Merge pull request #266 from HEPLean/Bump

chore: Bump to 4.14.0

HepLean/AnomalyCancellation/SM/Basic.lean

@@ -141,7 +141,7 @@ lemma accSU2_ext {S T : (SMCharges n).Charges}
     AddHom.coe_mk]
   repeat erw [Finset.sum_add_distrib]
   repeat erw [← Finset.mul_sum]
-  exact Mathlib.Tactic.LinearCombination.add_pf (congrArg (HMul.hMul 3) (hj 0)) (hj 3)
+  exact Mathlib.Tactic.LinearCombination.add_eq_eq (congrArg (HMul.hMul 3) (hj 0)) (hj 3)
 
 /-- The `SU(3)` anomaly equations. -/
 @[simp]

HepLean/BeyondTheStandardModel/TwoHDM/GaugeOrbits.lean

@@ -75,11 +75,11 @@ lemma prodMatrix_hermitian (Φ1 Φ2 : HiggsField) (x : SpaceTime) :
 
 /-- The map `prodMatrix` is a smooth function on spacetime. -/
 lemma prodMatrix_smooth (Φ1 Φ2 : HiggsField) :
-    Smooth 𝓘(ℝ, SpaceTime) 𝓘(ℝ, Matrix (Fin 2) (Fin 2) ℂ) (prodMatrix Φ1 Φ2) := by
+    ContMDiff 𝓘(ℝ, SpaceTime) 𝓘(ℝ, Matrix (Fin 2) (Fin 2) ℂ) ⊤ (prodMatrix Φ1 Φ2) := by
   rw [show 𝓘(ℝ, Matrix (Fin 2) (Fin 2) ℂ) = modelWithCornersSelf ℝ (Fin 2 → Fin 2 → ℂ) from rfl,
-    smooth_pi_space]
+    contMDiff_pi_space]
   intro i
-  rw [smooth_pi_space]
+  rw [contMDiff_pi_space]
   intro j
   fin_cases i <;> fin_cases j <;>
     simpa only [prodMatrix, Fin.zero_eta, Fin.isValue, of_apply, cons_val', cons_val_zero,

HepLean/Lorentz/ComplexTensor/PauliMatrices/Basis.lean

@@ -334,7 +334,7 @@ def pauliCoMap := ((Sum.elim ![Color.down, Color.down] ![Color.up, Color.upL, Co
   ⇑finSumFinEquiv.symm) ∘ Fin.succAbove 1 ∘ Fin.succAbove 1)
 
 lemma pauliMatrix_contr_down_0 :
-    (contr 1 1 rfl (((tensorNode (basisVector ![Color.down, Color.down] fun x => 0)).prod
+    (contr 1 1 rfl (((tensorNode (basisVector ![Color.down, Color.down] fun _ => 0)).prod
     (tensorNode pauliContr)))).tensor
     = basisVector pauliCoMap (fun | 0 => 0 | 1 => 0 | 2 => 0)
     + basisVector pauliCoMap (fun | 0 => 0 | 1 => 1 | 2 => 1) := by
@@ -379,7 +379,7 @@ lemma pauliMatrix_contr_down_0 :
     fin_cases k <;> rfl
 
 lemma pauliMatrix_contr_down_1 :
-    {(basisVector ![Color.down, Color.down] fun x => 1) | ν μ ⊗
+    {(basisVector ![Color.down, Color.down] fun _ => 1) | ν μ ⊗
       pauliContr | μ α β}ᵀ.tensor
     = basisVector pauliCoMap (fun | 0 => 1 | 1 => 0 | 2 => 1)
     + basisVector pauliCoMap (fun | 0 => 1 | 1 => 1 | 2 => 0) := by
@@ -424,7 +424,7 @@ lemma pauliMatrix_contr_down_1 :
     fin_cases k <;> rfl
 
