analysis.normed_space.ball_action
β·
Mathlib.Analysis.NormedSpace.BallAction
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/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth
-/
-import Mathbin.Analysis.Normed.Field.UnitBall
-import Mathbin.Analysis.NormedSpace.Basic
+import Analysis.Normed.Field.UnitBall
+import Analysis.NormedSpace.Basic
#align_import analysis.normed_space.ball_action from "leanprover-community/mathlib"@"86d1873c01a723aba6788f0b9051ae3d23b4c1c3"
mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504
@@ -39,7 +39,7 @@ instance mulActionClosedBallBall : MulAction (closedBall (0 : π) 1) (ball (0
mul_lt_mul' (mem_closedBall_zero_iff.1 c.2) (mem_ball_zero_iff.1 x.2) (norm_nonneg _)
one_posβ©
one_smul x := Subtype.ext <| one_smul π _
- mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
+ hMul_smul cβ cβ x := Subtype.ext <| hMul_smul _ _ _
#align mul_action_closed_ball_ball mulActionClosedBallBall
-/
@@ -59,7 +59,7 @@ instance mulActionClosedBallClosedBall : MulAction (closedBall (0 : π) 1) (cl
mul_le_mul (mem_closedBall_zero_iff.1 c.2) (mem_closedBall_zero_iff.1 x.2) (norm_nonneg _)
zero_le_oneβ©
one_smul x := Subtype.ext <| one_smul π _
- mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
+ hMul_smul cβ cβ x := Subtype.ext <| hMul_smul _ _ _
#align mul_action_closed_ball_closed_ball mulActionClosedBallClosedBall
-/
@@ -79,7 +79,7 @@ instance mulActionSphereBall : MulAction (sphere (0 : π) 1) (ball (0 : E) r)
where
smul c x := inclusion sphere_subset_closedBall c β’ x
one_smul x := Subtype.ext <| one_smul _ _
- mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
+ hMul_smul cβ cβ x := Subtype.ext <| hMul_smul _ _ _
#align mul_action_sphere_ball mulActionSphereBall
-/
@@ -94,7 +94,7 @@ instance mulActionSphereClosedBall : MulAction (sphere (0 : π) 1) (closedBall
where
smul c x := inclusion sphere_subset_closedBall c β’ x
one_smul x := Subtype.ext <| one_smul _ _
- mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
+ hMul_smul cβ cβ x := Subtype.ext <| hMul_smul _ _ _
#align mul_action_sphere_closed_ball mulActionSphereClosedBall
-/
@@ -114,7 +114,7 @@ instance mulActionSphereSphere : MulAction (sphere (0 : π) 1) (sphere (0 : E)
rw [norm_smul, mem_sphere_zero_iff_norm.1 c.coe_prop, mem_sphere_zero_iff_norm.1 x.coe_prop,
one_mul]β©
one_smul x := Subtype.ext <| one_smul _ _
- mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
+ hMul_smul cβ cβ x := Subtype.ext <| hMul_smul _ _ _
#align mul_action_sphere_sphere mulActionSphereSphere
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth
-
-! This file was ported from Lean 3 source module analysis.normed_space.ball_action
-! leanprover-community/mathlib commit 86d1873c01a723aba6788f0b9051ae3d23b4c1c3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Analysis.Normed.Field.UnitBall
import Mathbin.Analysis.NormedSpace.Basic
+#align_import analysis.normed_space.ball_action from "leanprover-community/mathlib"@"86d1873c01a723aba6788f0b9051ae3d23b4c1c3"
+
/-!
# Multiplicative actions of/on balls and spheres
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -32,6 +32,7 @@ variable {π π' E : Type _} [NormedField π] [NormedField π'] [Seminor
section ClosedBall
+#print mulActionClosedBallBall /-
instance mulActionClosedBallBall : MulAction (closedBall (0 : π) 1) (ball (0 : E) r)
where
smul c x :=
@@ -43,11 +44,15 @@ instance mulActionClosedBallBall : MulAction (closedBall (0 : π) 1) (ball (0
one_smul x := Subtype.ext <| one_smul π _
mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
#align mul_action_closed_ball_ball mulActionClosedBallBall
+-/
+#print continuousSMul_closedBall_ball /-
instance continuousSMul_closedBall_ball : ContinuousSMul (closedBall (0 : π) 1) (ball (0 : E) r) :=
β¨(continuous_subtype_val.fst'.smul continuous_subtype_val.snd').subtype_mk _β©
#align has_continuous_smul_closed_ball_ball continuousSMul_closedBall_ball
+-/
+#print mulActionClosedBallClosedBall /-
instance mulActionClosedBallClosedBall : MulAction (closedBall (0 : π) 1) (closedBall (0 : E) r)
where
smul c x :=
@@ -59,39 +64,51 @@ instance mulActionClosedBallClosedBall : MulAction (closedBall (0 : π) 1) (cl
one_smul x := Subtype.ext <| one_smul π _
mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
#align mul_action_closed_ball_closed_ball mulActionClosedBallClosedBall
+-/
+#print continuousSMul_closedBall_closedBall /-
instance continuousSMul_closedBall_closedBall :
ContinuousSMul (closedBall (0 : π) 1) (closedBall (0 : E) r) :=
β¨(continuous_subtype_val.fst'.smul continuous_subtype_val.snd').subtype_mk _β©
#align has_continuous_smul_closed_ball_closed_ball continuousSMul_closedBall_closedBall
+-/
end ClosedBall
section Sphere
+#print mulActionSphereBall /-
instance mulActionSphereBall : MulAction (sphere (0 : π) 1) (ball (0 : E) r)
where
smul c x := inclusion sphere_subset_closedBall c β’ x
one_smul x := Subtype.ext <| one_smul _ _
mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
#align mul_action_sphere_ball mulActionSphereBall
+-/
+#print continuousSMul_sphere_ball /-
instance continuousSMul_sphere_ball : ContinuousSMul (sphere (0 : π) 1) (ball (0 : E) r) :=
β¨(continuous_subtype_val.fst'.smul continuous_subtype_val.snd').subtype_mk _β©
#align has_continuous_smul_sphere_ball continuousSMul_sphere_ball
+-/
+#print mulActionSphereClosedBall /-
instance mulActionSphereClosedBall : MulAction (sphere (0 : π) 1) (closedBall (0 : E) r)
where
smul c x := inclusion sphere_subset_closedBall c β’ x
one_smul x := Subtype.ext <| one_smul _ _
mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
#align mul_action_sphere_closed_ball mulActionSphereClosedBall
+-/
+#print continuousSMul_sphere_closedBall /-
instance continuousSMul_sphere_closedBall :
ContinuousSMul (sphere (0 : π) 1) (closedBall (0 : E) r) :=
β¨(continuous_subtype_val.fst'.smul continuous_subtype_val.snd').subtype_mk _β©
#align has_continuous_smul_sphere_closed_ball continuousSMul_sphere_closedBall
+-/
+#print mulActionSphereSphere /-
instance mulActionSphereSphere : MulAction (sphere (0 : π) 1) (sphere (0 : E) r)
where
smul c x :=
@@ -102,10 +119,13 @@ instance mulActionSphereSphere : MulAction (sphere (0 : π) 1) (sphere (0 : E)
one_smul x := Subtype.ext <| one_smul _ _
mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
#align mul_action_sphere_sphere mulActionSphereSphere
+-/
+#print continuousSMul_sphere_sphere /-
instance continuousSMul_sphere_sphere : ContinuousSMul (sphere (0 : π) 1) (sphere (0 : E) r) :=
β¨(continuous_subtype_val.fst'.smul continuous_subtype_val.snd').subtype_mk _β©
#align has_continuous_smul_sphere_sphere continuousSMul_sphere_sphere
+-/
end Sphere
@@ -113,50 +133,68 @@ section IsScalarTower
variable [NormedAlgebra π π'] [IsScalarTower π π' E]
+#print isScalarTower_closedBall_closedBall_closedBall /-
instance isScalarTower_closedBall_closedBall_closedBall :
IsScalarTower (closedBall (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_closed_ball_closed_ball_closed_ball isScalarTower_closedBall_closedBall_closedBall
+-/
+#print isScalarTower_closedBall_closedBall_ball /-
instance isScalarTower_closedBall_closedBall_ball :
IsScalarTower (closedBall (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_closed_ball_closed_ball_ball isScalarTower_closedBall_closedBall_ball
+-/
+#print isScalarTower_sphere_closedBall_closedBall /-
instance isScalarTower_sphere_closedBall_closedBall :
IsScalarTower (sphere (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_sphere_closed_ball_closed_ball isScalarTower_sphere_closedBall_closedBall
+-/
+#print isScalarTower_sphere_closedBall_ball /-
instance isScalarTower_sphere_closedBall_ball :
IsScalarTower (sphere (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_sphere_closed_ball_ball isScalarTower_sphere_closedBall_ball
+-/
+#print isScalarTower_sphere_sphere_closedBall /-
instance isScalarTower_sphere_sphere_closedBall :
IsScalarTower (sphere (0 : π) 1) (sphere (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_sphere_sphere_closed_ball isScalarTower_sphere_sphere_closedBall
+-/
+#print isScalarTower_sphere_sphere_ball /-
instance isScalarTower_sphere_sphere_ball :
IsScalarTower (sphere (0 : π) 1) (sphere (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_sphere_sphere_ball isScalarTower_sphere_sphere_ball
+-/
+#print isScalarTower_sphere_sphere_sphere /-
instance isScalarTower_sphere_sphere_sphere :
IsScalarTower (sphere (0 : π) 1) (sphere (0 : π') 1) (sphere (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_sphere_sphere_sphere isScalarTower_sphere_sphere_sphere
+-/
+#print isScalarTower_sphere_ball_ball /-
instance isScalarTower_sphere_ball_ball :
IsScalarTower (sphere (0 : π) 1) (ball (0 : π') 1) (ball (0 : π') 1) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : π')β©
#align is_scalar_tower_sphere_ball_ball isScalarTower_sphere_ball_ball
+-/
+#print isScalarTower_closedBall_ball_ball /-
instance isScalarTower_closedBall_ball_ball :
IsScalarTower (closedBall (0 : π) 1) (ball (0 : π') 1) (ball (0 : π') 1) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : π')β©
#align is_scalar_tower_closed_ball_ball_ball isScalarTower_closedBall_ball_ball
+-/
end IsScalarTower
@@ -164,55 +202,75 @@ section SMulCommClass
variable [SMulCommClass π π' E]
+#print instSMulCommClass_closedBall_closedBall_closedBall /-
instance instSMulCommClass_closedBall_closedBall_closedBall :
SMulCommClass (closedBall (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
#align smul_comm_class_closed_ball_closed_ball_closed_ball instSMulCommClass_closedBall_closedBall_closedBall
+-/
+#print instSMulCommClass_closedBall_closedBall_ball /-
instance instSMulCommClass_closedBall_closedBall_ball :
SMulCommClass (closedBall (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
#align smul_comm_class_closed_ball_closed_ball_ball instSMulCommClass_closedBall_closedBall_ball
+-/
+#print instSMulCommClass_sphere_closedBall_closedBall /-
instance instSMulCommClass_sphere_closedBall_closedBall :
SMulCommClass (sphere (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
#align smul_comm_class_sphere_closed_ball_closed_ball instSMulCommClass_sphere_closedBall_closedBall
+-/
+#print instSMulCommClass_sphere_closedBall_ball /-
instance instSMulCommClass_sphere_closedBall_ball :
SMulCommClass (sphere (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
#align smul_comm_class_sphere_closed_ball_ball instSMulCommClass_sphere_closedBall_ball
+-/
+#print instSMulCommClass_sphere_ball_ball /-
instance instSMulCommClass_sphere_ball_ball [NormedAlgebra π π'] :
SMulCommClass (sphere (0 : π) 1) (ball (0 : π') 1) (ball (0 : π') 1) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : π')β©
#align smul_comm_class_sphere_ball_ball instSMulCommClass_sphere_ball_ball
+-/
+#print instSMulCommClass_sphere_sphere_closedBall /-
instance instSMulCommClass_sphere_sphere_closedBall :
SMulCommClass (sphere (0 : π) 1) (sphere (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
#align smul_comm_class_sphere_sphere_closed_ball instSMulCommClass_sphere_sphere_closedBall
+-/
+#print instSMulCommClass_sphere_sphere_ball /-
instance instSMulCommClass_sphere_sphere_ball :
SMulCommClass (sphere (0 : π) 1) (sphere (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
#align smul_comm_class_sphere_sphere_ball instSMulCommClass_sphere_sphere_ball
+-/
+#print instSMulCommClass_sphere_sphere_sphere /-
instance instSMulCommClass_sphere_sphere_sphere :
SMulCommClass (sphere (0 : π) 1) (sphere (0 : π') 1) (sphere (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
#align smul_comm_class_sphere_sphere_sphere instSMulCommClass_sphere_sphere_sphere
+-/
end SMulCommClass
variable (π) [CharZero π]
+#print ne_neg_of_mem_sphere /-
theorem ne_neg_of_mem_sphere {r : β} (hr : r β 0) (x : sphere (0 : E) r) : x β -x := fun h =>
ne_zero_of_mem_sphere hr x ((self_eq_neg π _).mp (by conv_lhs => rw [h]; simp))
#align ne_neg_of_mem_sphere ne_neg_of_mem_sphere
+-/
+#print ne_neg_of_mem_unit_sphere /-
theorem ne_neg_of_mem_unit_sphere (x : sphere (0 : E) 1) : x β -x :=
ne_neg_of_mem_sphere π one_ne_zero x
#align ne_neg_of_mem_unit_sphere ne_neg_of_mem_unit_sphere
+-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004
@@ -164,45 +164,45 @@ section SMulCommClass
variable [SMulCommClass π π' E]
-instance sMulCommClass_closedBall_closedBall_closedBall :
+instance instSMulCommClass_closedBall_closedBall_closedBall :
SMulCommClass (closedBall (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
-#align smul_comm_class_closed_ball_closed_ball_closed_ball sMulCommClass_closedBall_closedBall_closedBall
+#align smul_comm_class_closed_ball_closed_ball_closed_ball instSMulCommClass_closedBall_closedBall_closedBall
-instance sMulCommClass_closedBall_closedBall_ball :
+instance instSMulCommClass_closedBall_closedBall_ball :
SMulCommClass (closedBall (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
-#align smul_comm_class_closed_ball_closed_ball_ball sMulCommClass_closedBall_closedBall_ball
