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refactor: LInt

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jstoobysmith 2024-11-09 18:12:05 +00:00
parent e963be5ef8
commit d058f41689
11 changed files with 38 additions and 50 deletions
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28
HepLean/Lorentz/Group/Boosts.lean
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@ -39,7 +39,7 @@ def genBoostAux₁ (u v : FuturePointing d) : ContrMod d →ₗ[ℝ] ContrMod d
map_add' x y := by
simp [map_add, LinearMap.add_apply, tmul_add, add_tmul, mul_add, add_smul]
map_smul' c x := by
simp only [ Action.instMonoidalCategory_tensorObj_V,
simp only [Action.instMonoidalCategory_tensorObj_V,
Action.instMonoidalCategory_tensorUnit_V, CategoryTheory.Equivalence.symm_inverse,
Action.functorCategoryEquivalence_functor, Action.FunctorCategoryEquivalence.functor_obj_obj,
smul_tmul, tmul_smul, map_smul, smul_eq_mul, RingHom.id_apply]
@ -74,7 +74,7 @@ lemma genBoostAux₂_self (u : FuturePointing d) : genBoostAux₂ u u = - genBoo
congr 1
rw [u.1.2]
conv => lhs; lhs; rhs; rhs; change 1
rw [show 1 + (1 : ℝ) = (2 : ℝ ) by ring]
rw [show 1 + (1 : ℝ) = (2 : ℝ) by ring]
simp only [isUnit_iff_ne_zero, ne_eq, OfNat.ofNat_ne_zero, not_false_eq_true,
IsUnit.div_mul_cancel]
rw [← (two_smul ℝ u.val.val)]
@ -137,15 +137,15 @@ lemma toMatrix_mulVec (u v : FuturePointing d) (x : Contr d) :
open minkowskiMatrix in
@[simp]
lemma toMatrix_apply (u v : FuturePointing d) (μ ν : Fin 1 ⊕ Fin d) :
(toMatrix u v) μ ν = η μ μ * (toField d ⟪ContrMod.stdBasis μ, ContrMod.stdBasis ν⟫ₘ + 2 *
toField d ⟪ContrMod.stdBasis ν, u.val.val⟫ₘ * toField d ⟪ContrMod.stdBasis μ, v.val.val⟫ₘ
- toField d ⟪ContrMod.stdBasis μ, u.val.val + v.val.val⟫ₘ *
toField d ⟪ContrMod.stdBasis ν, u.val.val + v.val.val⟫ₘ /
(1 + toField d ⟪u.val.val, v.val.val⟫ₘ)) := by
(toMatrix u v) μ ν = η μ μ * (⟪ContrMod.stdBasis μ, ContrMod.stdBasis ν⟫ₘ + 2 *
⟪ContrMod.stdBasis ν, u.val.val⟫ₘ * ⟪ContrMod.stdBasis μ, v.val.val⟫ₘ
- ⟪ContrMod.stdBasis μ, u.val.val + v.val.val⟫ₘ *
⟪ContrMod.stdBasis ν, u.val.val + v.val.val⟫ₘ /
(1 + ⟪u.val.val, v.val.val⟫ₘ)) := by
rw [contrContrContractField.matrix_apply_stdBasis (Λ := toMatrix u v) μ ν, toMatrix_mulVec]
simp only [genBoost, genBoostAux₁, genBoostAux₂, map_add, smul_add, neg_smul, LinearMap.add_apply,
LinearMap.id_apply, LinearMap.coe_mk, AddHom.coe_mk, contrContrContractField.basis_left, map_smul, smul_eq_mul, map_neg,
mul_eq_mul_left_iff, toField_apply]
simp only [genBoost, genBoostAux₁, genBoostAux₂, smul_add, neg_smul, LinearMap.add_apply,
LinearMap.id_apply, LinearMap.coe_mk, AddHom.coe_mk, contrContrContractField.basis_left,
map_add, map_smul, map_neg, toField_apply, mul_eq_mul_left_iff]
ring_nf
simp only [Pi.add_apply, Action.instMonoidalCategory_tensorObj_V,
Action.instMonoidalCategory_tensorUnit_V, CategoryTheory.Equivalence.symm_inverse,
@ -186,9 +186,9 @@ lemma toMatrix_in_lorentzGroup (u v : FuturePointing d) : (toMatrix u v) ∈ Lor
rw [LorentzGroup.mem_iff_invariant]
intro x y
rw [toMatrix_mulVec, toMatrix_mulVec]
have h1 : (((1 + ⟪u.1.1, v.1.1⟫ₘ)) * (1 + ⟪u.1.1, v.1.1⟫ₘ)) •
(contrContrContractField ((genBoost u v) y ⊗ₜ[ℝ] (genBoost u v) x))
= (((1 + ⟪u.1.1, v.1.1⟫ₘ)) * (1 + ⟪u.1.1, v.1.1⟫ₘ)) • ⟪y, x⟫ₘ := by
have h1 : (((1 + ⟪u.1.1, v.1.1⟫ₘ)) * (1 + ⟪u.1.1, v.1.1⟫ₘ)) •
(contrContrContractField ((genBoost u v) y ⊗ₜ[ℝ] (genBoost u v) x))
= (((1 + ⟪u.1.1, v.1.1⟫ₘ)) * (1 + ⟪u.1.1, v.1.1⟫ₘ)) • ⟪y, x⟫ₘ := by
conv_lhs =>
erw [← map_smul]
rw [← smul_smul]
@ -200,7 +200,7 @@ lemma toMatrix_in_lorentzGroup (u v : FuturePointing d) : (toMatrix u v) ∈ Lor
contrContrContractField.symm u.1.1 x]
simp only [smul_eq_mul]
ring
have hn (a : ℝ ) {b c : ℝ} (h : a ≠ 0) (hab : a * b = a * c ) : b = c := by
have hn (a : ℝ) {b c : ℝ} (h : a ≠ 0) (hab : a * b = a * c) : b = c := by
simp_all only [smul_eq_mul, ne_eq, mul_eq_mul_left_iff, or_false]
refine hn _ ?_ h1
simpa using (FuturePointing.one_add_metric_non_zero u v)