Complement of a total Sigma-1 function graph ($f(\vec{x})\ne y⟺\exists z(f(\vec{x})=z\wedge z\ne y)$)

If a total single-valued numerical function has a Sigma-1 graph, the complement of that graph is also Sigma-1. An input-output pair is outside the graph exactly when some different output is in the graph. Totality and uniqueness are essential to that equivalence. Stage-comparison separation of enumerations of the graph and its complement then gives weak definability of a numerical function in a bounded-complete arithmetic first-order theory.