.{max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) 0 (Zero.zero.{max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (NormedAddGroupHom.hasZero.{u1, u2} G H _inst_1 _inst_2))))) (OfNat.ofNat.{max u1 u2} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) 0 (OfNat.mk.{max u1 u2} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) 0 (Zero.zero.{max u1 u2} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.hasZero.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))))))
+but is expected to have type
+ forall {G : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} G] {H : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} H], Eq.{max (succ u2) (succ u1)} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (NormedAddGroupHom.completion.{u2, u1} G _inst_1 H _inst_2 (OfNat.ofNat.{max u2 u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) 0 (Zero.toOfNat0.{max u2 u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) (NormedAddGroupHom.zero.{u2, u1} G H _inst_1 _inst_2)))) (OfNat.ofNat.{max u2 u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) 0 (Zero.toOfNat0.{max u2 u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (NormedAddGroupHom.zero.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2)))))
+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.zero_completion NormedAddGroupHom.zero_completionₓ'. -/
@[simp]
theorem NormedAddGroupHom.zero_completion : (0 : NormedAddGroupHom G H).Completion = 0 :=
normedAddGroupHomCompletionHom.map_zero
#align normed_add_group_hom.zero_completion NormedAddGroupHom.zero_completion
+/- warning: normed_add_comm_group.to_compl -> NormedAddCommGroup.toCompl is a dubious translation:
+lean 3 declaration is
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G], NormedAddGroupHom.{u1, u1} G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))
+but is expected to have type
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G], NormedAddGroupHom.{u1, u1} G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1))
+Case conversion may be inaccurate. Consider using '#align normed_add_comm_group.to_compl NormedAddCommGroup.toComplₓ'. -/
/-- The map from a normed group to its completion, as a normed group hom. -/
def NormedAddCommGroup.toCompl : NormedAddGroupHom G (Completion G)
where
@@ -167,14 +239,28 @@ def NormedAddCommGroup.toCompl : NormedAddGroupHom G (Completion G)
open NormedAddCommGroup
+#print NormedAddCommGroup.norm_toCompl /-
theorem NormedAddCommGroup.norm_toCompl (x : G) : ‖toCompl x‖ = ‖x‖ :=
Completion.norm_coe x
#align normed_add_comm_group.norm_to_compl NormedAddCommGroup.norm_toCompl
+-/
+/- warning: normed_add_comm_group.dense_range_to_compl -> NormedAddCommGroup.denseRange_toCompl is a dubious translation:
+lean 3 declaration is
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G], DenseRange.{u1, u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.toTopologicalSpace.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (PseudoMetricSpace.toUniformSpace.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) G (coeFn.{succ u1, succ u1} (NormedAddGroupHom.{u1, u1} G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))) (fun (_x : NormedAddGroupHom.{u1, u1} G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))) => G -> (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1)))) (NormedAddGroupHom.hasCoeToFun.{u1, u1} G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))) (NormedAddCommGroup.toCompl.{u1} G _inst_1))
+but is expected to have type
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G], DenseRange.{u1, u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.toTopologicalSpace.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (PseudoMetricSpace.toUniformSpace.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1))))) G (FunLike.coe.{succ u1, succ u1, succ u1} (NormedAddGroupHom.{u1, u1} G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1))) G (fun (_x : G) => UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (AddHomClass.toFunLike.{u1, u1, u1} (NormedAddGroupHom.{u1, u1} G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1))) G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (AddZeroClass.toAdd.{u1} G (AddMonoid.toAddZeroClass.{u1} G (SubNegMonoid.toAddMonoid.{u1} G (AddGroup.toSubNegMonoid.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1)))))) (AddZeroClass.toAdd.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (AddMonoid.toAddZeroClass.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SubNegMonoid.toAddMonoid.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (AddGroup.toSubNegMonoid.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1)))))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (NormedAddGroupHom.{u1, u1} G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1))) G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (AddMonoid.toAddZeroClass.{u1} G (SubNegMonoid.toAddMonoid.{u1} G (AddGroup.toSubNegMonoid.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SubNegMonoid.toAddMonoid.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (AddGroup.toSubNegMonoid.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1))))))) (NormedAddGroupHom.toAddMonoidHomClass.{u1, u1} G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1))))) (NormedAddCommGroup.toCompl.{u1} G _inst_1))
