Proposition: Finite fitting is monotone under compatible enlargement

Suppose an enlarged correction class uses the same target, domain, and evaluation prescription and contains the original contacts. Then $m_S$ remains fitted, and no separator exists on this same family against the enlarged class. Its rank and complete left kernel require a new coverage argument.

Proof. The existing allowed combination still gives $m_S$. Any annihilator of the enlarged image also annihilates that combination. The enlarged image may contain additional directions, so its rank and full kernel do not follow from the old matrix.