 lemma pauliMatrix_contr_down_2 :
-    {(basisVector ![Color.down, Color.down] fun x => 2) | μ ν ⊗
+    {(basisVector ![Color.down, Color.down] fun _ => 2) | μ ν ⊗
       pauliContr | ν α β}ᵀ.tensor
     = (- I) • basisVector pauliCoMap (fun | 0 => 2 | 1 => 0 | 2 => 1)
     + (I) • basisVector pauliCoMap (fun | 0 => 2 | 1 => 1 | 2 => 0) := by
@@ -464,7 +464,7 @@ lemma pauliMatrix_contr_down_2 :
   · decide
 
 lemma pauliMatrix_contr_down_3 :
-    {(basisVector ![Color.down, Color.down] fun x => 3) | μ ν ⊗
+    {(basisVector ![Color.down, Color.down] fun _ => 3) | μ ν ⊗
     pauliContr | ν α β}ᵀ.tensor
     = basisVector pauliCoMap (fun | 0 => 3 | 1 => 0 | 2 => 0)
     + (- 1 : ℂ) • basisVector pauliCoMap (fun | 0 => 3 | 1 => 1 | 2 => 1) := by

HepLean/Lorentz/Group/Basic.lean

@@ -241,17 +241,19 @@ lemma toProd_continuous : Continuous (@toProd d) := by
     MulOpposite.continuous_op.comp' ((continuous_const.matrix_mul (continuous_iff_le_induced.mpr
       fun U a => a).matrix_transpose).matrix_mul continuous_const)⟩
 
+open Topology
+
 /-- The embedding from the Lorentz Group into the monoid of matrices times the opposite of
   the monoid of matrices. -/
 lemma toProd_embedding : IsEmbedding (@toProd d) where
-  inj := toProd_injective
+  injective := toProd_injective
   eq_induced :=
     (isInducing_iff ⇑toProd).mp (IsInducing.of_comp toProd_continuous continuous_fst
       ((isInducing_iff (Prod.fst ∘ ⇑toProd)).mpr rfl))
 
 /-- The embedding from the Lorentz Group into `GL (Fin 4) ℝ`. -/
 lemma toGL_embedding : IsEmbedding (@toGL d).toFun where
-  inj := toGL_injective
+  injective := toGL_injective
   eq_induced := by
     refine ((fun {X} {t t'} => TopologicalSpace.ext_iff.mpr) fun _ ↦ ?_).symm
     rw [TopologicalSpace.ext_iff.mp toProd_embedding.eq_induced _, isOpen_induced_iff,

HepLean/Lorentz/RealVector/Contraction.lean

@@ -347,9 +347,7 @@ lemma _root_.LorentzGroup.mem_iff_norm : Λ ∈ LorentzGroup d ↔
     Action.FunctorCategoryEquivalence.functor_obj_obj, map_add, map_sub] at hp' hn'
   linear_combination (norm := ring_nf) (1 / 4) * hp' + (-1/ 4) * hn'
   rw [symm (Λ *ᵥ y) (Λ *ᵥ x), symm y x]
-  simp only [Action.instMonoidalCategory_tensorUnit_V, Action.instMonoidalCategory_tensorObj_V,
-    Equivalence.symm_inverse, Action.functorCategoryEquivalence_functor,
-    Action.FunctorCategoryEquivalence.functor_obj_obj, add_sub_cancel, neg_add_cancel, e]
+  ring
 
 /-!
 

HepLean/Lorentz/RealVector/Modules.lean

@@ -197,7 +197,7 @@ def toSpace (v : ContrMod d) : EuclideanSpace ℝ (Fin d) := v.val ∘ Sum.inr
 /-- The representation of the Lorentz group acting on `ContrℝModule d`. -/
 def rep : Representation ℝ (LorentzGroup d) (ContrMod d) where
   toFun g := Matrix.toLinAlgEquiv stdBasis g
-  map_one' := (MulEquivClass.map_eq_one_iff (Matrix.toLinAlgEquiv stdBasis)).mpr rfl
+  map_one' := EmbeddingLike.map_eq_one_iff.mpr rfl
   map_mul' x y := by
     simp only [lorentzGroupIsGroup_mul_coe, _root_.map_mul]
 
