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refactor: Lint

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jstoobysmith 2024-11-29 06:38:52 +00:00
parent 7ed5676db1
commit 1257327854
3 changed files with 14 additions and 16 deletions
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2
HepLean/FeynmanDiagrams/Wick/Algebra.lean
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@ -19,7 +19,7 @@ We will formally define the operator ring, in terms of the fields present in the
- https://physics.stackexchange.com/questions/258718/ and links therein
- Ryan Thorngren (https://physics.stackexchange.com/users/10336/ryan-thorngren), Fermions,
different species and (anti-)commutation rules, URL (version: 2019-02-20):
different species and (anti-)commutation rules, URL (version: 2019-02-20) :
https://physics.stackexchange.com/q/461929
-/

13
HepLean/FeynmanDiagrams/Wick/Contract.lean
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@ -25,8 +25,7 @@ open PreFeynmanRule
/-- A Wick contraction for a Wick string is a series of pairs `i` and `j` of indices
to be contracted, subject to ordering and subject to the condition that they can
be contracted. -/
inductive WickContract :
{ni : ℕ} → {i : Fin ni → 𝓔} → {n : ℕ} → {c : Fin n → 𝓔} →
inductive WickContract : {ni : ℕ} → {i : Fin ni → 𝓔} → {n : ℕ} → {c : Fin n → 𝓔} →
{no : ℕ} → {o : Fin no → 𝓔} →
(str : WickString i c o final) →
{k : ℕ} → (b1 : Fin k → Fin n) → (b2 : Fin k → Fin n) → Type where
@ -43,7 +42,7 @@ inductive WickContract :
namespace WickContract
/-- The number of nodes of a Wick contraction. -/
def size {ni : ℕ} {i : Fin ni → 𝓔} {n : ℕ} {c : Fin n → 𝓔}
def size {ni : ℕ} {i : Fin ni → 𝓔} {n : ℕ} {c : Fin n → 𝓔}
{no : ℕ} {o : Fin no → 𝓔} {str : WickString i c o final} {k : ℕ} {b1 b2 : Fin k → Fin n} :
WickContract str b1 b2 → ℕ := fun
| string => 0
@ -236,7 +235,7 @@ lemma boundFst_neq_boundSnd {ni : ℕ} {i : Fin ni → 𝓔} {n : ℕ} {c : Fin
proof that `b1 = b1'` and `b2 = b2'`, and that they are defined from the same `k = k'`. -/
def castMaps {ni : ℕ} {i : Fin ni → 𝓔} {n : ℕ} {c : Fin n → 𝓔}
{no : ℕ} {o : Fin no → 𝓔} {str : WickString i c o final}
{k k' : ℕ} {b1 b2 : Fin k → Fin n} {b1' b2' : Fin k' → Fin n}
{k k' : ℕ} {b1 b2 : Fin k → Fin n} {b1' b2' : Fin k' → Fin n}
(hk : k = k')
(hb1 : b1 = b1' ∘ Fin.cast hk) (hb2 : b2 = b2' ∘ Fin.cast hk) (w : WickContract str b1 b2) :
WickContract str b1' b2' :=
@ -303,7 +302,7 @@ lemma mem_snoc {ni : ℕ} {i : Fin ni → 𝓔} {n : ℕ} {c : Fin n → 𝓔}
lemma is_subsingleton {ni : ℕ} {i : Fin ni → 𝓔} {n : ℕ} {c : Fin n → 𝓔}
{no : ℕ} {o : Fin no → 𝓔} {str : WickString i c o final}
{k : ℕ} {b1 b2 : Fin k → Fin n} :
{k : ℕ} {b1 b2 : Fin k → Fin n} :
Subsingleton (WickContract str b1 b2) := Subsingleton.intro fun w1 w2 => by
induction k with
| zero =>
@ -364,7 +363,7 @@ def fromMaps {ni : ℕ} {i : Fin ni → 𝓔} {n : ℕ} {c : Fin n → 𝓔}
`k` contractions by dropping the last contraction (defined by the first index contracted). -/
def dropLast {ni : ℕ} {i : Fin ni → 𝓔} {n : ℕ} {c : Fin n → 𝓔}
{no : ℕ} {o : Fin no → 𝓔} {str : WickString i c o final}
{k : ℕ} {b1 b2 : Fin k.succ → Fin n}
{k : ℕ} {b1 b2 : Fin k.succ → Fin n}
(w : WickContract str b1 b2) : WickContract str (b1 ∘ Fin.castSucc) (b2 ∘ Fin.castSucc) :=
fromMaps (b1 ∘ Fin.castSucc) (b2 ∘ Fin.castSucc)
(fun i => color_boundSnd_eq_dual_boundFst w i.castSucc)
@ -375,7 +374,7 @@ def dropLast {ni : ℕ} {i : Fin ni → 𝓔} {n : ℕ} {c : Fin n → 𝓔}
lemma eq_from_maps {ni : ℕ} {i : Fin ni → 𝓔} {n : ℕ} {c : Fin n → 𝓔}
{no : ℕ} {o : Fin no → 𝓔} {str : WickString i c o final}
{k : ℕ} {b1 b2 : Fin k → Fin n}
{k : ℕ} {b1 b2 : Fin k → Fin n}
(w : WickContract str b1 b2) :
w = fromMaps w.boundFst w.boundSnd w.color_boundSnd_eq_dual_boundFst
w.boundFst_lt_boundSnd w.boundFst_strictMono w.boundFst_neq_boundSnd