+#align smul_comm_class_closed_ball_closed_ball_ball instSMulCommClass_closedBall_closedBall_ball
-instance sMulCommClass_sphere_closedBall_closedBall :
+instance instSMulCommClass_sphere_closedBall_closedBall :
SMulCommClass (sphere (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
-#align smul_comm_class_sphere_closed_ball_closed_ball sMulCommClass_sphere_closedBall_closedBall
+#align smul_comm_class_sphere_closed_ball_closed_ball instSMulCommClass_sphere_closedBall_closedBall
-instance sMulCommClass_sphere_closedBall_ball :
+instance instSMulCommClass_sphere_closedBall_ball :
SMulCommClass (sphere (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
-#align smul_comm_class_sphere_closed_ball_ball sMulCommClass_sphere_closedBall_ball
+#align smul_comm_class_sphere_closed_ball_ball instSMulCommClass_sphere_closedBall_ball
-instance sMulCommClass_sphere_ball_ball [NormedAlgebra π π'] :
+instance instSMulCommClass_sphere_ball_ball [NormedAlgebra π π'] :
SMulCommClass (sphere (0 : π) 1) (ball (0 : π') 1) (ball (0 : π') 1) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : π')β©
-#align smul_comm_class_sphere_ball_ball sMulCommClass_sphere_ball_ball
+#align smul_comm_class_sphere_ball_ball instSMulCommClass_sphere_ball_ball
-instance sMulCommClass_sphere_sphere_closedBall :
+instance instSMulCommClass_sphere_sphere_closedBall :
SMulCommClass (sphere (0 : π) 1) (sphere (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
-#align smul_comm_class_sphere_sphere_closed_ball sMulCommClass_sphere_sphere_closedBall
+#align smul_comm_class_sphere_sphere_closed_ball instSMulCommClass_sphere_sphere_closedBall
-instance sMulCommClass_sphere_sphere_ball :
+instance instSMulCommClass_sphere_sphere_ball :
SMulCommClass (sphere (0 : π) 1) (sphere (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
-#align smul_comm_class_sphere_sphere_ball sMulCommClass_sphere_sphere_ball
+#align smul_comm_class_sphere_sphere_ball instSMulCommClass_sphere_sphere_ball
-instance sMulCommClass_sphere_sphere_sphere :
+instance instSMulCommClass_sphere_sphere_sphere :
SMulCommClass (sphere (0 : π) 1) (sphere (0 : π') 1) (sphere (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
-#align smul_comm_class_sphere_sphere_sphere sMulCommClass_sphere_sphere_sphere
+#align smul_comm_class_sphere_sphere_sphere instSMulCommClass_sphere_sphere_sphere
end SMulCommClass
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -32,12 +32,6 @@ variable {π π' E : Type _} [NormedField π] [NormedField π'] [Seminor
section ClosedBall
-/- warning: mul_action_closed_ball_ball -> mulActionClosedBallBall is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align mul_action_closed_ball_ball mulActionClosedBallBallβ'. -/
instance mulActionClosedBallBall : MulAction (closedBall (0 : π) 1) (ball (0 : E) r)
where
smul c x :=
@@ -50,22 +44,10 @@ instance mulActionClosedBallBall : MulAction (closedBall (0 : π) 1) (ball (0
mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
#align mul_action_closed_ball_ball mulActionClosedBallBall
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-Case conversion may be inaccurate. Consider using '#align has_continuous_smul_closed_ball_ball continuousSMul_closedBall_ballβ'. -/
instance continuousSMul_closedBall_ball : ContinuousSMul (closedBall (0 : π) 1) (ball (0 : E) r) :=
β¨(continuous_subtype_val.fst'.smul continuous_subtype_val.snd').subtype_mk _β©
#align has_continuous_smul_closed_ball_ball continuousSMul_closedBall_ball
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-Case conversion may be inaccurate. Consider using '#align mul_action_closed_ball_closed_ball mulActionClosedBallClosedBallβ'. -/
instance mulActionClosedBallClosedBall : MulAction (closedBall (0 : π) 1) (closedBall (0 : E) r)
where
smul c x :=
@@ -78,12 +60,6 @@ instance mulActionClosedBallClosedBall : MulAction (closedBall (0 : π) 1) (cl
mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
#align mul_action_closed_ball_closed_ball mulActionClosedBallClosedBall
-/- warning: has_continuous_smul_closed_ball_closed_ball -> continuousSMul_closedBall_closedBall is a dubious translation:
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- forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, ContinuousSMul.{u1, u2} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} E (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} E (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall.{u1, u2} π E _inst_1 _inst_3 _inst_4 r)) (instTopologicalSpaceSubtype.{u1} π (fun (x : π) => Membership.mem.{u1, u1} π (Set.{u1} π) (Set.instMembershipSet.{u1} π) x (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (UniformSpace.toTopologicalSpace.{u1} π (PseudoMetricSpace.toUniformSpace.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))) (instTopologicalSpaceSubtype.{u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))))
-Case conversion may be inaccurate. Consider using '#align has_continuous_smul_closed_ball_closed_ball continuousSMul_closedBall_closedBallβ'. -/
instance continuousSMul_closedBall_closedBall :
ContinuousSMul (closedBall (0 : π) 1) (closedBall (0 : E) r) :=
β¨(continuous_subtype_val.fst'.smul continuous_subtype_val.snd').subtype_mk _β©
@@ -93,12 +69,6 @@ end ClosedBall
section Sphere
-/- warning: mul_action_sphere_ball -> mulActionSphereBall is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align mul_action_sphere_ball mulActionSphereBallβ'. -/
instance mulActionSphereBall : MulAction (sphere (0 : π) 1) (ball (0 : E) r)
where
smul c x := inclusion sphere_subset_closedBall c β’ x
@@ -106,22 +76,10 @@ instance mulActionSphereBall : MulAction (sphere (0 : π) 1) (ball (0 : E) r)
mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
#align mul_action_sphere_ball mulActionSphereBall
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-Case conversion may be inaccurate. Consider using '#align has_continuous_smul_sphere_ball continuousSMul_sphere_ballβ'. -/
instance continuousSMul_sphere_ball : ContinuousSMul (sphere (0 : π) 1) (ball (0 : E) r) :=
β¨(continuous_subtype_val.fst'.smul continuous_subtype_val.snd').subtype_mk _β©
#align has_continuous_smul_sphere_ball continuousSMul_sphere_ball
-/- warning: mul_action_sphere_closed_ball -> mulActionSphereClosedBall is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align mul_action_sphere_closed_ball mulActionSphereClosedBallβ'. -/
instance mulActionSphereClosedBall : MulAction (sphere (0 : π) 1) (closedBall (0 : E) r)
where
smul c x := inclusion sphere_subset_closedBall c β’ x
@@ -129,23 +87,11 @@ instance mulActionSphereClosedBall : MulAction (sphere (0 : π) 1) (closedBall
mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
#align mul_action_sphere_closed_ball mulActionSphereClosedBall
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-Case conversion may be inaccurate. Consider using '#align has_continuous_smul_sphere_closed_ball continuousSMul_sphere_closedBallβ'. -/
instance continuousSMul_sphere_closedBall :
ContinuousSMul (sphere (0 : π) 1) (closedBall (0 : E) r) :=
β¨(continuous_subtype_val.fst'.smul continuous_subtype_val.snd').subtype_mk _β©
#align has_continuous_smul_sphere_closed_ball continuousSMul_sphere_closedBall
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-Case conversion may be inaccurate. Consider using '#align mul_action_sphere_sphere mulActionSphereSphereβ'. -/
instance mulActionSphereSphere : MulAction (sphere (0 : π) 1) (sphere (0 : E) r)
where
smul c x :=
@@ -157,12 +103,6 @@ instance mulActionSphereSphere : MulAction (sphere (0 : π) 1) (sphere (0 : E)
mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
#align mul_action_sphere_sphere mulActionSphereSphere
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- forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, ContinuousSMul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u2} π E _inst_1 _inst_3 _inst_4 r)) (Subtype.topologicalSpace.{u1} π (fun (x : π) => Membership.Mem.{u1, u1} π (Set.{u1} π) (Set.hasMem.{u1} π) x (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (UniformSpace.toTopologicalSpace.{u1} π (PseudoMetricSpace.toUniformSpace.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))) (Subtype.topologicalSpace.{u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))))
-but is expected to have type
- forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, ContinuousSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} E (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} E (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u2} π E _inst_1 _inst_3 _inst_4 r)) (instTopologicalSpaceSubtype.{u1} π (fun (x : π) => Membership.mem.{u1, u1} π (Set.{u1} π) (Set.instMembershipSet.{u1} π) x (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (UniformSpace.toTopologicalSpace.{u1} π (PseudoMetricSpace.toUniformSpace.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))) (instTopologicalSpaceSubtype.{u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))))
-Case conversion may be inaccurate. Consider using '#align has_continuous_smul_sphere_sphere continuousSMul_sphere_sphereβ'. -/
instance continuousSMul_sphere_sphere : ContinuousSMul (sphere (0 : π) 1) (sphere (0 : E) r) :=
β¨(continuous_subtype_val.fst'.smul continuous_subtype_val.snd').subtype_mk _β©
#align has_continuous_smul_sphere_sphere continuousSMul_sphere_sphere
@@ -173,73 +113,46 @@ section IsScalarTower
variable [NormedAlgebra π π'] [IsScalarTower π π' E]
-/- warning: is_scalar_tower_closed_ball_closed_ball_closed_ball -> isScalarTower_closedBall_closedBall_closedBall is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_scalar_tower_closed_ball_closed_ball_closed_ball isScalarTower_closedBall_closedBall_closedBallβ'. -/
instance isScalarTower_closedBall_closedBall_closedBall :
IsScalarTower (closedBall (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_closed_ball_closed_ball_closed_ball isScalarTower_closedBall_closedBall_closedBall
-/- warning: is_scalar_tower_closed_ball_closed_ball_ball -> isScalarTower_closedBall_closedBall_ball is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_scalar_tower_closed_ball_closed_ball_ball isScalarTower_closedBall_closedBall_ballβ'. -/
instance isScalarTower_closedBall_closedBall_ball :
IsScalarTower (closedBall (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_closed_ball_closed_ball_ball isScalarTower_closedBall_closedBall_ball
-/- warning: is_scalar_tower_sphere_closed_ball_closed_ball -> isScalarTower_sphere_closedBall_closedBall is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_scalar_tower_sphere_closed_ball_closed_ball isScalarTower_sphere_closedBall_closedBallβ'. -/
instance isScalarTower_sphere_closedBall_closedBall :
IsScalarTower (sphere (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_sphere_closed_ball_closed_ball isScalarTower_sphere_closedBall_closedBall
-/- warning: is_scalar_tower_sphere_closed_ball_ball -> isScalarTower_sphere_closedBall_ball is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_scalar_tower_sphere_closed_ball_ball isScalarTower_sphere_closedBall_ballβ'. -/
instance isScalarTower_sphere_closedBall_ball :
IsScalarTower (sphere (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_sphere_closed_ball_ball isScalarTower_sphere_closedBall_ball
-/- warning: is_scalar_tower_sphere_sphere_closed_ball -> isScalarTower_sphere_sphere_closedBall is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_scalar_tower_sphere_sphere_closed_ball isScalarTower_sphere_sphere_closedBallβ'. -/
instance isScalarTower_sphere_sphere_closedBall :
IsScalarTower (sphere (0 : π) 1) (sphere (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_sphere_sphere_closed_ball isScalarTower_sphere_sphere_closedBall
-/- warning: is_scalar_tower_sphere_sphere_ball -> isScalarTower_sphere_sphere_ball is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_scalar_tower_sphere_sphere_ball isScalarTower_sphere_sphere_ballβ'. -/
instance isScalarTower_sphere_sphere_ball :
IsScalarTower (sphere (0 : π) 1) (sphere (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_sphere_sphere_ball isScalarTower_sphere_sphere_ball
-/- warning: is_scalar_tower_sphere_sphere_sphere -> isScalarTower_sphere_sphere_sphere is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_scalar_tower_sphere_sphere_sphere isScalarTower_sphere_sphere_sphereβ'. -/
instance isScalarTower_sphere_sphere_sphere :
IsScalarTower (sphere (0 : π) 1) (sphere (0 : π') 1) (sphere (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_sphere_sphere_sphere isScalarTower_sphere_sphere_sphere
-/- warning: is_scalar_tower_sphere_ball_ball -> isScalarTower_sphere_ball_ball is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_scalar_tower_sphere_ball_ball isScalarTower_sphere_ball_ballβ'. -/
instance isScalarTower_sphere_ball_ball :
IsScalarTower (sphere (0 : π) 1) (ball (0 : π') 1) (ball (0 : π') 1) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : π')β©
#align is_scalar_tower_sphere_ball_ball isScalarTower_sphere_ball_ball
