refactor: Rename ofCrAnFieldOp to ofCrAnOp

This commit is contained in:
jstoobysmith 2025-02-06 10:09:30 +00:00
parent 8cc273fe38
commit 2d561dd89d
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.
lemma timeOrder_superCommute_eq_time_mid {φ ψ : 𝓕.CrAnFieldOp}
(hφψ : crAnTimeOrderRel φ ψ) (hψφ : crAnTimeOrderRel ψ φ) (a b : 𝓕.FieldOpAlgebra) :
𝓣(a * [ofCrAnFieldOp φ, ofCrAnFieldOp ψ]ₛ * b) =
[ofCrAnFieldOp φ, ofCrAnFieldOp ψ]ₛ * 𝓣(a * b) := by
rw [ofCrAnFieldOp, ofCrAnFieldOp]
𝓣(a * [ofCrAnOp φ, ofCrAnOp ψ]ₛ * b) =
[ofCrAnOp φ, ofCrAnOp ψ]ₛ * 𝓣(a * b) := by
rw [ofCrAnOp, ofCrAnOp]
rw [superCommute_eq_ι_superCommuteF]
obtain ⟨a, rfl⟩ := ι_surjective a
obtain ⟨b, rfl⟩ := ι_surjective b
@ -449,17 +449,17 @@ lemma timeOrder_superCommute_eq_time_mid {φ ψ : 𝓕.CrAnFieldOp}
lemma timeOrder_superCommute_eq_time_left {φ ψ : 𝓕.CrAnFieldOp}
(hφψ : crAnTimeOrderRel φ ψ) (hψφ : crAnTimeOrderRel ψ φ) (b : 𝓕.FieldOpAlgebra) :
𝓣([ofCrAnFieldOp φ, ofCrAnFieldOp ψ]ₛ * b) =
[ofCrAnFieldOp φ, ofCrAnFieldOp ψ]ₛ * 𝓣(b) := by
trans 𝓣(1 * [ofCrAnFieldOp φ, ofCrAnFieldOp ψ]ₛ * b)
𝓣([ofCrAnOp φ, ofCrAnOp ψ]ₛ * b) =
[ofCrAnOp φ, ofCrAnOp ψ]ₛ * 𝓣(b) := by
trans 𝓣(1 * [ofCrAnOp φ, ofCrAnOp ψ]ₛ * b)
simp only [one_mul]
rw [timeOrder_superCommute_eq_time_mid hφψ hψφ]
simp
lemma timeOrder_superCommute_neq_time {φ ψ : 𝓕.CrAnFieldOp}
(hφψ : ¬ (crAnTimeOrderRel φ ψ ∧ crAnTimeOrderRel ψ φ)) :
𝓣([ofCrAnFieldOp φ, ofCrAnFieldOp ψ]ₛ) = 0 := by
rw [ofCrAnFieldOp, ofCrAnFieldOp]
𝓣([ofCrAnOp φ, ofCrAnOp ψ]ₛ) = 0 := by
rw [ofCrAnOp, ofCrAnOp]
rw [superCommute_eq_ι_superCommuteF]
rw [timeOrder_eq_ι_timeOrderF]
trans ι (timeOrderF (1 * (superCommuteF (ofCrAnOpF φ)) (ofCrAnOpF ψ) * 1))