refactor: Rename States to FieldOps
This commit is contained in:
jstoobysmith
parent
171e80fc04
commit
8f41de5785
36 changed files with 946 additions and 946 deletions
|
|
@ -20,7 +20,7 @@ open FieldOpAlgebra
|
|||
|
||||
open FieldStatistic
|
||||
|
||||
lemma stat_signFinset_right {φs : List 𝓕.States} (φsΛ : WickContraction φs.length)
|
||||
lemma stat_signFinset_right {φs : List 𝓕.FieldOp} (φsΛ : WickContraction φs.length)
|
||||
(φsucΛ : WickContraction [φsΛ]ᵘᶜ.length) (i j : Fin [φsΛ]ᵘᶜ.length) :
|
||||
(𝓕 |>ₛ ⟨[φsΛ]ᵘᶜ.get, φsucΛ.signFinset i j⟩) =
|
||||
(𝓕 |>ₛ ⟨φs.get, (φsucΛ.signFinset i j).map uncontractedListEmd⟩) := by
|
||||
|
|
@ -32,7 +32,7 @@ lemma stat_signFinset_right {φs : List 𝓕.States} (φsΛ : WickContraction φ
|
|||
intro i j h
|
||||
exact uncontractedListEmd_strictMono h
|
||||
|
||||
lemma signFinset_right_map_uncontractedListEmd_eq_filter {φs : List 𝓕.States}
|
||||
lemma signFinset_right_map_uncontractedListEmd_eq_filter {φs : List 𝓕.FieldOp}
|
||||
(φsΛ : WickContraction φs.length) (φsucΛ : WickContraction [φsΛ]ᵘᶜ.length)
|
||||
(i j : Fin [φsΛ]ᵘᶜ.length) : (φsucΛ.signFinset i j).map uncontractedListEmd =
|
||||
((join φsΛ φsucΛ).signFinset (uncontractedListEmd i) (uncontractedListEmd j)).filter
|
||||
|
|
@ -90,7 +90,7 @@ lemma signFinset_right_map_uncontractedListEmd_eq_filter {φs : List 𝓕.States
|
|||
exact hl
|
||||
exact fun _ _ h => uncontractedListEmd_strictMono h
|
||||
|
||||
lemma sign_right_eq_prod_mul_prod {φs : List 𝓕.States} (φsΛ : WickContraction φs.length)
|
||||
lemma sign_right_eq_prod_mul_prod {φs : List 𝓕.FieldOp} (φsΛ : WickContraction φs.length)
|
||||
(φsucΛ : WickContraction [φsΛ]ᵘᶜ.length) :
|
||||
φsucΛ.sign = (∏ a, 𝓢(𝓕|>ₛ [φsΛ]ᵘᶜ[φsucΛ.sndFieldOfContract a], 𝓕|>ₛ ⟨φs.get,
|
||||
((join φsΛ φsucΛ).signFinset (uncontractedListEmd (φsucΛ.fstFieldOfContract a))
|
||||
|
|
@ -107,7 +107,7 @@ lemma sign_right_eq_prod_mul_prod {φs : List 𝓕.States} (φsΛ : WickContract
|
|||
rw [stat_signFinset_right, signFinset_right_map_uncontractedListEmd_eq_filter]
|
||||
rw [ofFinset_filter]
|
||||
|
||||
lemma join_singleton_signFinset_eq_filter {φs : List 𝓕.States}
|
||||
lemma join_singleton_signFinset_eq_filter {φs : List 𝓕.FieldOp}
|
||||
{i j : Fin φs.length} (h : i < j)
|
||||
(φsucΛ : WickContraction [singleton h]ᵘᶜ.length) :
|
||||
(join (singleton h) φsucΛ).signFinset i j =
|
||||
|
|
@ -149,7 +149,7 @@ lemma join_singleton_signFinset_eq_filter {φs : List 𝓕.States}
|
|||
· simp only [Bool.not_eq_true, Option.not_isSome, Option.isNone_iff_eq_none] at h2'
|
||||