-/- warning: is_scalar_tower_closed_ball_ball_ball -> isScalarTower_closedBall_ball_ball is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_scalar_tower_closed_ball_ball_ball isScalarTower_closedBall_ball_ballβ'. -/
instance isScalarTower_closedBall_ball_ball :
IsScalarTower (closedBall (0 : π) 1) (ball (0 : π') 1) (ball (0 : π') 1) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : π')β©
@@ -251,65 +164,41 @@ section SMulCommClass
variable [SMulCommClass π π' E]
-/- warning: smul_comm_class_closed_ball_closed_ball_closed_ball -> sMulCommClass_closedBall_closedBall_closedBall is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align smul_comm_class_closed_ball_closed_ball_closed_ball sMulCommClass_closedBall_closedBall_closedBallβ'. -/
instance sMulCommClass_closedBall_closedBall_closedBall :
SMulCommClass (closedBall (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
#align smul_comm_class_closed_ball_closed_ball_closed_ball sMulCommClass_closedBall_closedBall_closedBall
-/- warning: smul_comm_class_closed_ball_closed_ball_ball -> sMulCommClass_closedBall_closedBall_ball is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align smul_comm_class_closed_ball_closed_ball_ball sMulCommClass_closedBall_closedBall_ballβ'. -/
instance sMulCommClass_closedBall_closedBall_ball :
SMulCommClass (closedBall (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
#align smul_comm_class_closed_ball_closed_ball_ball sMulCommClass_closedBall_closedBall_ball
-/- warning: smul_comm_class_sphere_closed_ball_closed_ball -> sMulCommClass_sphere_closedBall_closedBall is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align smul_comm_class_sphere_closed_ball_closed_ball sMulCommClass_sphere_closedBall_closedBallβ'. -/
instance sMulCommClass_sphere_closedBall_closedBall :
SMulCommClass (sphere (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
#align smul_comm_class_sphere_closed_ball_closed_ball sMulCommClass_sphere_closedBall_closedBall
-/- warning: smul_comm_class_sphere_closed_ball_ball -> sMulCommClass_sphere_closedBall_ball is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align smul_comm_class_sphere_closed_ball_ball sMulCommClass_sphere_closedBall_ballβ'. -/
instance sMulCommClass_sphere_closedBall_ball :
SMulCommClass (sphere (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
#align smul_comm_class_sphere_closed_ball_ball sMulCommClass_sphere_closedBall_ball
-/- warning: smul_comm_class_sphere_ball_ball -> sMulCommClass_sphere_ball_ball is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align smul_comm_class_sphere_ball_ball sMulCommClass_sphere_ball_ballβ'. -/
instance sMulCommClass_sphere_ball_ball [NormedAlgebra π π'] :
SMulCommClass (sphere (0 : π) 1) (ball (0 : π') 1) (ball (0 : π') 1) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : π')β©
#align smul_comm_class_sphere_ball_ball sMulCommClass_sphere_ball_ball
-/- warning: smul_comm_class_sphere_sphere_closed_ball -> sMulCommClass_sphere_sphere_closedBall is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align smul_comm_class_sphere_sphere_closed_ball sMulCommClass_sphere_sphere_closedBallβ'. -/
instance sMulCommClass_sphere_sphere_closedBall :
SMulCommClass (sphere (0 : π) 1) (sphere (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
#align smul_comm_class_sphere_sphere_closed_ball sMulCommClass_sphere_sphere_closedBall
-/- warning: smul_comm_class_sphere_sphere_ball -> sMulCommClass_sphere_sphere_ball is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align smul_comm_class_sphere_sphere_ball sMulCommClass_sphere_sphere_ballβ'. -/
instance sMulCommClass_sphere_sphere_ball :
SMulCommClass (sphere (0 : π) 1) (sphere (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
#align smul_comm_class_sphere_sphere_ball sMulCommClass_sphere_sphere_ball
-/- warning: smul_comm_class_sphere_sphere_sphere -> sMulCommClass_sphere_sphere_sphere is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align smul_comm_class_sphere_sphere_sphere sMulCommClass_sphere_sphere_sphereβ'. -/
instance sMulCommClass_sphere_sphere_sphere :
SMulCommClass (sphere (0 : π) 1) (sphere (0 : π') 1) (sphere (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
@@ -319,22 +208,10 @@ end SMulCommClass
variable (π) [CharZero π]
-/- warning: ne_neg_of_mem_sphere -> ne_neg_of_mem_sphere is a dubious translation:
-lean 3 declaration is
- forall (π : Type.{u1}) {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] [_inst_6 : CharZero.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (AddCommGroupWithOne.toAddGroupWithOne.{u1} π (Ring.toAddCommGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))] {r : Real}, (Ne.{1} Real r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (forall (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)), Ne.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) x (Neg.neg.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (InvolutiveNeg.toHasNeg.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (Metric.sphere.hasInvolutiveNeg.{u2} E _inst_3 r)) x))
-but is expected to have type
- forall (π : Type.{u2}) {E : Type.{u1}} [_inst_1 : NormedField.{u2} π] [_inst_3 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{u2, u1} π E _inst_1 _inst_3] [_inst_6 : CharZero.{u2} π (AddGroupWithOne.toAddMonoidWithOne.{u2} π (Ring.toAddGroupWithOne.{u2} π (NormedRing.toRing.{u2} π (NormedCommRing.toNormedRing.{u2} π (NormedField.toNormedCommRing.{u2} π _inst_1)))))] {r : Real}, (Ne.{1} Real r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (forall (x : Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) r)), Ne.{succ u1} (Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) r)) x (Neg.neg.{u1} (Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) r)) (InvolutiveNeg.toNeg.{u1} (Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) r)) (instInvolutiveNegElemSphereToPseudoMetricSpaceOfNatToOfNat0ToZeroToNegZeroClassToSubNegZeroMonoidToSubtractionMonoidToDivisionAddCommMonoidToAddCommGroup.{u1} E _inst_3 r)) x))
-Case conversion may be inaccurate. Consider using '#align ne_neg_of_mem_sphere ne_neg_of_mem_sphereβ'. -/
theorem ne_neg_of_mem_sphere {r : β} (hr : r β 0) (x : sphere (0 : E) r) : x β -x := fun h =>
ne_zero_of_mem_sphere hr x ((self_eq_neg π _).mp (by conv_lhs => rw [h]; simp))
#align ne_neg_of_mem_sphere ne_neg_of_mem_sphere
-/- warning: ne_neg_of_mem_unit_sphere -> ne_neg_of_mem_unit_sphere is a dubious translation:
-lean 3 declaration is
- forall (π : Type.{u1}) {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] [_inst_6 : CharZero.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (AddCommGroupWithOne.toAddGroupWithOne.{u1} π (Ring.toAddCommGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))] (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))), Ne.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) x (Neg.neg.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (InvolutiveNeg.toHasNeg.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.sphere.hasInvolutiveNeg.{u2} E _inst_3 (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) x)
-but is expected to have type
- forall (π : Type.{u2}) {E : Type.{u1}} [_inst_1 : NormedField.{u2} π] [_inst_3 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{u2, u1} π E _inst_1 _inst_3] [_inst_6 : CharZero.{u2} π (AddGroupWithOne.toAddMonoidWithOne.{u2} π (Ring.toAddGroupWithOne.{u2} π (NormedRing.toRing.{u2} π (NormedCommRing.toNormedRing.{u2} π (NormedField.toNormedCommRing.{u2} π _inst_1)))))] (x : Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))), Ne.{succ u1} (Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) x (Neg.neg.{u1} (Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (InvolutiveNeg.toNeg.{u1} (Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (instInvolutiveNegElemSphereToPseudoMetricSpaceOfNatToOfNat0ToZeroToNegZeroClassToSubNegZeroMonoidToSubtractionMonoidToDivisionAddCommMonoidToAddCommGroup.{u1} E _inst_3 (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) x)
-Case conversion may be inaccurate. Consider using '#align ne_neg_of_mem_unit_sphere ne_neg_of_mem_unit_sphereβ'. -/
theorem ne_neg_of_mem_unit_sphere (x : sphere (0 : E) 1) : x β -x :=
ne_neg_of_mem_sphere π one_ne_zero x
#align ne_neg_of_mem_unit_sphere ne_neg_of_mem_unit_sphere
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -326,11 +326,7 @@ but is expected to have type
forall (π : Type.{u2}) {E : Type.{u1}} [_inst_1 : NormedField.{u2} π] [_inst_3 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{u2, u1} π E _inst_1 _inst_3] [_inst_6 : CharZero.{u2} π (AddGroupWithOne.toAddMonoidWithOne.{u2} π (Ring.toAddGroupWithOne.{u2} π (NormedRing.toRing.{u2} π (NormedCommRing.toNormedRing.{u2} π (NormedField.toNormedCommRing.{u2} π _inst_1)))))] {r : Real}, (Ne.{1} Real r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (forall (x : Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) r)), Ne.{succ u1} (Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) r)) x (Neg.neg.{u1} (Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) r)) (InvolutiveNeg.toNeg.{u1} (Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) r)) (instInvolutiveNegElemSphereToPseudoMetricSpaceOfNatToOfNat0ToZeroToNegZeroClassToSubNegZeroMonoidToSubtractionMonoidToDivisionAddCommMonoidToAddCommGroup.{u1} E _inst_3 r)) x))
Case conversion may be inaccurate. Consider using '#align ne_neg_of_mem_sphere ne_neg_of_mem_sphereβ'. -/
theorem ne_neg_of_mem_sphere {r : β} (hr : r β 0) (x : sphere (0 : E) r) : x β -x := fun h =>
- ne_zero_of_mem_sphere hr x
- ((self_eq_neg π _).mp
- (by
- conv_lhs => rw [h]
- simp))
+ ne_zero_of_mem_sphere hr x ((self_eq_neg π _).mp (by conv_lhs => rw [h]; simp))
#align ne_neg_of_mem_sphere ne_neg_of_mem_sphere
/- warning: ne_neg_of_mem_unit_sphere -> ne_neg_of_mem_unit_sphere is a dubious translation:
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -174,10 +174,7 @@ section IsScalarTower
variable [NormedAlgebra π π'] [IsScalarTower π π' E]
/- warning: is_scalar_tower_closed_ball_closed_ball_closed_ball -> isScalarTower_closedBall_closedBall_closedBall is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π π' (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (NormedSpace.toModule.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.closedBall.monoid.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall._proof_1.{u1} π _inst_1)) (mulActionClosedBallClosedBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (mulActionClosedBallClosedBall._proof_1.{u2} π' _inst_2)) (mulActionClosedBallClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall._proof_1.{u1} π _inst_1)) (mulActionClosedBallClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
-but is expected to have type
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (Algebra.toSMul.{u1, u2} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))) (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (NormedAlgebra.toAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) _inst_6)) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (NormedDivisionRing.to_normOneClass.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2))) (mulActionClosedBallClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+<too large>
Case conversion may be inaccurate. Consider using '#align is_scalar_tower_closed_ball_closed_ball_closed_ball isScalarTower_closedBall_closedBall_closedBallβ'. -/
instance isScalarTower_closedBall_closedBall_closedBall :
IsScalarTower (closedBall (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
@@ -185,10 +182,7 @@ instance isScalarTower_closedBall_closedBall_closedBall :
#align is_scalar_tower_closed_ball_closed_ball_closed_ball isScalarTower_closedBall_closedBall_closedBall
/- warning: is_scalar_tower_closed_ball_closed_ball_ball -> isScalarTower_closedBall_closedBall_ball is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π π' (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (NormedSpace.toModule.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.closedBall.monoid.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall._proof_1.{u1} π _inst_1)) (mulActionClosedBallClosedBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (mulActionClosedBallBall._proof_1.{u2} π' _inst_2)) (mulActionClosedBallBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (mulActionClosedBallBall._proof_1.{u1} π _inst_1)) (mulActionClosedBallBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
-but is expected to have type
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (Algebra.toSMul.{u1, u2} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))) (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (NormedAlgebra.toAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) _inst_6)) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (NormedDivisionRing.to_normOneClass.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2))) (mulActionClosedBallBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))) (mulActionClosedBallBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+<too large>
