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feat: More results regarding index notation.

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This commit is contained in:
jstoobysmith 2024-08-06 08:10:47 -04:00
parent a36afa9212
commit cef7e574ca
12 changed files with 424 additions and 32 deletions
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24
HepLean/SpaceTime/LorentzTensor/IndexNotation/Basic.lean
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@ -107,6 +107,8 @@ instance : Decidable (listCharIndex X l) :=
e.g. `ᵘ¹²` or `ᵤ₄₃` etc. -/
def Index : Type := {s : String // listCharIndex X s.toList ∧ s.toList ≠ []}
instance : DecidableEq (Index X) := Subtype.instDecidableEq
namespace Index
variable {X : Type} [IndexNotation X] [Fintype X] [DecidableEq X]
@ -295,19 +297,19 @@ instance : DecidableEq l.contrSubtype :=
/-- Given a `i : l.contrSubtype` the proposition on a `j` in `Fin s.length` for
it to be an index of `s` contracting with `i`. -/
def getDualProp (i : l.contrSubtype) (j : Fin l.length) : Prop :=
i.1 ≠ j ∧ l.idMap i.1 = l.idMap j
def getDualProp (i j : Fin l.length) : Prop :=
i ≠ j ∧ l.idMap i = l.idMap j
instance (i : l.contrSubtype) (j : Fin l.length) :
instance (i j : Fin l.length) :
Decidable (l.getDualProp i j) :=
instDecidableAnd
/-- Given a `i : l.contrSubtype` the index of `s` contracting with `i`. -/
def getDualFin (i : l.contrSubtype) : Fin l.length :=
(Fin.find (l.getDualProp i)).get (by simpa [NoContr, Fin.isSome_find_iff] using i.prop)
(Fin.find (l.getDualProp i.1)).get (by simpa [NoContr, Fin.isSome_find_iff] using i.prop)
lemma some_getDualFin_eq_find (i : l.contrSubtype) :
Fin.find (l.getDualProp i) = some (l.getDualFin i) := by
Fin.find (l.getDualProp i.1) = some (l.getDualFin i) := by
simp [getDualFin]
lemma getDualFin_not_NoContr (i : l.contrSubtype) : ¬ l.NoContr (l.getDualFin i) := by
@ -333,6 +335,13 @@ lemma getDual_neq_self (i : l.contrSubtype) : i ≠ l.getDual i := by
rw [Fin.find_eq_some_iff] at h1
exact ne_of_apply_ne Subtype.val h1.1.1
lemma getDual_getDualProp (i : l.contrSubtype) : l.getDualProp i.1 (l.getDual i).1 := by
simp [getDual]
have h1 := l.some_getDualFin_eq_find i
rw [Fin.find_eq_some_iff] at h1
simp only [getDualProp, ne_eq, and_imp] at h1
exact h1.1
/-!
## Index lists with no contracting indices
@ -444,6 +453,11 @@ lemma getDual_not_lt_self_mem_contrPairSet {i : l.contrSubtype}
simp only
exact l.getDual_id i
/-- The list of elements of `l` which contract together. -/
def contrPairList : List (Fin l.length × Fin l.length) :=
(List.product (Fin.list l.length) (Fin.list l.length)).filterMap fun (i, j) => if
l.getDualProp i j then some (i, j) else none
end IndexList
end IndexNotation