Preservation of a restrained oracle computation ($B\upharpoonright u=B_s\upharpoonright u⟹{\Phi }_e^B(x)={\Phi }_e^{B_s}(x)$)

An oracle computation queries only finitely many positions. If the oracle remains unchanged below its use, the same computation has the same output. In a finite-injury priority construction, a successful requirement imposes this bound on lower priorities; the induction that higher priorities stop acting then makes the disagreement permanent.