Case conversion may be inaccurate. Consider using '#align is_scalar_tower_closed_ball_closed_ball_ball isScalarTower_closedBall_closedBall_ballβ'. -/
instance isScalarTower_closedBall_closedBall_ball :
IsScalarTower (closedBall (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
@@ -196,10 +190,7 @@ instance isScalarTower_closedBall_closedBall_ball :
#align is_scalar_tower_closed_ball_closed_ball_ball isScalarTower_closedBall_closedBall_ball
/- warning: is_scalar_tower_sphere_closed_ball_closed_ball -> isScalarTower_sphere_closedBall_closedBall is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π π' (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (NormedSpace.toModule.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (mulActionClosedBallClosedBall._proof_1.{u2} π' _inst_2)) (mulActionClosedBallClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
-but is expected to have type
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (Algebra.toSMul.{u1, u2} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))) (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (NormedAlgebra.toAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) _inst_6)) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (NormedDivisionRing.to_normOneClass.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2))) (mulActionClosedBallClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+<too large>
Case conversion may be inaccurate. Consider using '#align is_scalar_tower_sphere_closed_ball_closed_ball isScalarTower_sphere_closedBall_closedBallβ'. -/
instance isScalarTower_sphere_closedBall_closedBall :
IsScalarTower (sphere (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
@@ -207,10 +198,7 @@ instance isScalarTower_sphere_closedBall_closedBall :
#align is_scalar_tower_sphere_closed_ball_closed_ball isScalarTower_sphere_closedBall_closedBall
/- warning: is_scalar_tower_sphere_closed_ball_ball -> isScalarTower_sphere_closedBall_ball is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π π' (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (NormedSpace.toModule.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (mulActionClosedBallBall._proof_1.{u2} π' _inst_2)) (mulActionClosedBallBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
-but is expected to have type
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (Algebra.toSMul.{u1, u2} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))) (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (NormedAlgebra.toAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) _inst_6)) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (NormedDivisionRing.to_normOneClass.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2))) (mulActionClosedBallBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+<too large>
Case conversion may be inaccurate. Consider using '#align is_scalar_tower_sphere_closed_ball_ball isScalarTower_sphere_closedBall_ballβ'. -/
instance isScalarTower_sphere_closedBall_ball :
IsScalarTower (sphere (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
@@ -218,10 +206,7 @@ instance isScalarTower_sphere_closedBall_ball :
#align is_scalar_tower_sphere_closed_ball_ball isScalarTower_sphere_closedBall_ball
/- warning: is_scalar_tower_sphere_sphere_closed_ball -> isScalarTower_sphere_sphere_closedBall is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π π' (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (NormedSpace.toModule.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
-but is expected to have type
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (Algebra.toSMul.{u1, u2} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))) (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (NormedAlgebra.toAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) _inst_6)) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+<too large>
Case conversion may be inaccurate. Consider using '#align is_scalar_tower_sphere_sphere_closed_ball isScalarTower_sphere_sphere_closedBallβ'. -/
instance isScalarTower_sphere_sphere_closedBall :
IsScalarTower (sphere (0 : π) 1) (sphere (0 : π') 1) (closedBall (0 : E) r) :=
@@ -229,10 +214,7 @@ instance isScalarTower_sphere_sphere_closedBall :
#align is_scalar_tower_sphere_sphere_closed_ball isScalarTower_sphere_sphere_closedBall
/- warning: is_scalar_tower_sphere_sphere_ball -> isScalarTower_sphere_sphere_ball is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π π' (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (NormedSpace.toModule.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
-but is expected to have type
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (Algebra.toSMul.{u1, u2} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))) (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (NormedAlgebra.toAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) _inst_6)) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+<too large>
Case conversion may be inaccurate. Consider using '#align is_scalar_tower_sphere_sphere_ball isScalarTower_sphere_sphere_ballβ'. -/
instance isScalarTower_sphere_sphere_ball :
IsScalarTower (sphere (0 : π) 1) (sphere (0 : π') 1) (ball (0 : E) r) :=
@@ -240,10 +222,7 @@ instance isScalarTower_sphere_sphere_ball :
#align is_scalar_tower_sphere_sphere_ball isScalarTower_sphere_sphere_ball
/- warning: is_scalar_tower_sphere_sphere_sphere -> isScalarTower_sphere_sphere_sphere is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π π' (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (NormedSpace.toModule.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereSphere.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
-but is expected to have type
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (Algebra.toSMul.{u1, u2} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))) (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (NormedAlgebra.toAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) _inst_6)) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereSphere.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+<too large>
Case conversion may be inaccurate. Consider using '#align is_scalar_tower_sphere_sphere_sphere isScalarTower_sphere_sphere_sphereβ'. -/
instance isScalarTower_sphere_sphere_sphere :
IsScalarTower (sphere (0 : π) 1) (sphere (0 : π') 1) (sphere (0 : E) r) :=
@@ -251,10 +230,7 @@ instance isScalarTower_sphere_sphere_sphere :
#align is_scalar_tower_sphere_sphere_sphere isScalarTower_sphere_sphere_sphere
/- warning: is_scalar_tower_sphere_ball_ball -> isScalarTower_sphere_ball_ball is a dubious translation:
-lean 3 declaration is
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(SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π 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(NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
-but is expected to have type
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(NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Mul.toSMul.{u2} (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Semigroup.toMul.{u2} (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitBall.semigroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
+<too large>
Case conversion may be inaccurate. Consider using '#align is_scalar_tower_sphere_ball_ball isScalarTower_sphere_ball_ballβ'. -/
instance isScalarTower_sphere_ball_ball :
IsScalarTower (sphere (0 : π) 1) (ball (0 : π') 1) (ball (0 : π') 1) :=
@@ -262,10 +238,7 @@ instance isScalarTower_sphere_ball_ball :
#align is_scalar_tower_sphere_ball_ball isScalarTower_sphere_ball_ball
/- warning: is_scalar_tower_closed_ball_ball_ball -> isScalarTower_closedBall_ball_ball is a dubious translation:
-lean 3 declaration is
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(OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π 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(NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.closedBall.monoid.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (mulActionClosedBallBall._proof_1.{u1} π _inst_1)) (mulActionClosedBallBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Mul.toSMul.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} 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(NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' 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(OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
-but is expected to have type
- forall {π : Type.{u1}} {π' : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))], IsScalarTower.{u1, u2, u2} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))) (mulActionClosedBallBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Mul.toSMul.{u2} (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Semigroup.toMul.{u2} (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitBall.semigroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))) (mulActionClosedBallBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
+<too large>
Case conversion may be inaccurate. Consider using '#align is_scalar_tower_closed_ball_ball_ball isScalarTower_closedBall_ball_ballβ'. -/
instance isScalarTower_closedBall_ball_ball :
IsScalarTower (closedBall (0 : π) 1) (ball (0 : π') 1) (ball (0 : π') 1) :=
@@ -279,10 +252,7 @@ section SMulCommClass
variable [SMulCommClass π π' E]
/- warning: smul_comm_class_closed_ball_closed_ball_closed_ball -> sMulCommClass_closedBall_closedBall_closedBall is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall._proof_1.{u1} π _inst_1)) (mulActionClosedBallClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (mulActionClosedBallClosedBall._proof_1.{u2} π' _inst_2)) (mulActionClosedBallClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
-but is expected to have type
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (NormedDivisionRing.to_normOneClass.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2))) (mulActionClosedBallClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+<too large>
Case conversion may be inaccurate. Consider using '#align smul_comm_class_closed_ball_closed_ball_closed_ball sMulCommClass_closedBall_closedBall_closedBallβ'. -/
instance sMulCommClass_closedBall_closedBall_closedBall :
SMulCommClass (closedBall (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
@@ -290,10 +260,7 @@ instance sMulCommClass_closedBall_closedBall_closedBall :
#align smul_comm_class_closed_ball_closed_ball_closed_ball sMulCommClass_closedBall_closedBall_closedBall
/- warning: smul_comm_class_closed_ball_closed_ball_ball -> sMulCommClass_closedBall_closedBall_ball is a dubious translation:
-lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ 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u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (mulActionClosedBallBall._proof_1.{u2} π' _inst_2)) (mulActionClosedBallBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
-but is expected to have type
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))) (mulActionClosedBallBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (NormedDivisionRing.to_normOneClass.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2))) (mulActionClosedBallBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+<too large>
Case conversion may be inaccurate. Consider using '#align smul_comm_class_closed_ball_closed_ball_ball sMulCommClass_closedBall_closedBall_ballβ'. -/
instance sMulCommClass_closedBall_closedBall_ball :
SMulCommClass (closedBall (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
@@ -301,10 +268,7 @@ instance sMulCommClass_closedBall_closedBall_ball :
#align smul_comm_class_closed_ball_closed_ball_ball sMulCommClass_closedBall_closedBall_ball
/- warning: smul_comm_class_sphere_closed_ball_closed_ball -> sMulCommClass_sphere_closedBall_closedBall is a dubious translation:
-lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ 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(AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (mulActionClosedBallClosedBall._proof_1.{u2} π' _inst_2)) (mulActionClosedBallClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
-but is expected to have type
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (NormedDivisionRing.to_normOneClass.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2))) (mulActionClosedBallClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+<too large>
Case conversion may be inaccurate. Consider using '#align smul_comm_class_sphere_closed_ball_closed_ball sMulCommClass_sphere_closedBall_closedBallβ'. -/
instance sMulCommClass_sphere_closedBall_closedBall :
SMulCommClass (sphere (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
@@ -312,10 +276,7 @@ instance sMulCommClass_sphere_closedBall_closedBall :
#align smul_comm_class_sphere_closed_ball_closed_ball sMulCommClass_sphere_closedBall_closedBall
