refactor: Rename States to FieldOps
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jstoobysmith
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171e80fc04
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8f41de5785
36 changed files with 946 additions and 946 deletions
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@ -27,7 +27,7 @@ open FieldStatistic
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-/
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lemma stat_ofFinset_eq_one_of_gradingCompliant (φs : List 𝓕.States)
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lemma stat_ofFinset_eq_one_of_gradingCompliant (φs : List 𝓕.FieldOp)
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(a : Finset (Fin φs.length)) (φsΛ : WickContraction φs.length) (hg : GradingCompliant φs φsΛ)
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(hnon : ∀ i, φsΛ.getDual? i = none → i ∉ a)
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(hsom : ∀ i, (h : (φsΛ.getDual? i).isSome) → i ∈ a → (φsΛ.getDual? i).get h ∈ a) :
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@ -64,7 +64,7 @@ lemma stat_ofFinset_eq_one_of_gradingCompliant (φs : List 𝓕.States)
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rfl
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lemma signFinset_insertAndContract_some (φ : 𝓕.States) (φs : List 𝓕.States)
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lemma signFinset_insertAndContract_some (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
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(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (i1 i2 : Fin φs.length)
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(j : φsΛ.uncontracted) :
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(φsΛ ↩Λ φ i (some j)).signFinset (finCongr (insertIdx_length_fin φ φs i).symm
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@ -206,7 +206,7 @@ lemma signFinset_insertAndContract_some (φ : 𝓕.States) (φs : List 𝓕.Stat
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inserting `φ` into `φs` at position `i` and contracting it with `j : c.uncontracted`
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coming from contractions other then the `i` and `j` contraction but which
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are effected by this new contraction. -/
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def signInsertSomeProd (φ : 𝓕.States) (φs : List 𝓕.States) (φsΛ : WickContraction φs.length)
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def signInsertSomeProd (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp) (φsΛ : WickContraction φs.length)
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(i : Fin φs.length.succ) (j : φsΛ.uncontracted) : ℂ :=
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∏ (a : φsΛ.1),
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if i.succAbove (φsΛ.fstFieldOfContract a) < i ∧ i < i.succAbove (φsΛ.sndFieldOfContract a) ∧
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@ -223,7 +223,7 @@ def signInsertSomeProd (φ : 𝓕.States) (φs : List 𝓕.States) (φsΛ : Wick
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and an `i : Fin φs.length.succ`, the change in sign of the contraction associated with
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inserting `φ` into `φs` at position `i` and contracting it with `j : c.uncontracted`
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coming from putting `i` next to `j`. -/
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def signInsertSomeCoef (φ : 𝓕.States) (φs : List 𝓕.States) (φsΛ : WickContraction φs.length)
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def signInsertSomeCoef (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp) (φsΛ : WickContraction φs.length)
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(i : Fin φs.length.succ) (j : φsΛ.uncontracted) : ℂ :=
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let a : (φsΛ ↩Λ φ i (some j)).1 := congrLift (insertIdx_length_fin φ φs i).symm
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⟨{i, i.succAbove j}, by simp [insertAndContractNat]⟩;
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@ -235,11 +235,11 @@ def signInsertSomeCoef (φ : 𝓕.States) (φs : List 𝓕.States) (φsΛ : Wick
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/-- Given a Wick contraction `φsΛ` associated with a list of states `φs`
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and an `i : Fin φs.length.succ`, the change in sign of the contraction associated with
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inserting `φ` into `φs` at position `i` and contracting it with `j : c.uncontracted`. -/
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def signInsertSome (φ : 𝓕.States) (φs : List 𝓕.States) (φsΛ : WickContraction φs.length)
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def signInsertSome (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp) (φsΛ : WickContraction φs.length)
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(i : Fin φs.length.succ) (j : φsΛ.uncontracted) : ℂ :=
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signInsertSomeCoef φ φs φsΛ i j * signInsertSomeProd φ φs φsΛ i j
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lemma sign_insert_some (φ : 𝓕.States) (φs : List 𝓕.States) (φsΛ : WickContraction φs.length)