+Case conversion may be inaccurate. Consider using '#align normed_add_comm_group.dense_range_to_compl NormedAddCommGroup.denseRange_toComplₓ'. -/
theorem NormedAddCommGroup.denseRange_toCompl : DenseRange (toCompl : G → Completion G) :=
Completion.denseInducing_coe.dense
#align normed_add_comm_group.dense_range_to_compl NormedAddCommGroup.denseRange_toCompl
+/- warning: normed_add_group_hom.completion_to_compl -> NormedAddGroupHom.completion_toCompl is a dubious translation:
+lean 3 declaration is
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H] (f : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2), Eq.{max (succ u1) (succ u2)} (NormedAddGroupHom.{u1, u2} G (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.comp.{u1, u1, u2} G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2)) (NormedAddGroupHom.completion.{u1, u2} G _inst_1 H _inst_2 f) (NormedAddCommGroup.toCompl.{u1} G _inst_1)) (NormedAddGroupHom.comp.{u1, u2, u2} G H (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) _inst_1 _inst_2 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2)) (NormedAddCommGroup.toCompl.{u2} H _inst_2) f)
+but is expected to have type
+ forall {G : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} G] {H : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} H] (f : NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2), Eq.{max (succ u2) (succ u1)} (NormedAddGroupHom.{u2, u1} G (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (NormedAddGroupHom.comp.{u2, u2, u1} G (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2)) (NormedAddGroupHom.completion.{u2, u1} G _inst_1 H _inst_2 f) (NormedAddCommGroup.toCompl.{u2} G _inst_1)) (NormedAddGroupHom.comp.{u2, u1, u1} G H (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) _inst_1 _inst_2 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2)) (NormedAddCommGroup.toCompl.{u1} H _inst_2) f)
+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.completion_to_compl NormedAddGroupHom.completion_toComplₓ'. -/
@[simp]
theorem NormedAddGroupHom.completion_toCompl (f : NormedAddGroupHom G H) :
f.Completion.comp toCompl = toCompl.comp f :=
@@ -184,6 +270,12 @@ theorem NormedAddGroupHom.completion_toCompl (f : NormedAddGroupHom G H) :
simpa
#align normed_add_group_hom.completion_to_compl NormedAddGroupHom.completion_toCompl
+/- warning: normed_add_group_hom.norm_completion -> NormedAddGroupHom.norm_completion is a dubious translation:
+lean 3 declaration is
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H] (f : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2), Eq.{1} Real (Norm.norm.{max u1 u2} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.hasOpNorm.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (UniformSpace.Completion.normedAddCommGroup.{u2} H _inst_2))) (NormedAddGroupHom.completion.{u1, u2} G _inst_1 H _inst_2 f)) (Norm.norm.{max u1 u2} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (NormedAddGroupHom.hasOpNorm.{u1, u2} G H _inst_1 _inst_2) f)
+but is expected to have type
+ forall {G : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} G] {H : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} H] (f : NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2), Eq.{1} Real (Norm.norm.{max u2 u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (NormedAddGroupHom.hasOpNorm.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2))) (NormedAddGroupHom.completion.{u2, u1} G _inst_1 H _inst_2 f)) (Norm.norm.{max u2 u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) (NormedAddGroupHom.hasOpNorm.{u2, u1} G H _inst_1 _inst_2) f)
+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.norm_completion NormedAddGroupHom.norm_completionₓ'. -/
@[simp]
theorem NormedAddGroupHom.norm_completion (f : NormedAddGroupHom G H) : ‖f.Completion‖ = ‖f‖ :=
by
@@ -200,6 +292,12 @@ theorem NormedAddGroupHom.norm_completion (f : NormedAddGroupHom G H) : ‖f.Com
simpa using hN x
#align normed_add_group_hom.norm_completion NormedAddGroupHom.norm_completion