/- warning: smul_comm_class_sphere_closed_ball_ball -> sMulCommClass_sphere_closedBall_ball is a dubious translation:
-lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ 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(AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (mulActionClosedBallBall._proof_1.{u2} π' _inst_2)) (mulActionClosedBallBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
-but is expected to have type
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (NormedDivisionRing.to_normOneClass.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2))) (mulActionClosedBallBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+<too large>
Case conversion may be inaccurate. Consider using '#align smul_comm_class_sphere_closed_ball_ball sMulCommClass_sphere_closedBall_ballβ'. -/
instance sMulCommClass_sphere_closedBall_ball :
SMulCommClass (sphere (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
@@ -323,10 +284,7 @@ instance sMulCommClass_sphere_closedBall_ball :
#align smul_comm_class_sphere_closed_ball_ball sMulCommClass_sphere_closedBall_ball
/- warning: smul_comm_class_sphere_ball_ball -> sMulCommClass_sphere_ball_ball is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} {π' : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_7 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))], SMulCommClass.{u1, u2, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π 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(NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_7) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Mul.toSMul.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' 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(MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.ball.semigroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))
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+<too large>
Case conversion may be inaccurate. Consider using '#align smul_comm_class_sphere_ball_ball sMulCommClass_sphere_ball_ballβ'. -/
instance sMulCommClass_sphere_ball_ball [NormedAlgebra π π'] :
SMulCommClass (sphere (0 : π) 1) (ball (0 : π') 1) (ball (0 : π') 1) :=
@@ -334,10 +292,7 @@ instance sMulCommClass_sphere_ball_ball [NormedAlgebra π π'] :
#align smul_comm_class_sphere_ball_ball sMulCommClass_sphere_ball_ball
/- warning: smul_comm_class_sphere_sphere_closed_ball -> sMulCommClass_sphere_sphere_closedBall is a dubious translation:
-lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π 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(AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
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(SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+<too large>
Case conversion may be inaccurate. Consider using '#align smul_comm_class_sphere_sphere_closed_ball sMulCommClass_sphere_sphere_closedBallβ'. -/
instance sMulCommClass_sphere_sphere_closedBall :
SMulCommClass (sphere (0 : π) 1) (sphere (0 : π') 1) (closedBall (0 : E) r) :=
@@ -345,10 +300,7 @@ instance sMulCommClass_sphere_sphere_closedBall :
#align smul_comm_class_sphere_sphere_closed_ball sMulCommClass_sphere_sphere_closedBall
/- warning: smul_comm_class_sphere_sphere_ball -> sMulCommClass_sphere_sphere_ball is a dubious translation:
-lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ 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(Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
-but is expected to have type
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+<too large>
Case conversion may be inaccurate. Consider using '#align smul_comm_class_sphere_sphere_ball sMulCommClass_sphere_sphere_ballβ'. -/
instance sMulCommClass_sphere_sphere_ball :
SMulCommClass (sphere (0 : π) 1) (sphere (0 : π') 1) (ball (0 : E) r) :=
@@ -356,10 +308,7 @@ instance sMulCommClass_sphere_sphere_ball :
#align smul_comm_class_sphere_sphere_ball sMulCommClass_sphere_sphere_ball
/- warning: smul_comm_class_sphere_sphere_sphere -> sMulCommClass_sphere_sphere_sphere is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ 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(Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereSphere.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
-but is expected to have type
- forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereSphere.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+<too large>
Case conversion may be inaccurate. Consider using '#align smul_comm_class_sphere_sphere_sphere sMulCommClass_sphere_sphere_sphereβ'. -/
instance sMulCommClass_sphere_sphere_sphere :
SMulCommClass (sphere (0 : π) 1) (sphere (0 : π') 1) (sphere (0 : E) r) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/52932b3a083d4142e78a15dc928084a22fea9ba0
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth
! This file was ported from Lean 3 source module analysis.normed_space.ball_action
-! leanprover-community/mathlib commit 3339976e2bcae9f1c81e620836d1eb736e3c4700
+! leanprover-community/mathlib commit 86d1873c01a723aba6788f0b9051ae3d23b4c1c3
! 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.NormedSpace.Basic
/-!
# Multiplicative actions of/on balls and spheres
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
Let `E` be a normed vector space over a normed field `π`. In this file we define the following
multiplicative actions.
mathlib commit https://github.com/leanprover-community/mathlib/commit/cd8fafa2fac98e1a67097e8a91ad9901cfde48af
@@ -29,6 +29,12 @@ variable {π π' E : Type _} [NormedField π] [NormedField π'] [Seminor
section ClosedBall
+/- warning: mul_action_closed_ball_ball -> mulActionClosedBallBall is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, MulAction.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (mulActionClosedBallBall._proof_1.{u1} π _inst_1))
+but is expected to have type
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, MulAction.{u1, u2} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} E (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)))
+Case conversion may be inaccurate. Consider using '#align mul_action_closed_ball_ball mulActionClosedBallBallβ'. -/
instance mulActionClosedBallBall : MulAction (closedBall (0 : π) 1) (ball (0 : E) r)
where
smul c x :=
@@ -41,10 +47,22 @@ instance mulActionClosedBallBall : MulAction (closedBall (0 : π) 1) (ball (0
mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
#align mul_action_closed_ball_ball mulActionClosedBallBall
+/- warning: has_continuous_smul_closed_ball_ball -> continuousSMul_closedBall_ball is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, ContinuousSMul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (mulActionClosedBallBall._proof_1.{u1} π _inst_1)) (mulActionClosedBallBall.{u1, u2} π E _inst_1 _inst_3 _inst_4 r)) (Subtype.topologicalSpace.{u1} π (fun (x : π) => Membership.Mem.{u1, u1} π (Set.{u1} π) (Set.hasMem.{u1} π) x (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (UniformSpace.toTopologicalSpace.{u1} π (PseudoMetricSpace.toUniformSpace.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))) (Subtype.topologicalSpace.{u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))))
+but is expected to have type
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, ContinuousSMul.{u1, u2} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} E (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} E (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))) (mulActionClosedBallBall.{u1, u2} π E _inst_1 _inst_3 _inst_4 r)) (instTopologicalSpaceSubtype.{u1} π (fun (x : π) => Membership.mem.{u1, u1} π (Set.{u1} π) (Set.instMembershipSet.{u1} π) x (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (UniformSpace.toTopologicalSpace.{u1} π (PseudoMetricSpace.toUniformSpace.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))) (instTopologicalSpaceSubtype.{u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))))
+Case conversion may be inaccurate. Consider using '#align has_continuous_smul_closed_ball_ball continuousSMul_closedBall_ballβ'. -/
instance continuousSMul_closedBall_ball : ContinuousSMul (closedBall (0 : π) 1) (ball (0 : E) r) :=
β¨(continuous_subtype_val.fst'.smul continuous_subtype_val.snd').subtype_mk _β©
#align has_continuous_smul_closed_ball_ball continuousSMul_closedBall_ball
+/- warning: mul_action_closed_ball_closed_ball -> mulActionClosedBallClosedBall is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, MulAction.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall._proof_1.{u1} π _inst_1))
+but is expected to have type
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, MulAction.{u1, u2} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} E (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)))
+Case conversion may be inaccurate. Consider using '#align mul_action_closed_ball_closed_ball mulActionClosedBallClosedBallβ'. -/
instance mulActionClosedBallClosedBall : MulAction (closedBall (0 : π) 1) (closedBall (0 : E) r)
where
smul c x :=
@@ -57,6 +75,12 @@ instance mulActionClosedBallClosedBall : MulAction (closedBall (0 : π) 1) (cl
mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
#align mul_action_closed_ball_closed_ball mulActionClosedBallClosedBall
+/- warning: has_continuous_smul_closed_ball_closed_ball -> continuousSMul_closedBall_closedBall is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, ContinuousSMul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall._proof_1.{u1} π _inst_1)) (mulActionClosedBallClosedBall.{u1, u2} π E _inst_1 _inst_3 _inst_4 r)) (Subtype.topologicalSpace.{u1} π (fun (x : π) => Membership.Mem.{u1, u1} π (Set.{u1} π) (Set.hasMem.{u1} π) x (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (UniformSpace.toTopologicalSpace.{u1} π (PseudoMetricSpace.toUniformSpace.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))) (Subtype.topologicalSpace.{u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))))
+but is expected to have type
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, ContinuousSMul.{u1, u2} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} E (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} E (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall.{u1, u2} π E _inst_1 _inst_3 _inst_4 r)) (instTopologicalSpaceSubtype.{u1} π (fun (x : π) => Membership.mem.{u1, u1} π (Set.{u1} π) (Set.instMembershipSet.{u1} π) x (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (UniformSpace.toTopologicalSpace.{u1} π (PseudoMetricSpace.toUniformSpace.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))) (instTopologicalSpaceSubtype.{u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))))
+Case conversion may be inaccurate. Consider using '#align has_continuous_smul_closed_ball_closed_ball continuousSMul_closedBall_closedBallβ'. -/
instance continuousSMul_closedBall_closedBall :
ContinuousSMul (closedBall (0 : π) 1) (closedBall (0 : E) r) :=
β¨(continuous_subtype_val.fst'.smul continuous_subtype_val.snd').subtype_mk _β©
@@ -66,6 +90,12 @@ end ClosedBall
section Sphere
+/- warning: mul_action_sphere_ball -> mulActionSphereBall is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, MulAction.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))
+but is expected to have type
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, MulAction.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} E (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))
+Case conversion may be inaccurate. Consider using '#align mul_action_sphere_ball mulActionSphereBallβ'. -/
instance mulActionSphereBall : MulAction (sphere (0 : π) 1) (ball (0 : E) r)
where
smul c x := inclusion sphere_subset_closedBall c β’ x
@@ -73,10 +103,22 @@ instance mulActionSphereBall : MulAction (sphere (0 : π) 1) (ball (0 : E) r)
mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
#align mul_action_sphere_ball mulActionSphereBall
+/- warning: has_continuous_smul_sphere_ball -> continuousSMul_sphere_ball is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, ContinuousSMul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u2} π E _inst_1 _inst_3 _inst_4 r)) (Subtype.topologicalSpace.{u1} π (fun (x : π) => Membership.Mem.{u1, u1} π (Set.{u1} π) (Set.hasMem.{u1} π) x (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (UniformSpace.toTopologicalSpace.{u1} π (PseudoMetricSpace.toUniformSpace.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))) (Subtype.topologicalSpace.{u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))))
+but is expected to have type
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, ContinuousSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} E (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} E (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u2} π E _inst_1 _inst_3 _inst_4 r)) (instTopologicalSpaceSubtype.{u1} π (fun (x : π) => Membership.mem.{u1, u1} π (Set.{u1} π) (Set.instMembershipSet.{u1} π) x (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (UniformSpace.toTopologicalSpace.{u1} π (PseudoMetricSpace.toUniformSpace.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))) (instTopologicalSpaceSubtype.{u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))))