@@ -283,6 +283,8 @@ lemma toSelfAdjoint_symm_basis (i : Fin 1 ⊕ Fin 3) :
 instance : TopologicalSpace (ContrMod d) := TopologicalSpace.induced
   ContrMod.toFin1dℝEquiv (Pi.topologicalSpace)
 
+open Topology
+
 lemma toFin1dℝEquiv_isInducing : IsInducing (@ContrMod.toFin1dℝEquiv d) := by
   exact { eq_induced := rfl }
 

HepLean/Mathematics/LinearMaps.lean

@@ -71,7 +71,7 @@ def mk₂ (f : V × V → ℚ) (map_smul : ∀ a S T, f (a • S, T) = a * f (S,
       intro T1 T2
       simp only
       rw [swap, map_add]
-      exact Mathlib.Tactic.LinearCombination.add_pf (swap T1 S) (swap T2 S)
+      exact Mathlib.Tactic.LinearCombination.add_eq_eq (swap T1 S) (swap T2 S)
     map_smul' := by
       intro a T
       simp only [eq_ratCast, Rat.cast_eq_id, id_eq, smul_eq_mul]

HepLean/Mathematics/PiTensorProduct.lean

@@ -223,32 +223,32 @@ def domCoprod :
     MultilinearMap R (Sum.elim s1 s2) ((⨂[R] i : ι1, s1 i) ⊗[R] ⨂[R] i : ι2, s2 i) where
   toFun f := (PiTensorProduct.tprod R (pureInl f)) ⊗ₜ
     (PiTensorProduct.tprod R (pureInr f))
-  map_add' f xy v1 v2 := by
+  map_update_add' f xy v1 v2 := by
     haveI : DecidableEq (ι1 ⊕ ι2) := inferInstance
     haveI : DecidableEq ι1 :=
       @Function.Injective.decidableEq ι1 (ι1 ⊕ ι2) Sum.inl _ Sum.inl_injective
     haveI : DecidableEq ι2 :=
       @Function.Injective.decidableEq ι2 (ι1 ⊕ ι2) Sum.inr _ Sum.inr_injective
     match xy with
     | Sum.inl xy =>
-      simp only [Sum.elim_inl, pureInl_update_left, MultilinearMap.map_add, pureInr_update_left, ←
-        add_tmul]
+      simp only [Sum.elim_inl, pureInl_update_left, MultilinearMap.map_update_add,
+        pureInr_update_left, ← add_tmul]
     | Sum.inr xy =>
-      simp only [Sum.elim_inr, pureInr_update_right, MultilinearMap.map_add, pureInl_update_right, ←
-        tmul_add]
-  map_smul' f xy r p := by
+      simp only [Sum.elim_inr, pureInl_update_right, pureInr_update_right,
+        MultilinearMap.map_update_add, ← tmul_add]
+  map_update_smul' f xy r p := by
     haveI : DecidableEq (ι1 ⊕ ι2) := inferInstance
     haveI : DecidableEq ι1 :=
       @Function.Injective.decidableEq ι1 (ι1 ⊕ ι2) Sum.inl _ Sum.inl_injective
     haveI : DecidableEq ι2 :=
       @Function.Injective.decidableEq ι2 (ι1 ⊕ ι2) Sum.inr _ Sum.inr_injective
     match xy with
     | Sum.inl x =>
-      simp only [Sum.elim_inl, pureInl_update_left, MultilinearMap.map_smul, pureInr_update_left,
-        smul_tmul, tmul_smul]
+      simp only [Sum.elim_inl, pureInl_update_left, MultilinearMap.map_update_smul,
+        pureInr_update_left, smul_tmul, tmul_smul]
     | Sum.inr y =>
-      simp only [Sum.elim_inr, pureInl_update_right, pureInr_update_right, MultilinearMap.map_smul,
-        tmul_smul]
+      simp only [Sum.elim_inr, pureInl_update_right, pureInr_update_right,
+        MultilinearMap.map_update_smul, tmul_smul]
 
