feat: More fixes

HepLean/StandardModel/HiggsBoson/Basic.lean

@@ -88,7 +88,7 @@ We also define the Higgs bundle.
 abbrev HiggsBundle := Bundle.Trivial SpaceTime HiggsVec
 
 instance : SmoothVectorBundle HiggsVec HiggsBundle SpaceTime.asSmoothManifold :=
-  Bundle.Trivial.smoothVectorBundle HiggsVec 𝓘(ℝ, SpaceTime)
+  Bundle.Trivial.smoothVectorBundle HiggsVec
 
 /-- A Higgs field is a smooth section of the Higgs bundle. -/
 abbrev HiggsField : Type := SmoothSection SpaceTime.asSmoothManifold HiggsVec HiggsBundle

HepLean/StandardModel/HiggsBoson/GaugeAction.lean

@@ -135,10 +135,10 @@ def rotateGuageGroup {φ : HiggsVec} (hφ : φ ≠ 0) : GaugeGroupI :=
     ⟨1, ⟨(rotateMatrix φ), rotateMatrix_specialUnitary hφ⟩, 1⟩
 
 lemma rotateGuageGroup_apply {φ : HiggsVec} (hφ : φ ≠ 0) :
-    rep (rotateGuageGroup hφ) φ = ![0, Complex.ofReal ‖φ‖] := by
+    rep (rotateGuageGroup hφ) φ = ![0, Complex.ofRealHom ‖φ‖] := by
   rw [rep_apply]
   simp only [rotateGuageGroup, rotateMatrix, one_pow, one_smul,
-    Nat.succ_eq_add_one, Nat.reduceAdd, ofReal_eq_coe]
+    Nat.succ_eq_add_one, Nat.reduceAdd, ofRealHom_eq_coe]
   ext i
   fin_cases i
   · simp only [mulVec, Fin.zero_eta, Fin.isValue, cons_val', empty_val', cons_val_fin_one,
@@ -181,7 +181,7 @@ theorem rotate_fst_real_snd_zero (φ : HiggsVec) :
   rw [rep.map_mul]
   change rep P (rep g φ) = _
   rw [h, rep_apply]
-  simp only [one_pow, Nat.succ_eq_add_one, Nat.reduceAdd, ofReal_eq_coe, mulVec_cons, zero_smul,
+  simp only [one_pow, Nat.succ_eq_add_one, Nat.reduceAdd, ofRealHom_eq_coe, mulVec_cons, zero_smul,
     coe_smul, mulVec_empty, add_zero, zero_add, one_smul]
   funext i
   fin_cases i

HepLean/StandardModel/HiggsBoson/PointwiseInnerProd.lean

@@ -87,8 +87,7 @@ lemma innerProd_expand (φ1 φ2 : HiggsField) :
   nth_rewrite 1 [← RCLike.re_add_im (φ2 x 0)]
   nth_rewrite 1 [← RCLike.re_add_im (φ2 x 1)]
   ring_nf
-  repeat rw [show RCLike.ofReal _ = ofReal' _ by rfl]
-  simp only [Algebra.id.map_eq_id, RCLike.re_to_complex, RingHom.id_apply, RCLike.I_to_complex,
+  simp only [Fin.isValue, RCLike.re_to_complex, coe_algebraMap, RCLike.I_to_complex,
     RCLike.im_to_complex, I_sq, mul_neg, mul_one, neg_mul, sub_neg_eq_add, one_mul]
   ring
 
@@ -144,16 +143,15 @@ lemma normSq_eq_innerProd_self (φ : HiggsField) (x : SpaceTime) :
 
 @[simp]
 lemma normSq_apply_im_zero (φ : HiggsField) (x : SpaceTime) :
-    ((Complex.ofReal' ‖φ x‖) ^ 2).im = 0 := by
+    ((Complex.ofRealHom ‖φ x‖) ^ 2).im = 0 := by
   rw [sq]
-  simp only [Complex.ofReal_eq_coe, Complex.mul_im, Complex.ofReal_re, Complex.ofReal_im,
-    mul_zero, zero_mul, add_zero]
+  simp only [ofRealHom_eq_coe, mul_im, ofReal_re, ofReal_im, mul_zero, zero_mul, add_zero]
 
 @[simp]
 lemma normSq_apply_re_self (φ : HiggsField) (x : SpaceTime) :
-    ((Complex.ofReal' ‖φ x‖) ^ 2).re = φ.normSq x := by
+    ((Complex.ofRealHom ‖φ x‖) ^ 2).re = φ.normSq x := by
   rw [sq]
-  simp only [mul_re, ofReal_re, ofReal_im, mul_zero, sub_zero, normSq]
+  simp only [ofRealHom_eq_coe, mul_re, ofReal_re, ofReal_im, mul_zero, sub_zero, normSq]
   exact Eq.symm (pow_two ‖φ x‖)
 
 lemma toHiggsVec_norm (φ : HiggsField) (x : SpaceTime) :

HepLean/StandardModel/HiggsBoson/Potential.lean

@@ -126,7 +126,7 @@ def quadDiscrim (φ : HiggsField) (x : SpaceTime) : ℝ := discrim P.𝓵 (- P.
 lemma quadDiscrim_nonneg (h : P.𝓵 ≠ 0) (φ : HiggsField) (x : SpaceTime) :
     0 ≤ P.quadDiscrim φ x := by
   have h1 := P.as_quad φ x
-  rw [quadratic_eq_zero_iff_discrim_eq_sq] at h1
+  rw [mul_assoc, quadratic_eq_zero_iff_discrim_eq_sq] at h1
   · simp only [h1, ne_eq, quadDiscrim, div_eq_zero_iff, OfNat.ofNat_ne_zero, or_false]
     exact sq_nonneg (2 * P.𝓵 * ‖φ‖_H ^ 2 x + - P.μ2)
   · exact h
@@ -148,7 +148,7 @@ lemma quadDiscrim_eq_zero_iff_normSq (h : P.𝓵 ≠ 0) (φ : HiggsField) (x : S
   rw [P.quadDiscrim_eq_zero_iff h]
   refine Iff.intro (fun hV => ?_) (fun hF => ?_)
   · have h1 := P.as_quad φ x
-    rw [quadratic_eq_zero_iff_of_discrim_eq_zero h
+    rw [mul_assoc, quadratic_eq_zero_iff_of_discrim_eq_zero h
       ((P.quadDiscrim_eq_zero_iff h φ x).mpr hV)] at h1
     simp_rw [h1, neg_neg]
   · rw [toFun, hF]
@@ -241,6 +241,7 @@ lemma neg_𝓵_sol_exists_iff (h𝓵 : P.𝓵 < 0) (c : ℝ) : (∃ φ x, P.toFu
     have hdd : discrim P.𝓵 (- P.μ2) (-c) = Real.sqrt (discrim P.𝓵 (- P.μ2) (-c))
         * Real.sqrt (discrim P.𝓵 (- P.μ2) (-c)) := by
       exact (Real.mul_self_sqrt hd).symm
+    rw [mul_assoc]
     refine (quadratic_eq_zero_iff (ne_of_gt h𝓵).symm hdd _).mpr ?_
     simp only [neg_neg, or_true, a]