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lemma sign_insert_some (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp) (φsΛ : WickContraction φs.length)
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(i : Fin φs.length.succ) (j : φsΛ.uncontracted) :
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(φsΛ ↩Λ φ i (some j)).sign = (φsΛ.signInsertSome φ φs i j) * φsΛ.sign := by
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rw [sign]
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@ -280,7 +280,7 @@ lemma sign_insert_some (φ : 𝓕.States) (φs : List 𝓕.States) (φsΛ : Wick
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rw [stat_ofFinset_of_insertAndContractLiftFinset]
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simp_all
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lemma signInsertSomeProd_eq_one_if (φ : 𝓕.States) (φs : List 𝓕.States)
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lemma signInsertSomeProd_eq_one_if (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
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(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (j : φsΛ.uncontracted)
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(hφj : (𝓕 |>ₛ φ) = (𝓕 |>ₛ φs[j.1])) :
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φsΛ.signInsertSomeProd φ φs i j =
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@ -313,7 +313,7 @@ lemma signInsertSomeProd_eq_one_if (φ : 𝓕.States) (φs : List 𝓕.States)
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implies_true, and_true]
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omega
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lemma signInsertSomeProd_eq_prod_prod (φ : 𝓕.States) (φs : List 𝓕.States)
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lemma signInsertSomeProd_eq_prod_prod (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
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(φsΛ : WickContraction φs.length)
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(i : Fin φs.length.succ) (j : φsΛ.uncontracted) (hφj : (𝓕 |>ₛ φ) = (𝓕 |>ₛ φs[j.1]))
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(hg : GradingCompliant φs φsΛ) :
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@ -347,7 +347,7 @@ lemma signInsertSomeProd_eq_prod_prod (φ : 𝓕.States) (φs : List 𝓕.States
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· omega
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simp [hφj]
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lemma signInsertSomeProd_eq_prod_fin (φ : 𝓕.States) (φs : List 𝓕.States)
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lemma signInsertSomeProd_eq_prod_fin (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
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(φsΛ : WickContraction φs.length)
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(i : Fin φs.length.succ) (j : φsΛ.uncontracted) (hφj : (𝓕 |>ₛ φ) = (𝓕 |>ₛ φs[j.1]))
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(hg : GradingCompliant φs φsΛ) :
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@ -380,7 +380,7 @@ lemma signInsertSomeProd_eq_prod_fin (φ : 𝓕.States) (φs : List 𝓕.States)
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simp only [hφj, Fin.getElem_fin]
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exact hg
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lemma signInsertSomeProd_eq_list (φ : 𝓕.States) (φs : List 𝓕.States)
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lemma signInsertSomeProd_eq_list (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
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(φsΛ : WickContraction φs.length)
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(i : Fin φs.length.succ) (j : φsΛ.uncontracted) (hφj : (𝓕 |>ₛ φ) = (𝓕 |>ₛ φs[j.1]))
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(hg : GradingCompliant φs φsΛ) :
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@ -414,7 +414,7 @@ lemma signInsertSomeProd_eq_list (φ : 𝓕.States) (φs : List 𝓕.States)
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simp only [hφj, Fin.getElem_fin]
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exact hg
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lemma signInsertSomeProd_eq_finset (φ : 𝓕.States) (φs : List 𝓕.States)
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lemma signInsertSomeProd_eq_finset (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
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(φsΛ : WickContraction φs.length)
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(i : Fin φs.length.succ) (j : φsΛ.uncontracted) (hφj : (𝓕 |>ₛ φ) = (𝓕 |>ₛ φs[j.1]))
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(hg : GradingCompliant φs φsΛ) :
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@ -442,7 +442,7 @@ lemma signInsertSomeProd_eq_finset (φ : 𝓕.States) (φs : List 𝓕.States)
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simp only [hφj, Fin.getElem_fin]
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exact hg
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lemma signInsertSomeCoef_if (φ : 𝓕.States) (φs : List 𝓕.States) (φsΛ : WickContraction φs.length)
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lemma signInsertSomeCoef_if (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp) (φsΛ : WickContraction φs.length)