 /-- Expand `PiTensorProduct` on sums into a `TensorProduct` of two factors. -/
 def tmulSymm : (⨂[R] i : ι1 ⊕ ι2, (Sum.elim s1 s2) i) →ₗ[R]
@@ -308,21 +308,21 @@ def elimPureTensorMulLin : MultilinearMap R s1
     (MultilinearMap R s2 (⨂[R] i : ι1 ⊕ ι2, (Sum.elim s1 s2) i)) where
   toFun p := {
     toFun := fun q => PiTensorProduct.tprod R (elimPureTensor p q)
-    map_add' := fun m x v1 v2 => by
+    map_update_add' := fun m x v1 v2 => by
       haveI : DecidableEq ι2 := inferInstance
       haveI := Classical.decEq ι1
-      simp only [elimPureTensor_update_right, MultilinearMap.map_add]
-    map_smul' := fun m x r v => by
+      simp only [elimPureTensor_update_right, MultilinearMap.map_update_add]
+    map_update_smul' := fun m x r v => by
       haveI : DecidableEq ι2 := inferInstance
       haveI := Classical.decEq ι1
-      simp only [elimPureTensor_update_right, MultilinearMap.map_smul]}
-  map_add' p x v1 v2 := by
+      simp only [elimPureTensor_update_right, MultilinearMap.map_update_smul]}
+  map_update_add' p x v1 v2 := by
     haveI : DecidableEq ι1 := inferInstance
     haveI := Classical.decEq ι2
     apply MultilinearMap.ext
     intro y
     simp
-  map_smul' p x r v := by
+  map_update_smul' p x r v := by
     haveI : DecidableEq ι1 := inferInstance
     haveI := Classical.decEq ι2
     apply MultilinearMap.ext

HepLean/Mathematics/SO3/Basic.lean

@@ -26,7 +26,10 @@ instance SO3Group : Group SO3 where
     by
       simp only [det_mul, A.2.1, B.2.1, mul_one],
     by
-      simp only [transpose_mul, ← Matrix.mul_assoc, Matrix.mul_assoc, B.2.2, mul_one, A.2.2]⟩
+      simp only [transpose_mul, ← Matrix.mul_assoc, Matrix.mul_assoc, B.2.2, mul_one, A.2.2]
+      trans A.1 * ((B.1 * (B.1)ᵀ) * (A.1)ᵀ)
+      · noncomm_ring
+      · simp [Matrix.mul_assoc, B.2.2, mul_one, A.2.2]⟩
   mul_assoc A B C := Subtype.eq (Matrix.mul_assoc A.1 B.1 C.1)
   one := ⟨1, det_one, by rw [transpose_one, mul_one]⟩
   one_mul A := Subtype.eq (Matrix.one_mul A.1)
@@ -81,16 +84,18 @@ lemma toProd_continuous : Continuous toProd :=
     Continuous.comp' (MulOpposite.continuous_op)
       (Continuous.matrix_transpose (continuous_iff_le_induced.mpr fun _ a ↦ a))⟩
 
+open Topology
+
 /-- The embedding of `SO(3)` into the monoid of matrices times the opposite of
   the monoid of matrices. -/
 lemma toProd_embedding : IsEmbedding toProd where
-  inj := toProd_injective
+  injective := toProd_injective
   eq_induced := (isInducing_iff ⇑toProd).mp (IsInducing.of_comp toProd_continuous
     continuous_fst ((isInducing_iff (Prod.fst ∘ ⇑toProd)).mpr rfl))
 
 /-- The embedding of `SO(3)` into `GL (Fin 3) ℝ`. -/
 lemma toGL_embedding : IsEmbedding toGL.toFun where
-  inj := toGL_injective
+  injective := toGL_injective
   eq_induced := by
     refine ((fun {X} {t t'} => TopologicalSpace.ext_iff.mpr) ?_).symm
     intro s

