chore: Bump to 4.14.0

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