consider g being Element of FuncsC X, C1, C2 being Element of CSp X such that
A2: l = [[C1,C2],g] and
( union C2 = {} implies union C1 = {} ) and
g is Function of (union C1),(union C2) and
for x, y being set st {x,y} in C1 holds
{(g . x),(g . y)} in C2 by Th18;
( [C1,C2] = [[C1,C2],g] `1 & [C1,C2] `2 = C2 ) ;
hence (l `1) `2 is Element of CSp X by A2; :: thesis: verum