simp [h2']
|
||||
|
||||
lemma join_singleton_left_signFinset_eq_filter {φs : List 𝓕.States}
|
||||
lemma join_singleton_left_signFinset_eq_filter {φs : List 𝓕.FieldOp}
|
||||
{i j : Fin φs.length} (h : i < j)
|
||||
(φsucΛ : WickContraction [singleton h]ᵘᶜ.length) :
|
||||
(𝓕 |>ₛ ⟨φs.get, (singleton h).signFinset i j⟩)
|
||||
|
|
@ -166,7 +166,7 @@ lemma join_singleton_left_signFinset_eq_filter {φs : List 𝓕.States}
|
|||
|
||||
/-- The difference in sign between `φsucΛ.sign` and the direct contribution of `φsucΛ` to
|
||||
`(join (singleton h) φsucΛ)`. -/
|
||||
def joinSignRightExtra {φs : List 𝓕.States}
|
||||
def joinSignRightExtra {φs : List 𝓕.FieldOp}
|
||||
{i j : Fin φs.length} (h : i < j)
|
||||
(φsucΛ : WickContraction [singleton h]ᵘᶜ.length) : ℂ :=
|
||||
∏ a, 𝓢(𝓕|>ₛ [singleton h]ᵘᶜ[φsucΛ.sndFieldOfContract a], 𝓕|>ₛ ⟨φs.get,
|
||||
|
|
@ -176,7 +176,7 @@ def joinSignRightExtra {φs : List 𝓕.States}
|
|||
|
||||
/-- The difference in sign between `(singleton h).sign` and the direct contribution of
|
||||
`(singleton h)` to `(join (singleton h) φsucΛ)`. -/
|
||||
def joinSignLeftExtra {φs : List 𝓕.States}
|
||||
def joinSignLeftExtra {φs : List 𝓕.FieldOp}
|
||||
{i j : Fin φs.length} (h : i < j)
|
||||
(φsucΛ : WickContraction [singleton h]ᵘᶜ.length) : ℂ :=
|
||||
𝓢(𝓕 |>ₛ φs[j], (𝓕 |>ₛ ⟨φs.get, ((singleton h).signFinset i j).filter (fun c =>
|
||||
|
|
@ -184,7 +184,7 @@ def joinSignLeftExtra {φs : List 𝓕.States}
|
|||
((h1 : ((join (singleton h) φsucΛ).getDual? c).isSome) →
|
||||
(((join (singleton h) φsucΛ).getDual? c).get h1) < i)))⟩))
|
||||
|
||||
lemma join_singleton_sign_left {φs : List 𝓕.States}
|
||||
lemma join_singleton_sign_left {φs : List 𝓕.FieldOp}
|
||||
{i j : Fin φs.length} (h : i < j)
|
||||
(φsucΛ : WickContraction [singleton h]ᵘᶜ.length) :
|
||||
(singleton h).sign = 𝓢(𝓕 |>ₛ φs[j],
|
||||
|
|
@ -194,7 +194,7 @@ lemma join_singleton_sign_left {φs : List 𝓕.States}
|
|||
rw [map_mul]
|
||||
rfl
|
||||
|
||||
lemma join_singleton_sign_right {φs : List 𝓕.States}
|
||||
lemma join_singleton_sign_right {φs : List 𝓕.FieldOp}
|
||||
{i j : Fin φs.length} (h : i < j)
|
||||
(φsucΛ : WickContraction [singleton h]ᵘᶜ.length) :
|
||||
φsucΛ.sign =
|
||||
|
|
@ -206,7 +206,7 @@ lemma join_singleton_sign_right {φs : List 𝓕.States}
|
|||
rfl
|
||||
|
||||
|
||||
lemma joinSignRightExtra_eq_i_j_finset_eq_if {φs : List 𝓕.States}
|
||||
lemma joinSignRightExtra_eq_i_j_finset_eq_if {φs : List 𝓕.FieldOp}
|
||||
{i j : Fin φs.length} (h : i < j)
|
||||
(φsucΛ : WickContraction [singleton h]ᵘᶜ.length) :
|
