consider U being Subset of (P *) such that
A1: U = (Polish-expression-hierarchy (P,A)) . n and
(Polish-expression-hierarchy (P,A)) . (n + 1) = Polish-expression-layer (P,A,U) by Def9;
thus (Polish-expression-hierarchy (P,A)) . n is Subset of (P *) by A1; :: thesis: verum