reactor: Rename anPart and crPart
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jstoobysmith
parent
d25eab1754
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f7e669910c
9 changed files with 252 additions and 241 deletions
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@ -95,163 +95,163 @@ lemma superCommuteF_ofStateList_ofState (φs : List 𝓕.States) (φ : 𝓕.Stat
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rw [← ofStateList_singleton, superCommuteF_ofStateList_ofStatesList, ofStateList_singleton]
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simp
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lemma superCommuteF_anPart_crPart (φ φ' : 𝓕.States) :
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[anPart φ, crPart φ']ₛca =
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anPart φ * crPart φ' -
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𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') • crPart φ' * anPart φ := by
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lemma superCommuteF_anPartF_crPartF (φ φ' : 𝓕.States) :
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[anPartF φ, crPartF φ']ₛca =
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anPartF φ * crPartF φ' -
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𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') • crPartF φ' * anPartF φ := by
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match φ, φ' with
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| States.inAsymp φ, _ =>
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simp
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| _, States.outAsymp φ =>
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simp only [crPart_posAsymp, map_zero, mul_zero, instCommGroup.eq_1, smul_zero, zero_mul,
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simp only [crPartF_posAsymp, map_zero, mul_zero, instCommGroup.eq_1, smul_zero, zero_mul,
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sub_self]
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| States.position φ, States.position φ' =>
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simp only [anPart_position, crPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [anPartF_position, crPartF_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofCrAnList]
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simp [crAnStatistics, ← ofCrAnList_append]
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| States.outAsymp φ, States.position φ' =>
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simp only [anPart_posAsymp, crPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [anPartF_posAsymp, crPartF_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofCrAnList]
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simp [crAnStatistics, ← ofCrAnList_append]
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| States.position φ, States.inAsymp φ' =>
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simp only [anPart_position, crPart_negAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [anPartF_position, crPartF_negAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofCrAnList]
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simp only [List.singleton_append, instCommGroup.eq_1, crAnStatistics,
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FieldStatistic.ofList_singleton, Function.comp_apply, crAnStatesToStates_prod, ←
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ofCrAnList_append]
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| States.outAsymp φ, States.inAsymp φ' =>
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simp only [anPart_posAsymp, crPart_negAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [anPartF_posAsymp, crPartF_negAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofCrAnList]
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simp [crAnStatistics, ← ofCrAnList_append]
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lemma superCommuteF_crPart_anPart (φ φ' : 𝓕.States) :
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[crPart φ, anPart φ']ₛca =
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crPart φ * anPart φ' -
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lemma superCommuteF_crPartF_anPartF (φ φ' : 𝓕.States) :
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[crPartF φ, anPartF φ']ₛca =
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crPartF φ * anPartF φ' -
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𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') •
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anPart φ' * crPart φ := by
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anPartF φ' * crPartF φ := by
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match φ, φ' with
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| States.outAsymp φ, _ =>
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simp only [crPart_posAsymp, map_zero, LinearMap.zero_apply, zero_mul, instCommGroup.eq_1,
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simp only [crPartF_posAsymp, map_zero, LinearMap.zero_apply, zero_mul, instCommGroup.eq_1,
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mul_zero, sub_self]
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| _, States.inAsymp φ =>
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simp only [anPart_negAsymp, map_zero, mul_zero, instCommGroup.eq_1, smul_zero, zero_mul,
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simp only [anPartF_negAsymp, map_zero, mul_zero, instCommGroup.eq_1, smul_zero, zero_mul,
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sub_self]
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| States.position φ, States.position φ' =>
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simp only [crPart_position, anPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [crPartF_position, anPartF_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofCrAnList]
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simp [crAnStatistics, ← ofCrAnList_append]
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| States.position φ, States.outAsymp φ' =>
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simp only [crPart_position, anPart_posAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [crPartF_position, anPartF_posAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofCrAnList]
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simp [crAnStatistics, ← ofCrAnList_append]
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| States.inAsymp φ, States.position φ' =>
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simp only [crPart_negAsymp, anPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [crPartF_negAsymp, anPartF_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofCrAnList]
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simp [crAnStatistics, ← ofCrAnList_append]
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| States.inAsymp φ, States.outAsymp φ' =>
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simp only [crPart_negAsymp, anPart_posAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [crPartF_negAsymp, anPartF_posAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofCrAnList]
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simp [crAnStatistics, ← ofCrAnList_append]
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lemma superCommuteF_crPart_crPart (φ φ' : 𝓕.States) :
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[crPart φ, crPart φ']ₛca =
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crPart φ * crPart φ' -
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lemma superCommuteF_crPartF_crPartF (φ φ' : 𝓕.States) :
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[crPartF φ, crPartF φ']ₛca =
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crPartF φ * crPartF φ' -
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𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') •
