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reactor: Removal of double spaces

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jstoobysmith 2024-07-12 11:23:02 -04:00
parent ce92e1d649
commit 13f62a50eb
64 changed files with 550 additions and 546 deletions
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16
HepLean/SpaceTime/LorentzTensor/Basic.lean
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@ -47,7 +47,7 @@ instance (d : ℕ) (μ : RealLorentzTensor.Colors) : Fintype (RealLorentzTensor.
| RealLorentzTensor.Colors.down => instFintypeSum (Fin 1) (Fin d)
/-- An `IndexValue` is a set of actual values an index can take. e.g. for a
3-tensor (0, 1, 2). -/
3-tensor (0, 1, 2). -/
@[simp]
def RealLorentzTensor.IndexValue {X : FintypeCat} (d : ℕ ) (c : X → RealLorentzTensor.Colors) :
Type 0 := (x : X) → RealLorentzTensor.ColorsIndex d (c x)
@ -107,9 +107,9 @@ def congrColorsDual {μ ν : Colors} (h : μ = τ ν) :
ColorsIndex d μ ≃ ColorsIndex d ν :=
(castColorsIndex h).trans dualColorsIndex.symm
lemma congrColorsDual_symm {μ ν : Colors} (h : μ = τ ν) :
lemma congrColorsDual_symm {μ ν : Colors} (h : μ = τ ν) :
(congrColorsDual h).symm =
@congrColorsDual d _ _ ((Function.Involutive.eq_iff τ_involutive).mp h.symm) := by
@congrColorsDual d _ _ ((Function.Involutive.eq_iff τ_involutive).mp h.symm) := by
match μ, ν with
| Colors.up, Colors.down => rfl
| Colors.down, Colors.up => rfl
@ -124,7 +124,7 @@ lemma color_eq_dual_symm {μ ν : Colors} (h : μ = τ ν) : ν = τ μ :=
-/
/-- An equivalence of Index values from an equality of color maps. -/
def castIndexValue {X : FintypeCat} {T S : X → Colors} (h : T = S) :
def castIndexValue {X : FintypeCat} {T S : X → Colors} (h : T = S) :
IndexValue d T ≃ IndexValue d S where
toFun i := (fun μ => castColorsIndex (congrFun h μ) (i μ))
invFun i := (fun μ => (castColorsIndex (congrFun h μ)).symm (i μ))
@ -133,7 +133,7 @@ def castIndexValue {X : FintypeCat} {T S : X → Colors} (h : T = S) :
right_inv i := by
simp
lemma indexValue_eq {T₁ T₂ : X → RealLorentzTensor.Colors} (d : ℕ) (h : T₁ = T₂) :
lemma indexValue_eq {T₁ T₂ : X → RealLorentzTensor.Colors} (d : ℕ) (h : T₁ = T₂) :
IndexValue d T₁ = IndexValue d T₂ :=
pi_congr fun a => congrArg (ColorsIndex d) (congrFun h a)
@ -176,7 +176,7 @@ lemma ext' {T₁ T₂ : RealLorentzTensor d X} (h : T₁.color = T₂.color)
/-- An equivalence between `X → Fin 1 ⊕ Fin d` and `Y → Fin 1 ⊕ Fin d` given an isomorphism
between `X` and `Y`. -/
def congrSetIndexValue (d : ℕ) (f : X ≃ Y) (i : X → Colors) :
IndexValue d i ≃ IndexValue d (i ∘ f.symm) :=
IndexValue d i ≃ IndexValue d (i ∘ f.symm) :=
Equiv.piCongrLeft' _ f
/-- Given an equivalence of indexing sets, a map on Lorentz tensors. -/
@ -259,7 +259,7 @@ def inrIndexValue {Tc : X → Colors} {Sc : Y → Colors}
def sumCommIndexValue {X Y : FintypeCat} (Tc : X → Colors) (Sc : Y → Colors) :
IndexValue d (sumElimIndexColor Tc Sc) ≃ IndexValue d (sumElimIndexColor Sc Tc) :=
(congrSetIndexValue d (sumCommFintypeCat X Y) (sumElimIndexColor Tc Sc)).trans
(castIndexValue ((sumElimIndexColor_symm Sc Tc).symm))
(castIndexValue ((sumElimIndexColor_symm Sc Tc).symm))
lemma sumCommIndexValue_inlIndexValue {X Y : FintypeCat} {Tc : X → Colors} {Sc : Y → Colors}
(i : IndexValue d (sumElimIndexColor Tc Sc)) :
@ -300,7 +300,7 @@ def unmarkedColor (T : Marked d X n) : X → Colors :=
T.color ∘ Sum.inl
/-- The colors of marked indices. -/
def markedColor (T : Marked d X n) : FintypeCat.of (Σ _ : Fin n, PUnit) → Colors :=
def markedColor (T : Marked d X n) : FintypeCat.of (Σ _ : Fin n, PUnit) → Colors :=
T.color ∘ Sum.inr
/-- The index values restricted to unmarked indices. -/