+/- warning: normed_add_group_hom.ker_le_ker_completion -> NormedAddGroupHom.ker_le_ker_completion is a dubious translation:
+lean 3 declaration is
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H] (f : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2), LE.le.{u1} (AddSubgroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1))))) (Preorder.toLE.{u1} (AddSubgroup.{u1} 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(AddSubgroup.seminormedAddCommGroup.{u1} G _inst_1 (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toCompl.{u1} G _inst_1) (NormedAddGroupHom.incl.{u1} G _inst_1 (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)))) (NormedAddGroupHom.ker.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.ker_le_ker_completion NormedAddGroupHom.ker_le_ker_completionₓ'. -/
theorem NormedAddGroupHom.ker_le_ker_completion (f : NormedAddGroupHom G H) :
(toCompl.comp <| incl f.ker).range ≤ f.Completion.ker :=
by
@@ -211,6 +309,12 @@ theorem NormedAddGroupHom.ker_le_ker_completion (f : NormedAddGroupHom G H) :
simp [NormedAddGroupHom.mem_ker, f.completion_coe g, g_in, completion.coe_zero]
#align normed_add_group_hom.ker_le_ker_completion NormedAddGroupHom.ker_le_ker_completion
+/- warning: normed_add_group_hom.ker_completion -> NormedAddGroupHom.ker_completion is a dubious translation:
+lean 3 declaration is
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(SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1)))) (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (AddSubgroup.seminormedAddCommGroup.{u1} G _inst_1 (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddGroupHom.comp.{u1, u1, u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1))) G (AddSubgroup.setLike.{u1} G (SeminormedAddGroup.toAddGroup.{u1} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} G _inst_1)))) (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (AddSubgroup.seminormedAddCommGroup.{u1} G _inst_1 (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) (NormedAddCommGroup.toCompl.{u1} G _inst_1) (NormedAddGroupHom.incl.{u1} G _inst_1 (NormedAddGroupHom.ker.{u1, u2} G H _inst_1 _inst_2 f)))))))
+but is expected to have type
+ forall {G : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} G] {H : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} H] {f : NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2} {C : Real}, (NormedAddGroupHom.SurjectiveOnWith.{u2, u1} G H _inst_1 _inst_2 f (NormedAddGroupHom.range.{u2, u1} G H _inst_1 _inst_2 f) C) -> (Eq.{succ u2} (Set.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1)))) (SetLike.coe.{u2, u2} (AddSubgroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddSubgroup.instSetLikeAddSubgroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))) (NormedAddGroupHom.ker.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} H _inst_2)) (NormedAddGroupHom.completion.{u2, u1} G _inst_1 H _inst_2 f))) (closure.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))) (SetLike.coe.{u2, u2} (AddSubgroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddSubgroup.instSetLikeAddSubgroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))) (NormedAddGroupHom.range.{u2, u2} (Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (AddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))) G (AddSubgroup.instSetLikeAddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1)))) x (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f))) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddSubgroup.seminormedAddCommGroup.{u2} G _inst_1 (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddGroupHom.comp.{u2, u2, u2} (Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (AddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))) G (AddSubgroup.instSetLikeAddSubgroup.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1)))) x (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f))) G (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddSubgroup.seminormedAddCommGroup.{u2} G _inst_1 (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f)) _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) (NormedAddCommGroup.toCompl.{u2} G _inst_1) (NormedAddGroupHom.incl.{u2} G _inst_1 (NormedAddGroupHom.ker.{u2, u1} G H _inst_1 _inst_2 f)))))))
+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.ker_completion NormedAddGroupHom.ker_completionₓ'. -/
theorem NormedAddGroupHom.ker_completion {f : NormedAddGroupHom G H} {C : ℝ}
(h : f.SurjectiveOnWith f.range C) :
(f.Completion.ker : Set <| Completion G) = closure (toCompl.comp <| incl f.ker).range :=
@@ -272,6 +376,12 @@ variable {G : Type _} [SeminormedAddCommGroup G]
variable {H : Type _} [SeminormedAddCommGroup H] [SeparatedSpace H] [CompleteSpace H]
