Theorem. Nested wrapper composition [ftip-00EM]
Theorem. Nested wrapper composition [ftip-00EM]
If every wrapper leaves its inner solver and earlier libraries unchanged, then induction on \(d\) gives
\[S_d=M_d\circ M_{d-1}\circ \cdots \circ M_2\circ S_1.\]Proof. The case \(d=2\) is the definition. Substituting the induction hypothesis into \(S_d=M_d(C_d,S_{d-1})\) gives the displayed composition.