15
HepLean/FeynmanDiagrams/Wick/String.lean
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@ -104,26 +104,26 @@ inductive WickString : {ni : ℕ} → (i : Fin ni → 𝓔) → {n : ℕ} → (c
{no : ℕ} → (o : Fin no → 𝓔) → WickStringLast → Type where
| empty : WickString Fin.elim0 Fin.elim0 Fin.elim0 incoming
| incoming {n ni no : ℕ} {i : Fin ni → 𝓔} {c : Fin n → 𝓔}
{o : Fin no → 𝓔} (w : WickString i c o incoming) (e : 𝓔) :
{o : Fin no → 𝓔} (w : WickString i c o incoming) (e : 𝓔) :
WickString (Fin.cons e i) (Fin.cons e c) o incoming
| endIncoming {n ni no : ℕ} {i : Fin ni → 𝓔} {c : Fin n → 𝓔}
{o : Fin no → 𝓔} (w : WickString i c o incoming) : WickString i c o vertex
{o : Fin no → 𝓔} (w : WickString i c o incoming) : WickString i c o vertex
| vertex {n ni no : ℕ} {i : Fin ni → 𝓔} {c : Fin n → 𝓔}
{o : Fin no → 𝓔} (w : WickString i c o vertex) (v : 𝓥) :
{o : Fin no → 𝓔} (w : WickString i c o vertex) (v : 𝓥) :
WickString i (Fin.append (𝓥Edges v) c) o vertex
| endVertex {n ni no : ℕ} {i : Fin ni → 𝓔} {c : Fin n → 𝓔}
{o : Fin no → 𝓔} (w : WickString i c o vertex) : WickString i c o outgoing
{o : Fin no → 𝓔} (w : WickString i c o vertex) : WickString i c o outgoing
| outgoing {n ni no : ℕ} {i : Fin ni → 𝓔} {c : Fin n → 𝓔}
{o : Fin no → 𝓔} (w : WickString i c o outgoing) (e : 𝓔) :
{o : Fin no → 𝓔} (w : WickString i c o outgoing) (e : 𝓔) :
WickString i (Fin.cons e c) (Fin.cons e o) outgoing
| endOutgoing {n ni no : ℕ} {i : Fin ni → 𝓔} {c : Fin n → 𝓔}
{o : Fin no → 𝓔} (w : WickString i c o outgoing) : WickString i c o final
{o : Fin no → 𝓔} (w : WickString i c o outgoing) : WickString i c o final
namespace WickString
/-- The number of nodes in a Wick string. This is used to help prove termination. -/
def size {ni : ℕ} {i : Fin ni → 𝓔} {n : ℕ} {c : Fin n → 𝓔} {no : ℕ} {o : Fin no → 𝓔}
{f : WickStringLast} : WickString i c o f → ℕ := fun
{f : WickStringLast} : WickString i c o f → ℕ := fun
| empty => 0
| incoming w e => size w + 1
| endIncoming w => size w + 1
@ -154,7 +154,6 @@ def vertices {ni : ℕ} {i : Fin ni → 𝓔} {n : ℕ} {c : Fin n → 𝓔} {no
| outgoing w e => vertices w
| endOutgoing w => vertices w
end WickString
end TwoComplexScalar