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(i : Fin φs.length.succ) (j : φsΛ.uncontracted) (hφj : (𝓕 |>ₛ φ) = (𝓕 |>ₛ φs[j.1])) :
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φsΛ.signInsertSomeCoef φ φs i j =
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if i < i.succAbove j then
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@ -462,7 +462,7 @@ lemma signInsertSomeCoef_if (φ : 𝓕.States) (φs : List 𝓕.States) (φsΛ :
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· simp [hφj]
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lemma stat_signFinset_insert_some_self_fst
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(φ : 𝓕.States) (φs : List 𝓕.States) (φsΛ : WickContraction φs.length)
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(φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp) (φsΛ : WickContraction φs.length)
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(i : Fin φs.length.succ) (j : φsΛ.uncontracted) :
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(𝓕 |>ₛ ⟨(φs.insertIdx i φ).get,
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(signFinset (φsΛ ↩Λ φ i (some j)) (finCongr (insertIdx_length_fin φ φs i).symm i)
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@ -538,7 +538,7 @@ lemma stat_signFinset_insert_some_self_fst
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have hy2 := hy2 h
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simpa [Option.get_map] using hy2
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lemma stat_signFinset_insert_some_self_snd (φ : 𝓕.States) (φs : List 𝓕.States)
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lemma stat_signFinset_insert_some_self_snd (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
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(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (j : φsΛ.uncontracted) :
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(𝓕 |>ₛ ⟨(φs.insertIdx i φ).get,
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(signFinset (φsΛ ↩Λ φ i (some j))
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@ -618,7 +618,7 @@ lemma stat_signFinset_insert_some_self_snd (φ : 𝓕.States) (φs : List 𝓕.S
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simp only [Option.get_map, Function.comp_apply, Fin.coe_cast, Fin.val_fin_lt]
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exact Fin.succAbove_lt_succAbove_iff.mpr hy2
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lemma signInsertSomeCoef_eq_finset (φ : 𝓕.States) (φs : List 𝓕.States)
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lemma signInsertSomeCoef_eq_finset (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
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(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (j : φsΛ.uncontracted)
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(hφj : (𝓕 |>ₛ φ) = (𝓕 |>ₛ φs[j.1])) : φsΛ.signInsertSomeCoef φ φs i j =
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if i < i.succAbove j then
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@ -637,7 +637,7 @@ lemma signInsertSomeCoef_eq_finset (φ : 𝓕.States) (φs : List 𝓕.States)
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contracting it with `k` (`k < i`) is equal
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to the sign got by moving `φ` through each field `φ₀…φᵢ₋₁`
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multiplied by the sign got moving `φ` through each uncontracted field `φ₀…φₖ`. -/
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lemma signInsertSome_mul_filter_contracted_of_lt (φ : 𝓕.States) (φs : List 𝓕.States)
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lemma signInsertSome_mul_filter_contracted_of_lt (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
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(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (k : φsΛ.uncontracted)
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(hk : i.succAbove k < i) (hg : GradingCompliant φs φsΛ ∧ (𝓕 |>ₛ φ) = 𝓕 |>ₛ φs[k.1]) :
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signInsertSome φ φs φsΛ i k *
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@ -744,7 +744,7 @@ lemma signInsertSome_mul_filter_contracted_of_lt (φ : 𝓕.States) (φs : List
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contracting it with `k` (`i < k`) is equal
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to the sign got by moving `φ` through each field `φ₀…φᵢ₋₁`
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multiplied by the sign got moving `φ` through each uncontracted field `φ₀…φₖ₋₁`. -/
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lemma signInsertSome_mul_filter_contracted_of_not_lt (φ : 𝓕.States) (φs : List 𝓕.States)
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lemma signInsertSome_mul_filter_contracted_of_not_lt (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
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(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (k : φsΛ.uncontracted)
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(hk : ¬ i.succAbove k < i) (hg : GradingCompliant φs φsΛ ∧ (𝓕 |>ₛ φ) = 𝓕 |>ₛ φs[k.1]) :
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signInsertSome φ φs φsΛ i k *
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