||||
joinSignRightExtra h φsucΛ = ∏ a,
|
||||
|
|
@ -298,7 +298,7 @@ lemma joinSignRightExtra_eq_i_j_finset_eq_if {φs : List 𝓕.States}
|
|||
Option.get_some, forall_const, false_or, true_and]
|
||||
omega
|
||||
|
||||
lemma joinSignLeftExtra_eq_joinSignRightExtra {φs : List 𝓕.States}
|
||||
lemma joinSignLeftExtra_eq_joinSignRightExtra {φs : List 𝓕.FieldOp}
|
||||
{i j : Fin φs.length} (h : i < j) (hs : (𝓕 |>ₛ φs[i]) = (𝓕 |>ₛ φs[j]))
|
||||
(φsucΛ : WickContraction [singleton h]ᵘᶜ.length) :
|
||||
joinSignLeftExtra h φsucΛ = joinSignRightExtra h φsucΛ := by
|
||||
|
|
@ -380,7 +380,7 @@ lemma joinSignLeftExtra_eq_joinSignRightExtra {φs : List 𝓕.States}
|
|||
simp only [Finset.disjoint_singleton_right, Finset.mem_singleton]
|
||||
exact Fin.ne_of_lt h
|
||||
|
||||
lemma join_sign_singleton {φs : List 𝓕.States}
|
||||
lemma join_sign_singleton {φs : List 𝓕.FieldOp}
|
||||
{i j : Fin φs.length} (h : i < j) (hs : (𝓕 |>ₛ φs[i]) = (𝓕 |>ₛ φs[j]))
|
||||
(φsucΛ : WickContraction [singleton h]ᵘᶜ.length) :
|
||||
(join (singleton h) φsucΛ).sign = (singleton h).sign * φsucΛ.sign := by
|
||||
|
|
@ -401,7 +401,7 @@ lemma join_sign_singleton {φs : List 𝓕.States}
|
|||
· funext a
|
||||
simp
|
||||
|
||||
lemma join_sign_induction {φs : List 𝓕.States} (φsΛ : WickContraction φs.length)
|
||||
lemma join_sign_induction {φs : List 𝓕.FieldOp} (φsΛ : WickContraction φs.length)
|
||||
(φsucΛ : WickContraction [φsΛ]ᵘᶜ.length) (hc : φsΛ.GradingCompliant) :
|
||||
(n : ℕ) → (hn : φsΛ.1.card = n) →
|
||||
(join φsΛ φsucΛ).sign = φsΛ.sign * φsucΛ.sign
|
||||
|
|
@ -428,12 +428,12 @@ lemma join_sign_induction {φs : List 𝓕.States} (φsΛ : WickContraction φs.
|
|||
apply sign_congr
|
||||
exact join_uncontractedListGet (singleton hij) φsucΛ'
|
||||
|
||||
lemma join_sign {φs : List 𝓕.States} (φsΛ : WickContraction φs.length)
|
||||
lemma join_sign {φs : List 𝓕.FieldOp} (φsΛ : WickContraction φs.length)
|
||||
(φsucΛ : WickContraction [φsΛ]ᵘᶜ.length) (hc : φsΛ.GradingCompliant) :
|
||||
(join φsΛ φsucΛ).sign = φsΛ.sign * φsucΛ.sign := by
|
||||
exact join_sign_induction φsΛ φsucΛ hc (φsΛ).1.card rfl
|
||||
|
||||
lemma join_sign_timeContract {φs : List 𝓕.States} (φsΛ : WickContraction φs.length)
|
||||
lemma join_sign_timeContract {φs : List 𝓕.FieldOp} (φsΛ : WickContraction φs.length)
|
||||
(φsucΛ : WickContraction [φsΛ]ᵘᶜ.length) :
|
||||
(join φsΛ φsucΛ).sign • (join φsΛ φsucΛ).timeContract.1 =
|
||||
(φsΛ.sign • φsΛ.timeContract.1) * (φsucΛ.sign • φsucΛ.timeContract.1) := by
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue