analysis.inner_product_space.conformal_linear_map ⟷ Mathlib.Analysis.InnerProductSpace.ConformalLinearMap

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,8 +3,8 @@ Copyright (c) 2021 Yourong Zang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yourong Zang
 -/
-import Mathbin.Analysis.NormedSpace.ConformalLinearMap
-import Mathbin.Analysis.InnerProductSpace.Basic
+import Analysis.NormedSpace.ConformalLinearMap
+import Analysis.InnerProductSpace.Basic
 
 #align_import analysis.inner_product_space.conformal_linear_map from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Yourong Zang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yourong Zang
-
-! This file was ported from Lean 3 source module analysis.inner_product_space.conformal_linear_map
-! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.NormedSpace.ConformalLinearMap
 import Mathbin.Analysis.InnerProductSpace.Basic
 
+#align_import analysis.inner_product_space.conformal_linear_map from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
+
 /-!
 # Conformal maps between inner product spaces
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -31,6 +31,7 @@ open LinearIsometry ContinuousLinearMap
 
 open scoped RealInnerProductSpace
 
+#print isConformalMap_iff /-
 /-- A map between two inner product spaces is a conformal map if and only if it preserves inner
 products up to a scalar factor, i.e., there exists a positive `c : ℝ` such that `⟪f u, f v⟫ = c *
 ⟪u, v⟫` for all `u`, `v`. -/
@@ -52,4 +53,5 @@ theorem isConformalMap_iff (f : E →L[ℝ] F) :
     · ext1 x
       exact (smul_inv_smul₀ hc.ne' (f x)).symm
 #align is_conformal_map_iff isConformalMap_iff
+-/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -29,7 +29,7 @@ variable [InnerProductSpace ℝ E] [InnerProductSpace ℝ F]
 
 open LinearIsometry ContinuousLinearMap
 
-open RealInnerProductSpace
+open scoped RealInnerProductSpace
 
 /-- A map between two inner product spaces is a conformal map if and only if it preserves inner
 products up to a scalar factor, i.e., there exists a positive `c : ℝ` such that `⟪f u, f v⟫ = c *

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -31,9 +31,6 @@ open LinearIsometry ContinuousLinearMap
 
 open RealInnerProductSpace
 
-/- warning: is_conformal_map_iff -> isConformalMap_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_conformal_map_iff isConformalMap_iffₓ'. -/
 /-- A map between two inner product spaces is a conformal map if and only if it preserves inner
 products up to a scalar factor, i.e., there exists a positive `c : ℝ` such that `⟪f u, f v⟫ = c *
 ⟪u, v⟫` for all `u`, `v`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yourong Zang
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.conformal_linear_map
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
+! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
 ! 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.InnerProductSpace.Basic
 /-!
 # Conformal maps between inner product spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In an inner product space, a map is conformal iff it preserves inner products up to a scalar factor.
 -/
 
@@ -29,10 +32,7 @@ open LinearIsometry ContinuousLinearMap
 open RealInnerProductSpace
 
 /- warning: is_conformal_map_iff -> isConformalMap_iff is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_conformal_map_iff isConformalMap_iffₓ'. -/
 /-- A map between two inner product spaces is a conformal map if and only if it preserves inner
 products up to a scalar factor, i.e., there exists a positive `c : ℝ` such that `⟪f u, f v⟫ = c *

mathlib commit https://github.com/leanprover-community/mathlib/commit/e1a18cad9cd462973d760af7de36b05776b8811c