+/- warning: normed_add_group_hom.extension -> NormedAddGroupHom.extension is a dubious translation:
+lean 3 declaration is
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H] [_inst_3 : SeparatedSpace.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))] [_inst_4 : CompleteSpace.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))], (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) -> (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) _inst_2)
+but is expected to have type
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H] [_inst_3 : SeparatedSpace.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))] [_inst_4 : CompleteSpace.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))], (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) -> (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} G _inst_1)) _inst_2)
+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.extension NormedAddGroupHom.extensionₓ'. -/
/-- If `H` is complete, the extension of `f : normed_add_group_hom G H` to a
`normed_add_group_hom (completion G) H`. -/
def NormedAddGroupHom.extension (f : NormedAddGroupHom G H) : NormedAddGroupHom (Completion G) H :=
@@ -285,21 +395,45 @@ def NormedAddGroupHom.extension (f : NormedAddGroupHom G H) : NormedAddGroupHom
exact le_op_norm f a }
#align normed_add_group_hom.extension NormedAddGroupHom.extension
+/- warning: normed_add_group_hom.extension_def -> NormedAddGroupHom.extension_def is a dubious translation:
+lean 3 declaration is
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H] [_inst_3 : SeparatedSpace.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))] [_inst_4 : CompleteSpace.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))] (f : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (v : G), Eq.{succ u2} H (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) _inst_2) (fun (_x : NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) _inst_2) => (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) -> H) (NormedAddGroupHom.hasCoeToFun.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) _inst_2) (NormedAddGroupHom.extension.{u1, u2} G _inst_1 H _inst_2 _inst_3 _inst_4 f) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (HasLiftT.mk.{succ u1, succ u1} G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (CoeTCₓ.coe.{succ u1, succ u1} G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.hasCoeT.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))))) v)) (UniformSpace.Completion.extension.{u1, u2} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1)) H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (fun (_x : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) => G -> H) (NormedAddGroupHom.hasCoeToFun.{u1, u2} G H _inst_1 _inst_2) f) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (HasLiftT.mk.{succ u1, succ u1} G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (CoeTCₓ.coe.{succ u1, succ u1} G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.hasCoeT.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))))) v))
+but is expected to have type
+ forall {G : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} G] {H : Type.{u1}} [_inst_2 : SeminormedAddCommGroup.{u1} H] [_inst_3 : SeparatedSpace.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))] [_inst_4 : CompleteSpace.{u1} H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2))] (f : NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) (v : G), Eq.{succ u1} H (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) _inst_2) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (fun (_x : UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) => H) (AddHomClass.toFunLike.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) _inst_2) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (AddZeroClass.toAdd.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddMonoid.toAddZeroClass.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SubNegMonoid.toAddMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddGroup.toSubNegMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)))))))) (AddZeroClass.toAdd.{u1} H (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2)))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) _inst_2) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (AddMonoid.toAddZeroClass.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SubNegMonoid.toAddMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddGroup.toSubNegMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))))) (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2))))) (NormedAddGroupHom.toAddMonoidHomClass.