explain parity and ^^^

ITP/triple-orientations.tex

@@ -128,13 +128,18 @@
 structure σEquiv (S T : Set Point) where
   f : Point → Point
   bij : Set.BijOn f S T
-  parity : Bool -- See Section 4 for details on this field
+  parity : Bool
   σ_eq : ∀ (p ∈ S) (q ∈ S) (r ∈ S), σ p q r = parity ^^^ σ (f p) (f q) (f r)
 
 def OrientationProperty (P : Set Point → Prop) :=
   ∀ {{S T}}, S ≃σ T → P S → P T -- `≃σ` is infix notation for `σEquiv`
 \end{lstlisting}
 
+Our notion of \(\sigma\) equivalence allows for all orientations to be flipped.
+The \lstinline{^^^} (xor) operation does nothing when \lstinline{parity} is false,
+and negates the orientation when \lstinline{parity} is true.
+See~\Cref{sec:symmetry-breaking} for more details.
+
 To illustrate how these notions will be used, let us consider the property
 \(
   \pi_k(S) \triangleq \text{\em ``pointset } S \text{ contains an empty convex } k\text{-gon''}