HepLean/Meta/TransverseTactics.lean

@@ -70,7 +70,7 @@ def traverseForest (file : FilePath)
   let t := steps.map fun (env, infoState) ↦
     (infoState.trees.toList.map fun t ↦
       (Lean.Elab.InfoTree.foldInfo (visitInfo file env visitTacticInfo) [] t).reverse)
-  t.join.join
+  t.flatten.flatten
 
 end transverseTactics
 

HepLean/StandardModel/HiggsBoson/Basic.lean

@@ -53,8 +53,8 @@ def toFin2ℂ : HiggsVec →L[ℝ] (Fin 2 → ℂ) where
   map_smul' a x := rfl
 
 /-- The map `toFin2ℂ` is smooth. -/
-lemma smooth_toFin2ℂ : Smooth 𝓘(ℝ, HiggsVec) 𝓘(ℝ, Fin 2 → ℂ) toFin2ℂ :=
-  ContinuousLinearMap.smooth toFin2ℂ
+lemma smooth_toFin2ℂ : ContMDiff 𝓘(ℝ, HiggsVec) 𝓘(ℝ, Fin 2 → ℂ) ⊤ toFin2ℂ :=
+  ContinuousLinearMap.contMDiff toFin2ℂ
 
 /-- An orthonormal basis of `HiggsVec`. -/
 def orthonormBasis : OrthonormalBasis (Fin 2) ℂ HiggsVec :=
@@ -92,7 +92,7 @@ instance : SmoothVectorBundle HiggsVec HiggsBundle SpaceTime.asSmoothManifold :=
   Bundle.Trivial.smoothVectorBundle HiggsVec
 
 /-- A Higgs field is a smooth section of the Higgs bundle. -/
-abbrev HiggsField : Type := SmoothSection SpaceTime.asSmoothManifold HiggsVec HiggsBundle
+abbrev HiggsField : Type := ContMDiffSection SpaceTime.asSmoothManifold HiggsVec ⊤ HiggsBundle
 
 /-- Given a vector in `HiggsVec` the constant Higgs field with value equal to that
 section. -/
@@ -101,7 +101,7 @@ def HiggsVec.toField (φ : HiggsVec) : HiggsField where
   contMDiff_toFun := by
     intro x
     rw [Bundle.contMDiffAt_section]
-    exact smoothAt_const
+    exact contMDiffAt_const
 
 /-- For all spacetime points, the constant Higgs field defined by a Higgs vector,
   returns that Higgs Vector. -/
@@ -120,7 +120,8 @@ open HiggsVec
 /-- Given a `HiggsField`, the corresponding map from `SpaceTime` to `HiggsVec`. -/
 def toHiggsVec (φ : HiggsField) : SpaceTime → HiggsVec := φ
 
-lemma toHiggsVec_smooth (φ : HiggsField) : Smooth 𝓘(ℝ, SpaceTime) 𝓘(ℝ, HiggsVec) φ.toHiggsVec := by
+lemma toHiggsVec_smooth (φ : HiggsField) :
+    ContMDiff 𝓘(ℝ, SpaceTime) 𝓘(ℝ, HiggsVec) ⊤ φ.toHiggsVec := by
   intro x0
   have h1 := φ.contMDiff x0
   rw [Bundle.contMDiffAt_section] at h1
@@ -138,20 +139,20 @@ lemma toFin2ℂ_comp_toHiggsVec (φ : HiggsField) :
 
