Flipping a coordinate on the exact original-language body

The fresh exposed marker is inserted before the selected old marker. Deleting the old marker and swapping its label with the fresh last label gives the required final order. Thus no canonical boundary is asserted for the enlarged intermediate gadget. Hiding the last label puts that old coordinate before the two unchanged auxiliary blocks.

noncomputable def Cslib.Complexity.CSP.OrderedBoundary.GadgetWitness.flip {Rel : Type} {arity : Rel → ℕ} {sem : Rel → List Bool → Bool} {n : ℕ} {R : Set (Fin n → Bool)} {g : Logic.PL.CSP.PPGadget arity sem R} (w : GadgetWitness g) (j : Fin n) {d : Logic.PL.CSP.PPGadget arity sem Logic.PL.CSP.RelationMinor.disequality} (v : GadgetWitness d) : GadgetWitness (g.flip j d)

The exact existing flip interpreter has an actual ordered numerical witness. Its noncanonical enlarged boundary is used directly before hiding the old selected marker.