feat: Join of Wick contractions

HepLean/PerturbationTheory/WickContraction/Sign.lean

@@ -324,6 +324,16 @@ def sign (φs : List 𝓕.States) (φsΛ : WickContraction φs.length) : ℂ :=
   ∏ (a : φsΛ.1), 𝓢(𝓕 |>ₛ φs[φsΛ.sndFieldOfContract a],
     𝓕 |>ₛ ⟨φs.get, φsΛ.signFinset (φsΛ.fstFieldOfContract a) (φsΛ.sndFieldOfContract a)⟩)
 
+lemma sign_empty (φs : List 𝓕.States) :
+    sign φs empty = 1 := by
+  rw [sign]
+  simp [empty]
+
+lemma sign_congr {φs φs' : List 𝓕.States} (h : φs = φs') (φsΛ : WickContraction φs.length) :
+    sign φs' (congr (by simp [h]) φsΛ) = sign φs φsΛ := by
+  subst h
+  rfl
+
 /-!
 
 ## Sign insert