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) _inst_2))) (NormedAddGroupHom.extension.{u2, u1} G _inst_1 H _inst_2 _inst_3 _inst_4 f) (UniformSpace.Completion.coe'.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1)) v)) (UniformSpace.Completion.extension.{u2, u1} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1)) H (PseudoMetricSpace.toUniformSpace.{u1} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} H _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) G (fun (_x : G) => H) (AddHomClass.toFunLike.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) G H (AddZeroClass.toAdd.{u2} G (AddMonoid.toAddZeroClass.{u2} G (SubNegMonoid.toAddMonoid.{u2} G (AddGroup.toSubNegMonoid.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1)))))) (AddZeroClass.toAdd.{u1} H (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2)))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} G H _inst_1 _inst_2) G H (AddMonoid.toAddZeroClass.{u2} G (SubNegMonoid.toAddMonoid.{u2} G (AddGroup.toSubNegMonoid.{u2} G (SeminormedAddGroup.toAddGroup.{u2} G (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} G _inst_1))))) (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2))))) (NormedAddGroupHom.toAddMonoidHomClass.{u2, u1} G H _inst_1 _inst_2))) f) (UniformSpace.Completion.coe'.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1)) v))
+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.extension_def NormedAddGroupHom.extension_defₓ'. -/
theorem NormedAddGroupHom.extension_def (f : NormedAddGroupHom G H) (v : G) :
f.extension v = Completion.extension f v :=
rfl
#align normed_add_group_hom.extension_def NormedAddGroupHom.extension_def
+/- warning: normed_add_group_hom.extension_coe -> NormedAddGroupHom.extension_coe is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.extension_coe NormedAddGroupHom.extension_coeₓ'. -/
@[simp]
theorem NormedAddGroupHom.extension_coe (f : NormedAddGroupHom G H) (v : G) : f.extension v = f v :=
AddMonoidHom.extension_coe _ f.Continuous _
#align normed_add_group_hom.extension_coe NormedAddGroupHom.extension_coe
+/- warning: normed_add_group_hom.extension_coe_to_fun -> NormedAddGroupHom.extension_coe_to_fun is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.extension_coe_to_fun NormedAddGroupHom.extension_coe_to_funₓ'. -/
theorem NormedAddGroupHom.extension_coe_to_fun (f : NormedAddGroupHom G H) :
(f.extension : Completion G → H) = Completion.extension f :=
rfl
#align normed_add_group_hom.extension_coe_to_fun NormedAddGroupHom.extension_coe_to_fun
+/- warning: normed_add_group_hom.extension_unique -> NormedAddGroupHom.extension_unique is a dubious translation:
+lean 3 declaration is
+ forall {G : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} G] {H : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u2} H] [_inst_3 : SeparatedSpace.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))] [_inst_4 : CompleteSpace.{u2} H (PseudoMetricSpace.toUniformSpace.{u2} H (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} H _inst_2))] (f : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) {g : NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) _inst_2}, (forall (v : G), Eq.{succ u2} H (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) (fun (_x : NormedAddGroupHom.{u1, u2} G H _inst_1 _inst_2) => G -> H) (NormedAddGroupHom.hasCoeToFun.{u1, u2} G H _inst_1 _inst_2) f v) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) _inst_2) (fun (_x : NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) _inst_2) => (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) -> H) (NormedAddGroupHom.hasCoeToFun.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) _inst_2) g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (HasLiftT.mk.{succ u1, succ u1} G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (CoeTCₓ.coe.{succ u1, succ u1} G (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.hasCoeT.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))))) v))) -> (Eq.{max (succ u1) (succ u2)} (NormedAddGroupHom.{u1, u2} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} G (PseudoMetricSpace.toUniformSpace.{u1} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} G _inst_1))) (UniformSpace.Completion.normedAddCommGroup.{u1} G _inst_1)) _inst_2) (NormedAddGroupHom.extension.{u1, u2} G _inst_1 H _inst_2 _inst_3 _inst_4 f) g)
+but is expected to have type