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crPart φ' * crPart φ := by
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crPartF φ' * crPartF φ := by
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match φ, φ' with
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| States.outAsymp φ, _ =>
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simp only [crPart_posAsymp, map_zero, LinearMap.zero_apply, zero_mul, instCommGroup.eq_1,
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simp only [crPartF_posAsymp, map_zero, LinearMap.zero_apply, zero_mul, instCommGroup.eq_1,
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mul_zero, sub_self]
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| _, States.outAsymp φ =>
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simp only [crPart_posAsymp, map_zero, mul_zero, instCommGroup.eq_1, smul_zero, zero_mul, sub_self]
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simp only [crPartF_posAsymp, map_zero, mul_zero, instCommGroup.eq_1, smul_zero, zero_mul, sub_self]
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| States.position φ, States.position φ' =>
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simp only [crPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [crPartF_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofCrAnList]
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simp [crAnStatistics, ← ofCrAnList_append]
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| States.position φ, States.inAsymp φ' =>
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simp only [crPart_position, crPart_negAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [crPartF_position, crPartF_negAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofCrAnList]
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simp [crAnStatistics, ← ofCrAnList_append]
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| States.inAsymp φ, States.position φ' =>
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simp only [crPart_negAsymp, crPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [crPartF_negAsymp, crPartF_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofCrAnList]
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simp [crAnStatistics, ← ofCrAnList_append]
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| States.inAsymp φ, States.inAsymp φ' =>
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simp only [crPart_negAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [crPartF_negAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofCrAnList]
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simp [crAnStatistics, ← ofCrAnList_append]
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lemma superCommuteF_anPart_anPart (φ φ' : 𝓕.States) :
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[anPart φ, anPart φ']ₛca =
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anPart φ * anPart φ' -
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lemma superCommuteF_anPartF_anPartF (φ φ' : 𝓕.States) :
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[anPartF φ, anPartF φ']ₛca =
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anPartF φ * anPartF φ' -
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𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') •
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anPart φ' * anPart φ := by
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anPartF φ' * anPartF φ := by
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match φ, φ' with
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| States.inAsymp φ, _ =>
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simp
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| _, States.inAsymp φ =>
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simp
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| States.position φ, States.position φ' =>
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simp only [anPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [anPartF_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofCrAnList]
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simp [crAnStatistics, ← ofCrAnList_append]
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| States.position φ, States.outAsymp φ' =>
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simp only [anPart_position, anPart_posAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [anPartF_position, anPartF_posAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofCrAnList]
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simp [crAnStatistics, ← ofCrAnList_append]
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| States.outAsymp φ, States.position φ' =>
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simp only [anPart_posAsymp, anPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [anPartF_posAsymp, anPartF_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofCrAnList]
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simp [crAnStatistics, ← ofCrAnList_append]
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| States.outAsymp φ, States.outAsymp φ' =>
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simp only [anPart_posAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [anPartF_posAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofCrAnList]
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simp [crAnStatistics, ← ofCrAnList_append]
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lemma superCommuteF_crPart_ofStateList (φ : 𝓕.States) (φs : List 𝓕.States) :
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[crPart φ, ofStateList φs]ₛca =
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crPart φ * ofStateList φs - 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs) • ofStateList φs *
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crPart φ := by
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lemma superCommuteF_crPartF_ofStateList (φ : 𝓕.States) (φs : List 𝓕.States) :
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[crPartF φ, ofStateList φs]ₛca =
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crPartF φ * ofStateList φs - 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs) • ofStateList φs *
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crPartF φ := by
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match φ with
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| States.inAsymp φ =>
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simp only [crPart_negAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [crPartF_negAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofStatesList]
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simp [crAnStatistics]
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| States.position φ =>
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simp only [crPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [crPartF_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofStatesList]
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simp [crAnStatistics]
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| States.outAsymp φ =>
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simp
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lemma superCommuteF_anPart_ofStateList (φ : 𝓕.States) (φs : List 𝓕.States) :
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[anPart φ, ofStateList φs]ₛca =
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anPart φ * ofStateList φs - 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs) •
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ofStateList φs * anPart φ := by
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lemma superCommuteF_anPartF_ofStateList (φ : 𝓕.States) (φs : List 𝓕.States) :
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[anPartF φ, ofStateList φs]ₛca =
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anPartF φ * ofStateList φs - 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs) •
