refactor: Rename ofCrAnFieldOp to ofCrAnOp
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7 changed files with 165 additions and 165 deletions
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@ -435,9 +435,9 @@ lemma timeOrder_eq_maxTimeField_mul_finset (φ : 𝓕.FieldOp) (φs : List 𝓕.
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lemma timeOrder_superCommute_eq_time_mid {φ ψ : 𝓕.CrAnFieldOp}
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(hφψ : crAnTimeOrderRel φ ψ) (hψφ : crAnTimeOrderRel ψ φ) (a b : 𝓕.FieldOpAlgebra) :
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𝓣(a * [ofCrAnFieldOp φ, ofCrAnFieldOp ψ]ₛ * b) =
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[ofCrAnFieldOp φ, ofCrAnFieldOp ψ]ₛ * 𝓣(a * b) := by
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rw [ofCrAnFieldOp, ofCrAnFieldOp]
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𝓣(a * [ofCrAnOp φ, ofCrAnOp ψ]ₛ * b) =
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[ofCrAnOp φ, ofCrAnOp ψ]ₛ * 𝓣(a * b) := by
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rw [ofCrAnOp, ofCrAnOp]
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rw [superCommute_eq_ι_superCommuteF]
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obtain ⟨a, rfl⟩ := ι_surjective a
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obtain ⟨b, rfl⟩ := ι_surjective b
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@ -449,17 +449,17 @@ lemma timeOrder_superCommute_eq_time_mid {φ ψ : 𝓕.CrAnFieldOp}
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lemma timeOrder_superCommute_eq_time_left {φ ψ : 𝓕.CrAnFieldOp}
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(hφψ : crAnTimeOrderRel φ ψ) (hψφ : crAnTimeOrderRel ψ φ) (b : 𝓕.FieldOpAlgebra) :
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𝓣([ofCrAnFieldOp φ, ofCrAnFieldOp ψ]ₛ * b) =
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[ofCrAnFieldOp φ, ofCrAnFieldOp ψ]ₛ * 𝓣(b) := by
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trans 𝓣(1 * [ofCrAnFieldOp φ, ofCrAnFieldOp ψ]ₛ * b)
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𝓣([ofCrAnOp φ, ofCrAnOp ψ]ₛ * b) =
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[ofCrAnOp φ, ofCrAnOp ψ]ₛ * 𝓣(b) := by
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trans 𝓣(1 * [ofCrAnOp φ, ofCrAnOp ψ]ₛ * b)
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simp only [one_mul]
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rw [timeOrder_superCommute_eq_time_mid hφψ hψφ]
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simp
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lemma timeOrder_superCommute_neq_time {φ ψ : 𝓕.CrAnFieldOp}
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(hφψ : ¬ (crAnTimeOrderRel φ ψ ∧ crAnTimeOrderRel ψ φ)) :
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𝓣([ofCrAnFieldOp φ, ofCrAnFieldOp ψ]ₛ) = 0 := by
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rw [ofCrAnFieldOp, ofCrAnFieldOp]
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𝓣([ofCrAnOp φ, ofCrAnOp ψ]ₛ) = 0 := by
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rw [ofCrAnOp, ofCrAnOp]
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rw [superCommute_eq_ι_superCommuteF]
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rw [timeOrder_eq_ι_timeOrderF]
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trans ι (timeOrderF (1 * (superCommuteF (ofCrAnOpF φ)) (ofCrAnOpF ψ) * 1))
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