 -/
 
-lemma toVec_smooth (φ : HiggsField) : Smooth 𝓘(ℝ, SpaceTime) 𝓘(ℝ, Fin 2 → ℂ) φ :=
+lemma toVec_smooth (φ : HiggsField) : ContMDiff 𝓘(ℝ, SpaceTime) 𝓘(ℝ, Fin 2 → ℂ) ⊤ φ :=
   smooth_toFin2ℂ.comp φ.toHiggsVec_smooth
 
 lemma apply_smooth (φ : HiggsField) :
-    ∀ i, Smooth 𝓘(ℝ, SpaceTime) 𝓘(ℝ, ℂ) (fun (x : SpaceTime) => (φ x i)) :=
-  (smooth_pi_space).mp (φ.toVec_smooth)
+    ∀ i, ContMDiff 𝓘(ℝ, SpaceTime) 𝓘(ℝ, ℂ) ⊤ (fun (x : SpaceTime) => (φ x i)) :=
+  (contMDiff_pi_space).mp (φ.toVec_smooth)
 
 lemma apply_re_smooth (φ : HiggsField) (i : Fin 2) :
-    Smooth 𝓘(ℝ, SpaceTime) 𝓘(ℝ, ℝ) (reCLM ∘ (fun (x : SpaceTime) => (φ x i))) :=
-  (ContinuousLinearMap.smooth reCLM).comp (φ.apply_smooth i)
+    ContMDiff 𝓘(ℝ, SpaceTime) 𝓘(ℝ, ℝ) ⊤ (reCLM ∘ (fun (x : SpaceTime) => (φ x i))) :=
+  (ContinuousLinearMap.contMDiff reCLM).comp (φ.apply_smooth i)
 
 lemma apply_im_smooth (φ : HiggsField) (i : Fin 2) :
-    Smooth 𝓘(ℝ, SpaceTime) 𝓘(ℝ, ℝ) (imCLM ∘ (fun (x : SpaceTime) => (φ x i))) :=
-  (ContinuousLinearMap.smooth imCLM).comp (φ.apply_smooth i)
+    ContMDiff 𝓘(ℝ, SpaceTime) 𝓘(ℝ, ℝ) ⊤ (imCLM ∘ (fun (x : SpaceTime) => (φ x i))) :=
+  (ContinuousLinearMap.contMDiff imCLM).comp (φ.apply_smooth i)
 
 /-!
 

HepLean/StandardModel/HiggsBoson/GaugeAction.lean

@@ -124,14 +124,21 @@ lemma rotateMatrix_unitary {φ : HiggsVec} (hφ : φ ≠ 0) :
   erw [mul_fin_two, one_fin_two]
   have : (‖φ‖ : ℂ) ≠ 0 := ofReal_inj.mp.mt (norm_ne_zero_iff.mpr hφ)
   ext i j
-  fin_cases i <;> fin_cases j <;> field_simp
-  <;> rw [← ofReal_mul, ← sq, ← @real_inner_self_eq_norm_sq]
-  · simp [PiLp.inner_apply, Complex.inner, neg_mul, sub_neg_eq_add,
+  fin_cases i <;> fin_cases j
+  · field_simp
+    rw [← ofReal_mul, ← sq, ← @real_inner_self_eq_norm_sq]
+    simp [PiLp.inner_apply, Complex.inner, neg_mul, sub_neg_eq_add,
       Fin.sum_univ_two, ofReal_add, ofReal_mul, mul_conj, mul_comm, add_comm]
-  · ring_nf
-  · ring_nf
-  · simp [PiLp.inner_apply, Complex.inner, neg_mul, sub_neg_eq_add,
-      Fin.sum_univ_two, ofReal_add, ofReal_mul, mul_conj, mul_comm]
+  · simp only [Fin.isValue, Fin.zero_eta, Fin.mk_one, of_apply, cons_val', cons_val_one, head_cons,
+    empty_val', cons_val_fin_one, cons_val_zero]
+    ring_nf
+  · simp only [Fin.isValue, Fin.mk_one, Fin.zero_eta, of_apply, cons_val', cons_val_zero,
+    empty_val', cons_val_fin_one, cons_val_one, head_fin_const]
+    ring_nf
+  · field_simp
+    rw [← ofReal_mul, ← sq, ← @real_inner_self_eq_norm_sq]
+    simp only [Fin.isValue, mul_comm, mul_conj, PiLp.inner_apply, Complex.inner, ofReal_re,
+    Fin.sum_univ_two, ofReal_add]
 