+Case conversion may be inaccurate. Consider using '#align has_continuous_smul_sphere_ball continuousSMul_sphere_ballβ'. -/
instance continuousSMul_sphere_ball : ContinuousSMul (sphere (0 : π) 1) (ball (0 : E) r) :=
β¨(continuous_subtype_val.fst'.smul continuous_subtype_val.snd').subtype_mk _β©
#align has_continuous_smul_sphere_ball continuousSMul_sphere_ball
+/- warning: mul_action_sphere_closed_ball -> mulActionSphereClosedBall is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, MulAction.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))
+but is expected to have type
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, MulAction.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} E (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))
+Case conversion may be inaccurate. Consider using '#align mul_action_sphere_closed_ball mulActionSphereClosedBallβ'. -/
instance mulActionSphereClosedBall : MulAction (sphere (0 : π) 1) (closedBall (0 : E) r)
where
smul c x := inclusion sphere_subset_closedBall c β’ x
@@ -84,11 +126,23 @@ instance mulActionSphereClosedBall : MulAction (sphere (0 : π) 1) (closedBall
mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
#align mul_action_sphere_closed_ball mulActionSphereClosedBall
+/- warning: has_continuous_smul_sphere_closed_ball -> continuousSMul_sphere_closedBall is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, ContinuousSMul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u2} π E _inst_1 _inst_3 _inst_4 r)) (Subtype.topologicalSpace.{u1} π (fun (x : π) => Membership.Mem.{u1, u1} π (Set.{u1} π) (Set.hasMem.{u1} π) x (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (UniformSpace.toTopologicalSpace.{u1} π (PseudoMetricSpace.toUniformSpace.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))) (Subtype.topologicalSpace.{u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))))
+but is expected to have type
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, ContinuousSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} E (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} E (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u2} π E _inst_1 _inst_3 _inst_4 r)) (instTopologicalSpaceSubtype.{u1} π (fun (x : π) => Membership.mem.{u1, u1} π (Set.{u1} π) (Set.instMembershipSet.{u1} π) x (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (UniformSpace.toTopologicalSpace.{u1} π (PseudoMetricSpace.toUniformSpace.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))) (instTopologicalSpaceSubtype.{u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))))
+Case conversion may be inaccurate. Consider using '#align has_continuous_smul_sphere_closed_ball continuousSMul_sphere_closedBallβ'. -/
instance continuousSMul_sphere_closedBall :
ContinuousSMul (sphere (0 : π) 1) (closedBall (0 : E) r) :=
β¨(continuous_subtype_val.fst'.smul continuous_subtype_val.snd').subtype_mk _β©
#align has_continuous_smul_sphere_closed_ball continuousSMul_sphere_closedBall
+/- warning: mul_action_sphere_sphere -> mulActionSphereSphere is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, MulAction.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))
+but is expected to have type
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, MulAction.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} E (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))
+Case conversion may be inaccurate. Consider using '#align mul_action_sphere_sphere mulActionSphereSphereβ'. -/
instance mulActionSphereSphere : MulAction (sphere (0 : π) 1) (sphere (0 : E) r)
where
smul c x :=
@@ -100,6 +154,12 @@ instance mulActionSphereSphere : MulAction (sphere (0 : π) 1) (sphere (0 : E)
mul_smul cβ cβ x := Subtype.ext <| mul_smul _ _ _
#align mul_action_sphere_sphere mulActionSphereSphere
+/- warning: has_continuous_smul_sphere_sphere -> continuousSMul_sphere_sphere is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, ContinuousSMul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u2} π E _inst_1 _inst_3 _inst_4 r)) (Subtype.topologicalSpace.{u1} π (fun (x : π) => Membership.Mem.{u1, u1} π (Set.{u1} π) (Set.hasMem.{u1} π) x (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (UniformSpace.toTopologicalSpace.{u1} π (PseudoMetricSpace.toUniformSpace.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))) (Subtype.topologicalSpace.{u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))))
+but is expected to have type
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] {r : Real}, ContinuousSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} E (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} E (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u2} π E _inst_1 _inst_3 _inst_4 r)) (instTopologicalSpaceSubtype.{u1} π (fun (x : π) => Membership.mem.{u1, u1} π (Set.{u1} π) (Set.instMembershipSet.{u1} π) x (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (UniformSpace.toTopologicalSpace.{u1} π (PseudoMetricSpace.toUniformSpace.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))) (instTopologicalSpaceSubtype.{u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))))) r)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))))
+Case conversion may be inaccurate. Consider using '#align has_continuous_smul_sphere_sphere continuousSMul_sphere_sphereβ'. -/
instance continuousSMul_sphere_sphere : ContinuousSMul (sphere (0 : π) 1) (sphere (0 : E) r) :=
β¨(continuous_subtype_val.fst'.smul continuous_subtype_val.snd').subtype_mk _β©
#align has_continuous_smul_sphere_sphere continuousSMul_sphere_sphere
@@ -110,46 +170,100 @@ section IsScalarTower
variable [NormedAlgebra π π'] [IsScalarTower π π' E]
+/- warning: is_scalar_tower_closed_ball_closed_ball_closed_ball -> isScalarTower_closedBall_closedBall_closedBall is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π π' (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (NormedSpace.toModule.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.closedBall.monoid.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall._proof_1.{u1} π _inst_1)) (mulActionClosedBallClosedBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (mulActionClosedBallClosedBall._proof_1.{u2} π' _inst_2)) (mulActionClosedBallClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall._proof_1.{u1} π _inst_1)) (mulActionClosedBallClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+but is expected to have type
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (Algebra.toSMul.{u1, u2} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))) (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (NormedAlgebra.toAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) _inst_6)) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (NormedDivisionRing.to_normOneClass.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2))) (mulActionClosedBallClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+Case conversion may be inaccurate. Consider using '#align is_scalar_tower_closed_ball_closed_ball_closed_ball isScalarTower_closedBall_closedBall_closedBallβ'. -/
instance isScalarTower_closedBall_closedBall_closedBall :
IsScalarTower (closedBall (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_closed_ball_closed_ball_closed_ball isScalarTower_closedBall_closedBall_closedBall
+/- warning: is_scalar_tower_closed_ball_closed_ball_ball -> isScalarTower_closedBall_closedBall_ball is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π π' (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (NormedSpace.toModule.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.closedBall.monoid.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall._proof_1.{u1} π _inst_1)) (mulActionClosedBallClosedBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (mulActionClosedBallBall._proof_1.{u2} π' _inst_2)) (mulActionClosedBallBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (mulActionClosedBallBall._proof_1.{u1} π _inst_1)) (mulActionClosedBallBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+but is expected to have type
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (Algebra.toSMul.{u1, u2} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))) (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (NormedAlgebra.toAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) _inst_6)) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (NormedDivisionRing.to_normOneClass.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2))) (mulActionClosedBallBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))) (mulActionClosedBallBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+Case conversion may be inaccurate. Consider using '#align is_scalar_tower_closed_ball_closed_ball_ball isScalarTower_closedBall_closedBall_ballβ'. -/
instance isScalarTower_closedBall_closedBall_ball :
IsScalarTower (closedBall (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_closed_ball_closed_ball_ball isScalarTower_closedBall_closedBall_ball
+/- warning: is_scalar_tower_sphere_closed_ball_closed_ball -> isScalarTower_sphere_closedBall_closedBall is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π π' (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (NormedSpace.toModule.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (mulActionClosedBallClosedBall._proof_1.{u2} π' _inst_2)) (mulActionClosedBallClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+but is expected to have type
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (Algebra.toSMul.{u1, u2} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))) (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (NormedAlgebra.toAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) _inst_6)) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (NormedDivisionRing.to_normOneClass.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2))) (mulActionClosedBallClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+Case conversion may be inaccurate. Consider using '#align is_scalar_tower_sphere_closed_ball_closed_ball isScalarTower_sphere_closedBall_closedBallβ'. -/
instance isScalarTower_sphere_closedBall_closedBall :
IsScalarTower (sphere (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_sphere_closed_ball_closed_ball isScalarTower_sphere_closedBall_closedBall
+/- warning: is_scalar_tower_sphere_closed_ball_ball -> isScalarTower_sphere_closedBall_ball is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π π' (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (NormedSpace.toModule.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (mulActionClosedBallBall._proof_1.{u2} π' _inst_2)) (mulActionClosedBallBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+but is expected to have type
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (Algebra.toSMul.{u1, u2} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))) (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (NormedAlgebra.toAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) _inst_6)) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (NormedDivisionRing.to_normOneClass.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2))) (mulActionClosedBallBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+Case conversion may be inaccurate. Consider using '#align is_scalar_tower_sphere_closed_ball_ball isScalarTower_sphere_closedBall_ballβ'. -/
instance isScalarTower_sphere_closedBall_ball :
IsScalarTower (sphere (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_sphere_closed_ball_ball isScalarTower_sphere_closedBall_ball
+/- warning: is_scalar_tower_sphere_sphere_closed_ball -> isScalarTower_sphere_sphere_closedBall is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π π' (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (NormedSpace.toModule.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+but is expected to have type
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (Algebra.toSMul.{u1, u2} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))) (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (NormedAlgebra.toAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) _inst_6)) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+Case conversion may be inaccurate. Consider using '#align is_scalar_tower_sphere_sphere_closed_ball isScalarTower_sphere_sphere_closedBallβ'. -/
instance isScalarTower_sphere_sphere_closedBall :
IsScalarTower (sphere (0 : π) 1) (sphere (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_sphere_sphere_closed_ball isScalarTower_sphere_sphere_closedBall
+/- warning: is_scalar_tower_sphere_sphere_ball -> isScalarTower_sphere_sphere_ball is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π π' (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (NormedSpace.toModule.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+but is expected to have type