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(SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2))))) (NormedAddGroupHom.toAddMonoidHomClass.{u2, u1} G H _inst_1 _inst_2))) f v) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) _inst_2) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (fun (_x : UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) => H) (AddHomClass.toFunLike.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) _inst_2) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (AddZeroClass.toAdd.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddMonoid.toAddZeroClass.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SubNegMonoid.toAddMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddGroup.toSubNegMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)))))))) (AddZeroClass.toAdd.{u1} H (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2)))))) (AddMonoidHomClass.toAddHomClass.{max u2 u1, u2, u1} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) _inst_2) (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (AddMonoid.toAddZeroClass.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SubNegMonoid.toAddMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (AddGroup.toSubNegMonoid.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddGroup.toAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1))))))) (AddMonoid.toAddZeroClass.{u1} H (SubNegMonoid.toAddMonoid.{u1} H (AddGroup.toSubNegMonoid.{u1} H (SeminormedAddGroup.toAddGroup.{u1} H (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} H _inst_2))))) (NormedAddGroupHom.toAddMonoidHomClass.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) _inst_2))) g (UniformSpace.Completion.coe'.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1)) v))) -> (Eq.{max (succ u2) (succ u1)} (NormedAddGroupHom.{u2, u1} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) H (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_1))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} G _inst_1)) _inst_2) (NormedAddGroupHom.extension.{u2, u1} G _inst_1 H _inst_2 _inst_3 _inst_4 f) g)
+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.extension_unique NormedAddGroupHom.extension_uniqueₓ'. -/
theorem NormedAddGroupHom.extension_unique (f : NormedAddGroupHom G H)
{g : NormedAddGroupHom (Completion G) H} (hg : ∀ v, f v = g v) : f.extension = g :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442
@@ -235,7 +235,7 @@ theorem NormedAddGroupHom.ker_completion {f : NormedAddGroupHom G H} {C : ℝ}
_ = ‖f.completion g - 0‖ := by rw [sub_zero _]
_ = ‖f.completion g - f.completion hatg‖ := by rw [(f.completion.mem_ker _).mp hatg_in]
_ = ‖f.completion (g - hatg)‖ := by rw [map_sub]
- _ ≤ ‖f.completion‖ * ‖(g : completion G) - hatg‖ := f.completion.le_op_norm _
+ _ ≤ ‖f.completion‖ * ‖(g : completion G) - hatg‖ := (f.completion.le_op_norm _)
_ = ‖f‖ * ‖hatg - g‖ := by rw [norm_sub_rev, f.norm_completion]
have : ‖(g' : completion G)‖ ≤ C' * ‖f‖ * ‖hatg - g‖
@@ -254,9 +254,9 @@ theorem NormedAddGroupHom.ker_completion {f : NormedAddGroupHom G H} {C : ℝ}
·
calc
‖hatg - (g - g')‖ = ‖hatg - g + g'‖ := by abel
- _ ≤ ‖hatg - g‖ + ‖(g' : completion G)‖ := norm_add_le _ _
+ _ ≤ ‖hatg - g‖ + ‖(g' : completion G)‖ := (norm_add_le _ _)
_ < δ + C' * ‖f‖ * ‖hatg - g‖ := by linarith
- _ ≤ δ + C' * ‖f‖ * δ := add_le_add_left (mul_le_mul_of_nonneg_left hg.le hCf) δ
+ _ ≤ δ + C' * ‖f‖ * δ := (add_le_add_left (mul_le_mul_of_nonneg_left hg.le hCf) δ)
_ = (1 + C' * ‖f‖) * δ := by ring
_ = ε := mul_div_cancel' _ ineq.ne.symm
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Empty lines were removed by executing the following Python script twice
import os
import re
# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
for filename in files:
if filename.endswith('.lean'):
file_path = os.path.join(dir_path, filename)
# Open the file and read its contents
with open(file_path, 'r') as file:
content = file.read()
# Use a regular expression to replace sequences of "variable" lines separated by empty lines
# with sequences without empty lines
modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)
# Write the modified content back to the file
with open(file_path, 'w') as file:
file.write(modified_content)
@@ -198,7 +198,6 @@ end Completion
section Extension
variable {G : Type*} [SeminormedAddCommGroup G]
-
variable {H : Type*} [SeminormedAddCommGroup H] [T0Space H] [CompleteSpace H]
/-- If `H` is complete, the extension of `f : NormedAddGroupHom G H` to a
separationRel
(#10644)
We had duplicated API between topological spaces and uniform spaces. In this PR I mostly deduplicate it with some exceptions:
SeparationQuotient.lift'
and SeparationQuotient.map
are leftovers from the old version
that are designed to work with uniform spaces;UniformSpace
when TopologicalSpace
would work.Outside of UniformSpace/Separation
, I mostly changed SeparatedSpace
to T0Space
and separationRel
to Inseparable
. I also rewrote a few proofs that were broken by the API change.