 /-- The `rotateMatrix` for a non-zero Higgs vector is special unitary. -/
 lemma rotateMatrix_specialUnitary {φ : HiggsVec} (hφ : φ ≠ 0) :

HepLean/StandardModel/HiggsBoson/PointwiseInnerProd.lean

@@ -91,9 +91,9 @@ lemma innerProd_expand (φ1 φ2 : HiggsField) :
     RCLike.im_to_complex, I_sq, mul_neg, mul_one, neg_mul, sub_neg_eq_add, one_mul]
   ring
 
-lemma smooth_innerProd (φ1 φ2 : HiggsField) : Smooth 𝓘(ℝ, SpaceTime) 𝓘(ℝ, ℂ) ⟪φ1, φ2⟫_H := by
+lemma smooth_innerProd (φ1 φ2 : HiggsField) : ContMDiff 𝓘(ℝ, SpaceTime) 𝓘(ℝ, ℂ) ⊤ ⟪φ1, φ2⟫_H := by
   rw [innerProd_expand]
-  exact (ContinuousLinearMap.smooth (equivRealProdCLM.symm : ℝ × ℝ →L[ℝ] ℂ)).comp $
+  exact (ContinuousLinearMap.contMDiff (equivRealProdCLM.symm : ℝ × ℝ →L[ℝ] ℂ)).comp $
     (((((φ1.apply_re_smooth 0).smul (φ2.apply_re_smooth 0)).add
     ((φ1.apply_re_smooth 1).smul (φ2.apply_re_smooth 1))).add
     ((φ1.apply_im_smooth 0).smul (φ2.apply_im_smooth 0))).add
@@ -171,9 +171,9 @@ lemma normSq_zero (φ : HiggsField) (x : SpaceTime) : φ.normSq x = 0 ↔ φ x =
   simp [normSq, ne_eq, OfNat.ofNat_ne_zero, not_false_eq_true, pow_eq_zero_iff, norm_eq_zero]
 
 /-- The norm squared of the Higgs field is a smooth function on space-time. -/
-lemma normSq_smooth (φ : HiggsField) : Smooth 𝓘(ℝ, SpaceTime) 𝓘(ℝ, ℝ) φ.normSq := by
+lemma normSq_smooth (φ : HiggsField) : ContMDiff 𝓘(ℝ, SpaceTime) 𝓘(ℝ, ℝ) ⊤ φ.normSq := by
   rw [normSq_expand]
-  refine Smooth.add ?_ ?_
+  refine ContMDiff.add ?_ ?_
   · simp only [mul_re, conj_re, conj_im, neg_mul, sub_neg_eq_add]
     exact ((φ.apply_re_smooth 0).smul (φ.apply_re_smooth 0)).add $
       (φ.apply_im_smooth 0).smul (φ.apply_im_smooth 0)

HepLean/StandardModel/HiggsBoson/Potential.lean

@@ -50,10 +50,10 @@ def toFun (φ : HiggsField) (x : SpaceTime) : ℝ :=
 
 /-- The potential is smooth. -/
 lemma toFun_smooth (φ : HiggsField) :
-    Smooth 𝓘(ℝ, SpaceTime) 𝓘(ℝ, ℝ) (fun x => P.toFun φ x) := by
+    ContMDiff 𝓘(ℝ, SpaceTime) 𝓘(ℝ, ℝ) ⊤ (fun x => P.toFun φ x) := by
   simp only [toFun, normSq, neg_mul]
-  exact (smooth_const.smul φ.normSq_smooth).neg.add
-    ((smooth_const.smul φ.normSq_smooth).smul φ.normSq_smooth)
+  exact (contMDiff_const.smul φ.normSq_smooth).neg.add
+    ((contMDiff_const.smul φ.normSq_smooth).smul φ.normSq_smooth)
 
 /-- The Higgs potential formed by negating the mass squared and the quartic coupling. -/
 def neg : Potential where