@@ -28,6 +28,12 @@ open LinearIsometry ContinuousLinearMap
 
 open RealInnerProductSpace
 
+/- warning: is_conformal_map_iff -> isConformalMap_iff is a dubious translation:
+lean 3 declaration is
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(Inner.inner.{0, u1} Real E (InnerProductSpace.toHasInner.{0, u1} Real E Real.isROrC _inst_1 _inst_3) u v)))))
+but is expected to have type
+  forall {E : Type.{u2}} {F : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u2} E] [_inst_2 : NormedAddCommGroup.{u1} F] [_inst_3 : InnerProductSpace.{0, u2} Real E Real.isROrC _inst_1] [_inst_4 : InnerProductSpace.{0, u1} Real F Real.isROrC _inst_2] (f : ContinuousLinearMap.{0, 0, u2, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{0, u2} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_1 _inst_3)) (NormedSpace.toModule.{0, u1} Real F Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real F Real.isROrC _inst_2 _inst_4))), Iff (IsConformalMap.{0, u2, u1} Real E F Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_2) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_1 _inst_3) (InnerProductSpace.toNormedSpace.{0, u1} Real F Real.isROrC _inst_2 _inst_4) f) (Exists.{1} Real (fun (c : Real) => And (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) c) (forall (u : E) (v : E), Eq.{1} Real (Inner.inner.{0, u1} Real ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) u) (InnerProductSpace.toInner.{0, u1} Real ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) u) Real.isROrC _inst_2 _inst_4) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{0, 0, u2, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{0, u2} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_1 _inst_3)) (NormedSpace.toModule.{0, u1} Real F Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real F Real.isROrC _inst_2 _inst_4))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{0, 0, u2, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F 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(ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, 0, 0, u2, u1} (ContinuousLinearMap.{0, 0, u2, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{0, u2} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_1 _inst_3)) (NormedSpace.toModule.{0, u1} Real F Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real F Real.isROrC _inst_2 _inst_4))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{0, u2} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_1 _inst_3)) (NormedSpace.toModule.{0, u1} Real F Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real F Real.isROrC _inst_2 _inst_4)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u2, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{0, u2} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_1 _inst_3)) (NormedSpace.toModule.{0, u1} Real F Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real F Real.isROrC _inst_2 _inst_4))))) f u) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{0, 0, u2, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{0, u2} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_1 _inst_3)) (NormedSpace.toModule.{0, u1} Real F Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real F Real.isROrC _inst_2 _inst_4))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{0, 0, u2, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{0, u2} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_1 _inst_3)) (NormedSpace.toModule.{0, u1} Real F Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real F Real.isROrC _inst_2 _inst_4))) E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1)))) (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_2)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, 0, 0, u2, u1} (ContinuousLinearMap.{0, 0, u2, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_2)) (NormedSpace.toModule.{0, u2} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_1 _inst_3)) (NormedSpace.toModule.{0, u1} Real F Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real F Real.isROrC _inst_2 _inst_4))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) F (UniformSpace.toTopologicalSpace.{u1} F 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+Case conversion may be inaccurate. Consider using '#align is_conformal_map_iff isConformalMap_iffₓ'. -/
 /-- A map between two inner product spaces is a conformal map if and only if it preserves inner
 products up to a scalar factor, i.e., there exists a positive `c : ℝ` such that `⟪f u, f v⟫ = c *
 ⟪u, v⟫` for all `u`, `v`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yourong Zang
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.conformal_linear_map
-! leanprover-community/mathlib commit a148d797a1094ab554ad4183a4ad6f130358ef64
+! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,7 +18,11 @@ In an inner product space, a map is conformal iff it preserves inner products up
 -/
 
 
-variable {E F : Type _} [InnerProductSpace ℝ E] [InnerProductSpace ℝ F]
+variable {E F : Type _}
+
+variable [NormedAddCommGroup E] [NormedAddCommGroup F]
+
+variable [InnerProductSpace ℝ E] [InnerProductSpace ℝ F]
 
 open LinearIsometry ContinuousLinearMap
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

This adds the notation √r for Real.sqrt r. The precedence is such that √x⁻¹ is parsed as √(x⁻¹); not because this is particularly desirable, but because it's the default and the choice doesn't really matter.

This is extracted from #7907, which adds a more general nth root typeclass. The idea is to perform all the boring substitutions downstream quickly, so that we can play around with custom elaborators with a much slower rate of code-rot. This PR also won't rot as quickly, as it does not forbid writing x.sqrt as that PR does.

While perhaps claiming √ for Real.sqrt is greedy; it:

• Is far more common thatn NNReal.sqrt and Nat.sqrt
• Is far more interesting to mathlib than sqrt on Float
• Can be overloaded anyway, so this does not prevent downstream code using the notation on their own types.
• Will be replaced by a more general typeclass in a future PR.