Fixes #2031
@@ -199,7 +199,7 @@ section Extension
variable {G : Type*} [SeminormedAddCommGroup G]
-variable {H : Type*} [SeminormedAddCommGroup H] [SeparatedSpace H] [CompleteSpace H]
+variable {H : Type*} [SeminormedAddCommGroup H] [T0Space H] [CompleteSpace H]
/-- If `H` is complete, the extension of `f : NormedAddGroupHom G H` to a
`NormedAddGroupHom (completion G) H`. -/
Homogenises porting notes via capitalisation and addition of whitespace.
It makes the following changes:
@@ -74,7 +74,7 @@ theorem NormedAddGroupHom.completion_coe_to_fun (f : NormedAddGroupHom G H) :
(f.completion : Completion G → Completion H) = Completion.map f := rfl
#align normed_add_group_hom.completion_coe_to_fun NormedAddGroupHom.completion_coe_to_fun
--- porting note: `@[simp]` moved to the next lemma
+-- Porting note: `@[simp]` moved to the next lemma
theorem NormedAddGroupHom.completion_coe (f : NormedAddGroupHom G H) (g : G) :
f.completion g = f g :=
Completion.map_coe f.uniformContinuous _
@@ -134,7 +134,7 @@ theorem NormedAddGroupHom.zero_completion : (0 : NormedAddGroupHom G H).completi
#align normed_add_group_hom.zero_completion NormedAddGroupHom.zero_completion
/-- The map from a normed group to its completion, as a normed group hom. -/
-@[simps] -- porting note: added `@[simps]`
+@[simps] -- Porting note: added `@[simps]`
def NormedAddCommGroup.toCompl : NormedAddGroupHom G (Completion G) where
toFun := (↑)
map_add' := Completion.toCompl.map_add
have
, replace
and suffices
(#10640)
No changes to tactic file, it's just boring fixes throughout the library.
This follows on from #6964.
Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
@@ -182,8 +182,8 @@ theorem NormedAddGroupHom.ker_completion {f : NormedAddGroupHom G H} {C : ℝ}
obtain ⟨g' : G, hgg' : f g' = f g, hfg : ‖g'‖ ≤ C' * ‖f g‖⟩ := hC' (f g) (mem_range_self _ g)
have mem_ker : g - g' ∈ f.ker := by rw [f.mem_ker, map_sub, sub_eq_zero.mpr hgg'.symm]
refine ⟨_, ⟨⟨g - g', mem_ker⟩, rfl⟩, ?_⟩
- have : ‖f g‖ ≤ ‖f‖ * δ
- calc ‖f g‖ ≤ ‖f‖ * ‖hatg - g‖ := by simpa [hatg_in] using f.completion.le_opNorm (hatg - g)
+ have : ‖f g‖ ≤ ‖f‖ * δ := calc
+ ‖f g‖ ≤ ‖f‖ * ‖hatg - g‖ := by simpa [hatg_in] using f.completion.le_opNorm (hatg - g)
_ ≤ ‖f‖ * δ := by gcongr
calc ‖hatg - ↑(g - g')‖ = ‖hatg - g + g'‖ := by rw [Completion.coe_sub, sub_add]
_ ≤ ‖hatg - g‖ + ‖(g' : Completion G)‖ := norm_add_le _ _
@@ -13,7 +13,7 @@ import Mathlib.Analysis.Normed.Group.Completion
Given two (semi) normed groups `G` and `H` and a normed group hom `f : NormedAddGroupHom G H`,
we build and study a normed group hom
-`f.completion : NormedAddGroupHom (completion G) (completion H)` such that the diagram