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (Algebra.toSMul.{u1, u2} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))) (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (NormedAlgebra.toAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) _inst_6)) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+Case conversion may be inaccurate. Consider using '#align is_scalar_tower_sphere_sphere_ball isScalarTower_sphere_sphere_ballβ'. -/
instance isScalarTower_sphere_sphere_ball :
IsScalarTower (sphere (0 : π) 1) (sphere (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_sphere_sphere_ball isScalarTower_sphere_sphere_ball
+/- warning: is_scalar_tower_sphere_sphere_sphere -> isScalarTower_sphere_sphere_sphere is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π π' (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (NormedSpace.toModule.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereSphere.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+but is expected to have type
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (Algebra.toSMul.{u1, u2} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))) (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (NormedAlgebra.toAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) _inst_6)) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4)))))], IsScalarTower.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereSphere.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u3} π E _inst_1 _inst_3 _inst_4 r))
+Case conversion may be inaccurate. Consider using '#align is_scalar_tower_sphere_sphere_sphere isScalarTower_sphere_sphere_sphereβ'. -/
instance isScalarTower_sphere_sphere_sphere :
IsScalarTower (sphere (0 : π) 1) (sphere (0 : π') 1) (sphere (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : E)β©
#align is_scalar_tower_sphere_sphere_sphere isScalarTower_sphere_sphere_sphere
+/- warning: is_scalar_tower_sphere_ball_ball -> isScalarTower_sphere_ball_ball is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {π' : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))], IsScalarTower.{u1, u2, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Mul.toSMul.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Semigroup.toHasMul.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.ball.semigroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
+but is expected to have type
+ forall {π : Type.{u1}} {π' : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))], IsScalarTower.{u1, u2, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Mul.toSMul.{u2} (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Semigroup.toMul.{u2} (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitBall.semigroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
+Case conversion may be inaccurate. Consider using '#align is_scalar_tower_sphere_ball_ball isScalarTower_sphere_ball_ballβ'. -/
instance isScalarTower_sphere_ball_ball :
IsScalarTower (sphere (0 : π) 1) (ball (0 : π') 1) (ball (0 : π') 1) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : π')β©
#align is_scalar_tower_sphere_ball_ball isScalarTower_sphere_ball_ball
+/- warning: is_scalar_tower_closed_ball_ball_ball -> isScalarTower_closedBall_ball_ball is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {π' : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))], IsScalarTower.{u1, u2, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.closedBall.monoid.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (mulActionClosedBallBall._proof_1.{u1} π _inst_1)) (mulActionClosedBallBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Mul.toSMul.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Semigroup.toHasMul.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.ball.semigroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.closedBall.monoid.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (mulActionClosedBallBall._proof_1.{u1} π _inst_1)) (mulActionClosedBallBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
+but is expected to have type
+ forall {π : Type.{u1}} {π' : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_6 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))], IsScalarTower.{u1, u2, u2} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))) (mulActionClosedBallBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Mul.toSMul.{u2} (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Semigroup.toMul.{u2} (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitBall.semigroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))) (mulActionClosedBallBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_6) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
+Case conversion may be inaccurate. Consider using '#align is_scalar_tower_closed_ball_ball_ball isScalarTower_closedBall_ball_ballβ'. -/
instance isScalarTower_closedBall_ball_ball :
IsScalarTower (closedBall (0 : π) 1) (ball (0 : π') 1) (ball (0 : π') 1) :=
β¨fun a b c => Subtype.ext <| smul_assoc (a : π) (b : π') (c : π')β©
@@ -161,41 +275,89 @@ section SMulCommClass
variable [SMulCommClass π π' E]
+/- warning: smul_comm_class_closed_ball_closed_ball_closed_ball -> sMulCommClass_closedBall_closedBall_closedBall is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall._proof_1.{u1} π _inst_1)) (mulActionClosedBallClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (mulActionClosedBallClosedBall._proof_1.{u2} π' _inst_2)) (mulActionClosedBallClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+but is expected to have type
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))) (mulActionClosedBallClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (NormedDivisionRing.to_normOneClass.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2))) (mulActionClosedBallClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+Case conversion may be inaccurate. Consider using '#align smul_comm_class_closed_ball_closed_ball_closed_ball sMulCommClass_closedBall_closedBall_closedBallβ'. -/
instance sMulCommClass_closedBall_closedBall_closedBall :
SMulCommClass (closedBall (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
#align smul_comm_class_closed_ball_closed_ball_closed_ball sMulCommClass_closedBall_closedBall_closedBall
+/- warning: smul_comm_class_closed_ball_closed_ball_ball -> sMulCommClass_closedBall_closedBall_ball is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (mulActionClosedBallBall._proof_1.{u1} π _inst_1)) (mulActionClosedBallBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (mulActionClosedBallBall._proof_1.{u2} π' _inst_2)) (mulActionClosedBallBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+but is expected to have type
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.closedBall.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))) (NormedDivisionRing.to_normOneClass.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1))) (mulActionClosedBallBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (NormedDivisionRing.to_normOneClass.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2))) (mulActionClosedBallBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+Case conversion may be inaccurate. Consider using '#align smul_comm_class_closed_ball_closed_ball_ball sMulCommClass_closedBall_closedBall_ballβ'. -/
instance sMulCommClass_closedBall_closedBall_ball :
SMulCommClass (closedBall (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
#align smul_comm_class_closed_ball_closed_ball_ball sMulCommClass_closedBall_closedBall_ball
+/- warning: smul_comm_class_sphere_closed_ball_closed_ball -> sMulCommClass_sphere_closedBall_closedBall is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (mulActionClosedBallClosedBall._proof_1.{u2} π' _inst_2)) (mulActionClosedBallClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+but is expected to have type
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (NormedDivisionRing.to_normOneClass.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2))) (mulActionClosedBallClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+Case conversion may be inaccurate. Consider using '#align smul_comm_class_sphere_closed_ball_closed_ball sMulCommClass_sphere_closedBall_closedBallβ'. -/
instance sMulCommClass_sphere_closedBall_closedBall :
SMulCommClass (sphere (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
#align smul_comm_class_sphere_closed_ball_closed_ball sMulCommClass_sphere_closedBall_closedBall
+/- warning: smul_comm_class_sphere_closed_ball_ball -> sMulCommClass_sphere_closedBall_ball is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.closedBall.monoid.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (mulActionClosedBallBall._proof_1.{u2} π' _inst_2)) (mulActionClosedBallBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+but is expected to have type
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.closedBall.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitClosedBall.monoid.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))) (NormedDivisionRing.to_normOneClass.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2))) (mulActionClosedBallBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+Case conversion may be inaccurate. Consider using '#align smul_comm_class_sphere_closed_ball_ball sMulCommClass_sphere_closedBall_ballβ'. -/
instance sMulCommClass_sphere_closedBall_ball :
SMulCommClass (sphere (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
#align smul_comm_class_sphere_closed_ball_ball sMulCommClass_sphere_closedBall_ball
+/- warning: smul_comm_class_sphere_ball_ball -> sMulCommClass_sphere_ball_ball is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {π' : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_7 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))], SMulCommClass.{u1, u2, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (MulAction.toHasSmul.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_7) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Mul.toSMul.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Semigroup.toHasMul.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.ball.semigroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))
+but is expected to have type
+ forall {π : Type.{u1}} {π' : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_7 : NormedAlgebra.{u1, u2} π π' _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))], SMulCommClass.{u1, u2, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (MulAction.toSMul.{u1, u2} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u2} π π' _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π _inst_1 π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)) _inst_7) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Mul.toSMul.{u2} (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Semigroup.toMul.{u2} (Set.Elem.{u2} π' (Metric.ball.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Metric.unitBall.semigroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))
+Case conversion may be inaccurate. Consider using '#align smul_comm_class_sphere_ball_ball sMulCommClass_sphere_ball_ballβ'. -/
instance sMulCommClass_sphere_ball_ball [NormedAlgebra π π'] :
SMulCommClass (sphere (0 : π) 1) (ball (0 : π') 1) (ball (0 : π') 1) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : π')β©
#align smul_comm_class_sphere_ball_ball sMulCommClass_sphere_ball_ball
+/- warning: smul_comm_class_sphere_sphere_closed_ball -> sMulCommClass_sphere_sphere_closedBall is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+but is expected to have type
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereClosedBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.closedBall.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereClosedBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+Case conversion may be inaccurate. Consider using '#align smul_comm_class_sphere_sphere_closed_ball sMulCommClass_sphere_sphere_closedBallβ'. -/
instance sMulCommClass_sphere_sphere_closedBall :
SMulCommClass (sphere (0 : π) 1) (sphere (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
#align smul_comm_class_sphere_sphere_closed_ball sMulCommClass_sphere_sphere_closedBall
+/- warning: smul_comm_class_sphere_sphere_ball -> sMulCommClass_sphere_sphere_ball is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+but is expected to have type
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereBall.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.ball.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereBall.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+Case conversion may be inaccurate. Consider using '#align smul_comm_class_sphere_sphere_ball sMulCommClass_sphere_sphere_ballβ'. -/
instance sMulCommClass_sphere_sphere_ball :
SMulCommClass (sphere (0 : π) 1) (sphere (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
#align smul_comm_class_sphere_sphere_ball sMulCommClass_sphere_sphere_ball
