chore: Bump to lean v.4.12.0

HepLean/SpaceTime/LorentzAlgebra/Basic.lean

@@ -31,7 +31,8 @@ open minkowskiMatrix
 lemma transpose_eta (A : lorentzAlgebra) : A.1ᵀ * η = - η * A.1 := by
   have h1 := A.2
   erw [mem_skewAdjointMatricesLieSubalgebra] at h1
-  simpa [LieAlgebra.Orthogonal.so', IsSkewAdjoint, IsAdjointPair] using h1
+  simpa only [neg_mul, mem_skewAdjointMatricesSubmodule, IsSkewAdjoint, IsAdjointPair,
+    mul_neg] using h1
 
 lemma mem_of_transpose_eta_eq_eta_mul_self {A : Matrix (Fin 1 ⊕ Fin 3) (Fin 1 ⊕ Fin 3) ℝ}
     (h : Aᵀ * η = - η * A) : A ∈ lorentzAlgebra := by
@@ -96,8 +97,7 @@ instance lorentzVectorAsLieRingModule : LieRingModule lorentzAlgebra (LorentzVec
 
 @[simps!]
 instance spaceTimeAsLieModule : LieModule ℝ lorentzAlgebra (LorentzVector 3) where
-  smul_lie r Λ x := by
-    simp [Bracket.bracket, smul_mulVec_assoc]
+  smul_lie r Λ x := smul_mulVec_assoc r Λ.1 x
   lie_smul r Λ x := by
     simp only [Bracket.bracket]
     rw [mulVec_smul]

HepLean/SpaceTime/LorentzGroup/Boosts.lean

@@ -98,7 +98,7 @@ lemma toMatrix_apply (u v : FuturePointing d) (μ ν : Fin 1 ⊕ Fin d) :
     LinearMap.id_apply, LinearMap.coe_mk, AddHom.coe_mk, basis_left, map_smul, smul_eq_mul, map_neg,
     mul_eq_mul_left_iff]
   ring_nf
-  exact (true_or_iff (η μ μ = 0)).mpr trivial
+  exact (true_or (η μ μ = 0)).mpr trivial
 
 open minkowskiMatrix LorentzVector in
 lemma toMatrix_continuous (u : FuturePointing d) : Continuous (toMatrix u) := by