+`f.completion : NormedAddGroupHom (completion G) (completion H)` such that the diagram
```
f
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -55,8 +55,8 @@ open Set NormedAddGroupHom UniformSpace
section Completion
-variable {G : Type _} [SeminormedAddCommGroup G] {H : Type _} [SeminormedAddCommGroup H]
- {K : Type _} [SeminormedAddCommGroup K]
+variable {G : Type*} [SeminormedAddCommGroup G] {H : Type*} [SeminormedAddCommGroup H]
+ {K : Type*} [SeminormedAddCommGroup K]
/-- The normed group hom induced between completions. -/
def NormedAddGroupHom.completion (f : NormedAddGroupHom G H) :
@@ -197,9 +197,9 @@ end Completion
section Extension
-variable {G : Type _} [SeminormedAddCommGroup G]
+variable {G : Type*} [SeminormedAddCommGroup G]
-variable {H : Type _} [SeminormedAddCommGroup H] [SeparatedSpace H] [CompleteSpace H]
+variable {H : Type*} [SeminormedAddCommGroup H] [SeparatedSpace H] [CompleteSpace H]
/-- If `H` is complete, the extension of `f : NormedAddGroupHom G H` to a
`NormedAddGroupHom (completion G) H`. -/
@@ -2,15 +2,12 @@
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-
-! This file was ported from Lean 3 source module analysis.normed.group.hom_completion
-! leanprover-community/mathlib commit 17ef379e997badd73e5eabb4d38f11919ab3c4b3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Analysis.Normed.Group.Hom
import Mathlib.Analysis.Normed.Group.Completion
+#align_import analysis.normed.group.hom_completion from "leanprover-community/mathlib"@"17ef379e997badd73e5eabb4d38f11919ab3c4b3"
+
/-!
# Completion of normed group homs
@@ -187,12 +187,12 @@ theorem NormedAddGroupHom.ker_completion {f : NormedAddGroupHom G H} {C : ℝ}
refine ⟨_, ⟨⟨g - g', mem_ker⟩, rfl⟩, ?_⟩
have : ‖f g‖ ≤ ‖f‖ * δ
calc ‖f g‖ ≤ ‖f‖ * ‖hatg - g‖ := by simpa [hatg_in] using f.completion.le_opNorm (hatg - g)
- _ ≤ ‖f‖ * δ := mul_le_mul_of_nonneg_left hg.le (norm_nonneg f)
+ _ ≤ ‖f‖ * δ := by gcongr
calc ‖hatg - ↑(g - g')‖ = ‖hatg - g + g'‖ := by rw [Completion.coe_sub, sub_add]
_ ≤ ‖hatg - g‖ + ‖(g' : Completion G)‖ := norm_add_le _ _
_ = ‖hatg - g‖ + ‖g'‖ := by rw [Completion.norm_coe]
_ < δ + C' * ‖f g‖ := add_lt_add_of_lt_of_le hg hfg
- _ ≤ δ + C' * (‖f‖ * δ) := add_le_add_left (mul_le_mul_of_nonneg_left this C'_pos.le) _
+ _ ≤ δ + C' * (‖f‖ * δ) := by gcongr
_ < ε := by simpa only [add_mul, one_mul, mul_assoc] using hδ
#align normed_add_group_hom.ker_completion NormedAddGroupHom.ker_completion
The unported dependencies are
algebra.order.module
init.core
algebra.order.monoid.cancel.defs
algebra.abs
algebra.group_power.lemmas
init.data.list.basic
algebra.order.monoid.cancel.basic
init.data.list.default
topology.subset_properties
init.logic
The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file