+/- warning: smul_comm_class_sphere_sphere_sphere -> sMulCommClass_sphere_sphere_sphere is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (MulAction.toHasSmul.{u1, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} π) Type.{u1} (Set.hasCoeToSort.{u1} π) (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSemiNormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (OfNat.mk.{u1} π 0 (Zero.zero.{u1} π (MulZeroClass.toHasZero.{u1} π (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} π (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} π (NonAssocRing.toNonUnitalNonAssocRing.{u1} π (Ring.toNonAssocRing.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toHasSmul.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} π') Type.{u2} (Set.hasCoeToSort.{u2} π') (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (OfNat.mk.{u2} π' 0 (Zero.zero.{u2} π' (MulZeroClass.toHasZero.{u2} π' (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} π' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} π' (NonAssocRing.toNonUnitalNonAssocRing.{u2} π' (Ring.toNonAssocRing.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2))))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} E) Type.{u3} (Set.hasCoeToSort.{u3} E) (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (OfNat.mk.{u3} E 0 (Zero.zero.{u3} E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (SeminormedAddGroup.toAddGroup.{u3} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} E _inst_3))))))))) r)) (Metric.sphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereSphere.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+but is expected to have type
+ forall {π : Type.{u1}} {π' : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedField.{u2} π'] [_inst_3 : SeminormedAddCommGroup.{u3} E] [_inst_4 : NormedSpace.{u1, u3} π E _inst_1 _inst_3] [_inst_5 : NormedSpace.{u2, u3} π' E _inst_2 _inst_3] {r : Real} [_inst_6 : SMulCommClass.{u1, u2, u3} π π' E (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u1, u3} π E _inst_1 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u2, u3} π' E (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} π' E (DivisionSemiring.toSemiring.{u2} π' (Semifield.toDivisionSemiring.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)) (NormedSpace.toModule.{u2, u3} π' E _inst_2 _inst_3 _inst_5)))))], SMulCommClass.{u1, u2, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (MulAction.toSMul.{u1, u3} (Set.Elem.{u1} π (Metric.sphere.{u1} π (SeminormedRing.toPseudoMetricSpace.{u1} π (SeminormedCommRing.toSeminormedRing.{u1} π (NormedCommRing.toSeminormedCommRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (OfNat.ofNat.{u1} π 0 (Zero.toOfNat0.{u1} π (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u1} π (NormedField.toNormedDivisionRing.{u1} π _inst_1)) (mulActionSphereSphere.{u1, u3} π E _inst_1 _inst_3 _inst_4 r)) (MulAction.toSMul.{u2, u3} (Set.Elem.{u2} π' (Metric.sphere.{u2} π' (SeminormedRing.toPseudoMetricSpace.{u2} π' (SeminormedCommRing.toSeminormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' _inst_2)))) (OfNat.ofNat.{u2} π' 0 (Zero.toOfNat0.{u2} π' (CommMonoidWithZero.toZero.{u2} π' (CommGroupWithZero.toCommMonoidWithZero.{u2} π' (Semifield.toCommGroupWithZero.{u2} π' (Field.toSemifield.{u2} π' (NormedField.toField.{u2} π' _inst_2))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.Elem.{u3} E (Metric.sphere.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_3) (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_3)))))))) r)) (Metric.unitSphere.monoid.{u2} π' (NormedField.toNormedDivisionRing.{u2} π' _inst_2)) (mulActionSphereSphere.{u2, u3} π' E _inst_2 _inst_3 _inst_5 r))
+Case conversion may be inaccurate. Consider using '#align smul_comm_class_sphere_sphere_sphere sMulCommClass_sphere_sphere_sphereβ'. -/
instance sMulCommClass_sphere_sphere_sphere :
SMulCommClass (sphere (0 : π) 1) (sphere (0 : π') 1) (sphere (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
@@ -205,6 +367,12 @@ end SMulCommClass
variable (π) [CharZero π]
+/- warning: ne_neg_of_mem_sphere -> ne_neg_of_mem_sphere is a dubious translation:
+lean 3 declaration is
+ forall (π : Type.{u1}) {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] [_inst_6 : CharZero.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (AddCommGroupWithOne.toAddGroupWithOne.{u1} π (Ring.toAddCommGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))] {r : Real}, (Ne.{1} Real r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (forall (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)), Ne.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) x (Neg.neg.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (InvolutiveNeg.toHasNeg.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) r)) (Metric.sphere.hasInvolutiveNeg.{u2} E _inst_3 r)) x))
+but is expected to have type
+ forall (π : Type.{u2}) {E : Type.{u1}} [_inst_1 : NormedField.{u2} π] [_inst_3 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{u2, u1} π E _inst_1 _inst_3] [_inst_6 : CharZero.{u2} π (AddGroupWithOne.toAddMonoidWithOne.{u2} π (Ring.toAddGroupWithOne.{u2} π (NormedRing.toRing.{u2} π (NormedCommRing.toNormedRing.{u2} π (NormedField.toNormedCommRing.{u2} π _inst_1)))))] {r : Real}, (Ne.{1} Real r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (forall (x : Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) r)), Ne.{succ u1} (Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) r)) x (Neg.neg.{u1} (Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) r)) (InvolutiveNeg.toNeg.{u1} (Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) r)) (instInvolutiveNegElemSphereToPseudoMetricSpaceOfNatToOfNat0ToZeroToNegZeroClassToSubNegZeroMonoidToSubtractionMonoidToDivisionAddCommMonoidToAddCommGroup.{u1} E _inst_3 r)) x))
+Case conversion may be inaccurate. Consider using '#align ne_neg_of_mem_sphere ne_neg_of_mem_sphereβ'. -/
theorem ne_neg_of_mem_sphere {r : β} (hr : r β 0) (x : sphere (0 : E) r) : x β -x := fun h =>
ne_zero_of_mem_sphere hr x
((self_eq_neg π _).mp
@@ -213,6 +381,12 @@ theorem ne_neg_of_mem_sphere {r : β} (hr : r β 0) (x : sphere (0 : E) r) : x
simp))
#align ne_neg_of_mem_sphere ne_neg_of_mem_sphere
+/- warning: ne_neg_of_mem_unit_sphere -> ne_neg_of_mem_unit_sphere is a dubious translation:
+lean 3 declaration is
+ forall (π : Type.{u1}) {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : NormedSpace.{u1, u2} π E _inst_1 _inst_3] [_inst_6 : CharZero.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (AddCommGroupWithOne.toAddGroupWithOne.{u1} π (Ring.toAddCommGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1))))))] (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))), Ne.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) x (Neg.neg.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (InvolutiveNeg.toHasNeg.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} E) Type.{u2} (Set.hasCoeToSort.{u2} E) (Metric.sphere.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Metric.sphere.hasInvolutiveNeg.{u2} E _inst_3 (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) x)
+but is expected to have type
+ forall (π : Type.{u2}) {E : Type.{u1}} [_inst_1 : NormedField.{u2} π] [_inst_3 : SeminormedAddCommGroup.{u1} E] [_inst_4 : NormedSpace.{u2, u1} π E _inst_1 _inst_3] [_inst_6 : CharZero.{u2} π (AddGroupWithOne.toAddMonoidWithOne.{u2} π (Ring.toAddGroupWithOne.{u2} π (NormedRing.toRing.{u2} π (NormedCommRing.toNormedRing.{u2} π (NormedField.toNormedCommRing.{u2} π _inst_1)))))] (x : Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))), Ne.{succ u1} (Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) x (Neg.neg.{u1} (Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (InvolutiveNeg.toNeg.{u1} (Set.Elem.{u1} E (Metric.sphere.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_3) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_3)))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (instInvolutiveNegElemSphereToPseudoMetricSpaceOfNatToOfNat0ToZeroToNegZeroClassToSubNegZeroMonoidToSubtractionMonoidToDivisionAddCommMonoidToAddCommGroup.{u1} E _inst_3 (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) x)
+Case conversion may be inaccurate. Consider using '#align ne_neg_of_mem_unit_sphere ne_neg_of_mem_unit_sphereβ'. -/
theorem ne_neg_of_mem_unit_sphere (x : sphere (0 : E) 1) : x β -x :=
ne_neg_of_mem_sphere π one_ne_zero x
#align ne_neg_of_mem_unit_sphere ne_neg_of_mem_unit_sphere
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)
@@ -197,7 +197,6 @@ instance instSMulCommClass_sphere_sphere_sphere :
end SMulCommClass
variable (π)
-
variable [CharZero π]
theorem ne_neg_of_mem_sphere {r : β} (hr : r β 0) (x : sphere (0 : E) r) : x β -x := fun h =>
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -21,7 +21,7 @@ multiplicative actions.
open Metric Set
-variable {π π' E : Type _} [NormedField π] [NormedField π'] [SeminormedAddCommGroup E]
+variable {π π' E : Type*} [NormedField π] [NormedField π'] [SeminormedAddCommGroup E]
[NormedSpace π E] [NormedSpace π' E] {r : β}
section ClosedBall
@@ -2,15 +2,12 @@
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth
-
-! This file was ported from Lean 3 source module analysis.normed_space.ball_action
-! leanprover-community/mathlib commit 3339976e2bcae9f1c81e620836d1eb736e3c4700
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Analysis.Normed.Field.UnitBall
import Mathlib.Analysis.NormedSpace.Basic
+#align_import analysis.normed_space.ball_action from "leanprover-community/mathlib"@"3339976e2bcae9f1c81e620836d1eb736e3c4700"
+
/-!
# Multiplicative actions of/on balls and spheres
@@ -157,45 +157,45 @@ section SMulCommClass
variable [SMulCommClass π π' E]
-instance sMulCommClass_closedBall_closedBall_closedBall :
+instance instSMulCommClass_closedBall_closedBall_closedBall :
SMulCommClass (closedBall (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
-#align smul_comm_class_closed_ball_closed_ball_closed_ball sMulCommClass_closedBall_closedBall_closedBall
+#align smul_comm_class_closed_ball_closed_ball_closed_ball instSMulCommClass_closedBall_closedBall_closedBall
-instance sMulCommClass_closedBall_closedBall_ball :
+instance instSMulCommClass_closedBall_closedBall_ball :
SMulCommClass (closedBall (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
-#align smul_comm_class_closed_ball_closed_ball_ball sMulCommClass_closedBall_closedBall_ball
+#align smul_comm_class_closed_ball_closed_ball_ball instSMulCommClass_closedBall_closedBall_ball
-instance sMulCommClass_sphere_closedBall_closedBall :
+instance instSMulCommClass_sphere_closedBall_closedBall :
SMulCommClass (sphere (0 : π) 1) (closedBall (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
-#align smul_comm_class_sphere_closed_ball_closed_ball sMulCommClass_sphere_closedBall_closedBall
+#align smul_comm_class_sphere_closed_ball_closed_ball instSMulCommClass_sphere_closedBall_closedBall
-instance sMulCommClass_sphere_closedBall_ball :
+instance instSMulCommClass_sphere_closedBall_ball :
SMulCommClass (sphere (0 : π) 1) (closedBall (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
-#align smul_comm_class_sphere_closed_ball_ball sMulCommClass_sphere_closedBall_ball
+#align smul_comm_class_sphere_closed_ball_ball instSMulCommClass_sphere_closedBall_ball
-instance sMulCommClass_sphere_ball_ball [NormedAlgebra π π'] :
+instance instSMulCommClass_sphere_ball_ball [NormedAlgebra π π'] :
SMulCommClass (sphere (0 : π) 1) (ball (0 : π') 1) (ball (0 : π') 1) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : π')β©
-#align smul_comm_class_sphere_ball_ball sMulCommClass_sphere_ball_ball
+#align smul_comm_class_sphere_ball_ball instSMulCommClass_sphere_ball_ball
-instance sMulCommClass_sphere_sphere_closedBall :
+instance instSMulCommClass_sphere_sphere_closedBall :
SMulCommClass (sphere (0 : π) 1) (sphere (0 : π') 1) (closedBall (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
-#align smul_comm_class_sphere_sphere_closed_ball sMulCommClass_sphere_sphere_closedBall
+#align smul_comm_class_sphere_sphere_closed_ball instSMulCommClass_sphere_sphere_closedBall
-instance sMulCommClass_sphere_sphere_ball :
+instance instSMulCommClass_sphere_sphere_ball :
SMulCommClass (sphere (0 : π) 1) (sphere (0 : π') 1) (ball (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
-#align smul_comm_class_sphere_sphere_ball sMulCommClass_sphere_sphere_ball
+#align smul_comm_class_sphere_sphere_ball instSMulCommClass_sphere_sphere_ball
-instance sMulCommClass_sphere_sphere_sphere :
+instance instSMulCommClass_sphere_sphere_sphere :
SMulCommClass (sphere (0 : π) 1) (sphere (0 : π') 1) (sphere (0 : E) r) :=
β¨fun a b c => Subtype.ext <| smul_comm (a : π) (b : π') (c : E)β©
-#align smul_comm_class_sphere_sphere_sphere sMulCommClass_sphere_sphere_sphere
+#align smul_comm_class_sphere_sphere_sphere instSMulCommClass_sphere_sphere_sphere
end SMulCommClass
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