Zulip

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -35,7 +35,7 @@ theorem isConformalMap_iff (f : E →L[ℝ] F) :
       coe_toContinuousLinearMap, Pi.smul_apply, inner_map_map]
   · rintro ⟨c₁, hc₁, huv⟩
     obtain ⟨c, hc, rfl⟩ : ∃ c : ℝ, 0 < c ∧ c₁ = c * c :=
-      ⟨Real.sqrt c₁, Real.sqrt_pos.2 hc₁, (Real.mul_self_sqrt hc₁.le).symm⟩
+      ⟨√c₁, Real.sqrt_pos.2 hc₁, (Real.mul_self_sqrt hc₁.le).symm⟩
     refine' ⟨c, hc.ne', (c⁻¹ • f : E →ₗ[ℝ] F).isometryOfInner fun u v => _, _⟩
     · simp only [real_inner_smul_left, real_inner_smul_right, huv, mul_assoc, coe_smul,
         inv_mul_cancel_left₀ hc.ne', LinearMap.smul_apply, ContinuousLinearMap.coe_coe]

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)

@@ -16,9 +16,7 @@ In an inner product space, a map is conformal iff it preserves inner products up
 
 
 variable {E F : Type*}
-
 variable [NormedAddCommGroup E] [NormedAddCommGroup F]
-
 variable [InnerProductSpace ℝ E] [InnerProductSpace ℝ F]
 
 open LinearIsometry ContinuousLinearMap

This covers many instances, but is not exhaustive.

Independently of whether that syntax should be avoided (similar to #10534), I think all these changes are small improvements.

@@ -36,8 +36,8 @@ theorem isConformalMap_iff (f : E →L[ℝ] F) :
     simp only [real_inner_smul_left, real_inner_smul_right, mul_assoc, coe_smul',
       coe_toContinuousLinearMap, Pi.smul_apply, inner_map_map]
   · rintro ⟨c₁, hc₁, huv⟩
-    obtain ⟨c, hc, rfl⟩ : ∃ c : ℝ, 0 < c ∧ c₁ = c * c
-    exact ⟨Real.sqrt c₁, Real.sqrt_pos.2 hc₁, (Real.mul_self_sqrt hc₁.le).symm⟩
+    obtain ⟨c, hc, rfl⟩ : ∃ c : ℝ, 0 < c ∧ c₁ = c * c :=
+      ⟨Real.sqrt c₁, Real.sqrt_pos.2 hc₁, (Real.mul_self_sqrt hc₁.le).symm⟩
     refine' ⟨c, hc.ne', (c⁻¹ • f : E →ₗ[ℝ] F).isometryOfInner fun u v => _, _⟩
     · simp only [real_inner_smul_left, real_inner_smul_right, huv, mul_assoc, coe_smul,
         inv_mul_cancel_left₀ hc.ne', LinearMap.smul_apply, ContinuousLinearMap.coe_coe]

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -15,7 +15,7 @@ In an inner product space, a map is conformal iff it preserves inner products up
 -/
 
 
-variable {E F : Type _}
+variable {E F : Type*}
 
 variable [NormedAddCommGroup E] [NormedAddCommGroup F]
 

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Yourong Zang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yourong Zang
-
-! This file was ported from Lean 3 source module analysis.inner_product_space.conformal_linear_map
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.NormedSpace.ConformalLinearMap
 import Mathlib.Analysis.InnerProductSpace.Basic
 
+#align_import analysis.inner_product_space.conformal_linear_map from "leanprover-community/mathlib"@"46b633fd842bef9469441c0209906f6dddd2b4f5"
+
 /-!
 # Conformal maps between inner product spaces
 

I wrote a script to find lines that contain an odd number of backticks

@@ -29,8 +29,8 @@ open LinearIsometry ContinuousLinearMap
 open RealInnerProductSpace
 
 /-- A map between two inner product spaces is a conformal map if and only if it preserves inner
-products up to a scalar factor, i.e., there exists a positive `c : ℝ` such that `⟪f u, f v⟫ = c *
-⟪u, v⟫` for all `u`, `v`. -/
+products up to a scalar factor, i.e., there exists a positive `c : ℝ` such that
+`⟪f u, f v⟫ = c * ⟪u, v⟫` for all `u`, `v`. -/
 theorem isConformalMap_iff (f : E →L[ℝ] F) :
     IsConformalMap f ↔ ∃ c : ℝ, 0 < c ∧ ∀ u v : E, ⟪f u, f v⟫ = c * ⟪u, v⟫ := by
   constructor