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ofStateList φs * anPartF φ := by
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match φ with
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| States.inAsymp φ =>
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simp
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| States.position φ =>
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simp only [anPart_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [anPartF_position, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofStatesList]
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simp [crAnStatistics]
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| States.outAsymp φ =>
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simp only [anPart_posAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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simp only [anPartF_posAsymp, instCommGroup.eq_1, Algebra.smul_mul_assoc]
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rw [← ofCrAnList_singleton, superCommuteF_ofCrAnList_ofStatesList]
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simp [crAnStatistics]
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lemma superCommuteF_crPart_ofState (φ φ' : 𝓕.States) :
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[crPart φ, ofState φ']ₛca =
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crPart φ * ofState φ' -
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𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') • ofState φ' * crPart φ := by
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rw [← ofStateList_singleton, superCommuteF_crPart_ofStateList]
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lemma superCommuteF_crPartF_ofState (φ φ' : 𝓕.States) :
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[crPartF φ, ofState φ']ₛca =
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crPartF φ * ofState φ' -
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𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') • ofState φ' * crPartF φ := by
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rw [← ofStateList_singleton, superCommuteF_crPartF_ofStateList]
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simp
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lemma superCommuteF_anPart_ofState (φ φ' : 𝓕.States) :
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[anPart φ, ofState φ']ₛca =
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anPart φ * ofState φ' -
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𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') • ofState φ' * anPart φ := by
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rw [← ofStateList_singleton, superCommuteF_anPart_ofStateList]
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lemma superCommuteF_anPartF_ofState (φ φ' : 𝓕.States) :
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[anPartF φ, ofState φ']ₛca =
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anPartF φ * ofState φ' -
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𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') • ofState φ' * anPartF φ := by
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rw [← ofStateList_singleton, superCommuteF_anPartF_ofStateList]
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simp
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/-!
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@ -292,32 +292,32 @@ lemma ofStateList_mul_ofState_eq_superCommuteF (φs : List 𝓕.States) (φ :
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rw [superCommuteF_ofStateList_ofState]
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simp
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lemma crPart_mul_anPart_eq_superCommuteF (φ φ' : 𝓕.States) :
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crPart φ * anPart φ' =
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𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') • anPart φ' * crPart φ +
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[crPart φ, anPart φ']ₛca := by
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rw [superCommuteF_crPart_anPart]
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lemma crPartF_mul_anPartF_eq_superCommuteF (φ φ' : 𝓕.States) :
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crPartF φ * anPartF φ' =
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𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') • anPartF φ' * crPartF φ +
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[crPartF φ, anPartF φ']ₛca := by
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rw [superCommuteF_crPartF_anPartF]
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simp
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lemma anPart_mul_crPart_eq_superCommuteF (φ φ' : 𝓕.States) :
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anPart φ * crPart φ' =
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lemma anPartF_mul_crPartF_eq_superCommuteF (φ φ' : 𝓕.States) :
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anPartF φ * crPartF φ' =
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𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') •
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crPart φ' * anPart φ +
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[anPart φ, crPart φ']ₛca := by
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rw [superCommuteF_anPart_crPart]
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crPartF φ' * anPartF φ +
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[anPartF φ, crPartF φ']ₛca := by
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rw [superCommuteF_anPartF_crPartF]
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simp
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lemma crPart_mul_crPart_eq_superCommuteF (φ φ' : 𝓕.States) :
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crPart φ * crPart φ' =
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𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') • crPart φ' * crPart φ +
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[crPart φ, crPart φ']ₛca := by
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rw [superCommuteF_crPart_crPart]
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lemma crPartF_mul_crPartF_eq_superCommuteF (φ φ' : 𝓕.States) :
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crPartF φ * crPartF φ' =
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𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') • crPartF φ' * crPartF φ +
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[crPartF φ, crPartF φ']ₛca := by
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rw [superCommuteF_crPartF_crPartF]
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simp
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lemma anPart_mul_anPart_eq_superCommuteF (φ φ' : 𝓕.States) :
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anPart φ * anPart φ' = 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') • anPart φ' * anPart φ +
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[anPart φ, anPart φ']ₛca := by
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rw [superCommuteF_anPart_anPart]
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lemma anPartF_mul_anPartF_eq_superCommuteF (φ φ' : 𝓕.States) :
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anPartF φ * anPartF φ' = 𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φ') • anPartF φ' * anPartF φ +
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[anPartF φ, anPartF φ']ₛca := by
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rw [superCommuteF_anPartF_anPartF]
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simp
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lemma ofCrAnList_mul_ofStateList_eq_superCommuteF (φs : List 𝓕.CrAnStates) (φs' : List 𝓕.States) :
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