HepLean/SpaceTime/LorentzVector/AsSelfAdjointMatrix.lean

@@ -98,20 +98,36 @@ noncomputable def toSelfAdjointMatrix :
     · rw [show (x + y) (Sum.inl 0) = x (Sum.inl 0) + y (Sum.inl 0) from rfl]
       rw [show (x + y) (Sum.inr 2) = x (Sum.inr 2) + y (Sum.inr 2) from rfl]
       simp only [Fin.isValue, ofReal_add, Fin.zero_eta, cons_val_zero]
+      simp only [Fin.isValue, toSelfAdjointMatrix', toMatrix, LorentzVector.time,
+        LorentzVector.space, Function.comp_apply, AddMemClass.mk_add_mk, of_add_of, add_cons,
+        head_cons, tail_cons, empty_add_empty, of_apply, cons_val', cons_val_zero, empty_val',
+        cons_val_fin_one]
       ring
     · rw [show (x + y) (Sum.inr 0) = x (Sum.inr 0) + y (Sum.inr 0) from rfl]
       rw [show (x + y) (Sum.inr 1) = x (Sum.inr 1) + y (Sum.inr 1) from rfl]
       simp only [Fin.isValue, ofReal_add, Fin.mk_one, cons_val_one, head_cons, Fin.zero_eta,
         cons_val_zero]
+      simp only [Fin.isValue, toSelfAdjointMatrix', toMatrix, LorentzVector.time,
+        LorentzVector.space, Function.comp_apply, AddMemClass.mk_add_mk, of_add_of, add_cons,
+        head_cons, tail_cons, empty_add_empty, of_apply, cons_val', cons_val_one, empty_val',
+        cons_val_fin_one, cons_val_zero]
       ring
     · rw [show (x + y) (Sum.inr 0) = x (Sum.inr 0) + y (Sum.inr 0) from rfl]
       rw [show (x + y) (Sum.inr 1) = x (Sum.inr 1) + y (Sum.inr 1) from rfl]
       simp only [Fin.isValue, ofReal_add, Fin.zero_eta, cons_val_zero, Fin.mk_one, cons_val_one,
         head_fin_const]
+      simp only [Fin.isValue, toSelfAdjointMatrix', toMatrix, LorentzVector.time,
+        LorentzVector.space, Function.comp_apply, AddMemClass.mk_add_mk, of_add_of, add_cons,
+        head_cons, tail_cons, empty_add_empty, of_apply, cons_val', cons_val_zero, empty_val',
+        cons_val_fin_one, cons_val_one, head_fin_const]
       ring
     · rw [show (x + y) (Sum.inl 0) = x (Sum.inl 0) + y (Sum.inl 0) from rfl]
       rw [show (x + y) (Sum.inr 2) = x (Sum.inr 2) + y (Sum.inr 2) from rfl]
       simp only [Fin.isValue, ofReal_add, Fin.mk_one, cons_val_one, head_cons, head_fin_const]
+      simp only [Fin.isValue, toSelfAdjointMatrix', toMatrix, LorentzVector.time,
+        LorentzVector.space, Function.comp_apply, AddMemClass.mk_add_mk, of_add_of, add_cons,
+        head_cons, tail_cons, empty_add_empty, of_apply, cons_val', cons_val_one, empty_val',
+        cons_val_fin_one, head_fin_const]
       ring
   map_smul' r x := by
     ext i j : 2

HepLean/SpaceTime/LorentzVector/Basic.lean

@@ -97,7 +97,8 @@ noncomputable abbrev timeVec : (LorentzVector d) := e (Sum.inl 0)
 
 lemma timeVec_space : (@timeVec d).space = 0 := by
   funext i
-  simp only [space, Function.comp_apply, stdBasis_apply, Fin.isValue, ↓reduceIte, PiLp.zero_apply]
+  simp only [space, Function.comp_apply, stdBasis_apply, Fin.isValue, reduceCtorEq, ↓reduceIte,
+    PiLp.zero_apply]
 
 lemma timeVec_time: (@timeVec d).time = 1 := by
   simp only [time, Fin.isValue, stdBasis_apply, ↓reduceIte]

HepLean/SpaceTime/LorentzVector/NormOne.lean

@@ -156,6 +156,7 @@ lemma one_add_metric_non_zero : 1 + ⟪f, f'.1.1⟫ₘ ≠ 0 := by
 
 section
 variable {v w : NormOneLorentzVector d}
+open InnerProductSpace
 
 lemma metric_reflect_mem_mem (h : v ∈ FuturePointing d) (hw : w ∈ FuturePointing d) :
     0 ≤ ⟪v.1, w.1.spaceReflection⟫ₘ := by

HepLean/SpaceTime/MinkowskiMetric.lean

@@ -17,7 +17,7 @@ of Lorentz vectors in d dimensions.
 -/
 
 open Matrix
-
+open InnerProductSpace
 /-!
 
 # The definition of the Minkowski Matrix

HepLean/SpaceTime/SL2C/Basic.lean

@@ -63,6 +63,7 @@ def toLinearMapSelfAdjointMatrix (M : SL(2, ℂ)) :
         conjTranspose_mul, conjTranspose_conjTranspose,
         (star_eq_conjTranspose A.1).symm.trans $ selfAdjoint.mem_iff.mp A.2]⟩
   map_add' A B := by
+    simp only [AddSubgroup.coe_add, AddMemClass.mk_add_mk, Subtype.mk.injEq]
     noncomm_ring [AddSubmonoid.coe_add, AddSubgroup.coe_toAddSubmonoid, AddSubmonoid.mk_add_mk,
       Subtype.mk.injEq]
   map_smul' r A := by