deffunc H₁( set ) -> Element of REAL = Sum |.(seq_id $1).|;
A1: for z being set st z in the_set_of_l1ComplexSequences holds
H₁(z) in REAL ;
ex f being Function of the_set_of_l1ComplexSequences ,REAL st
for x being set st x in the_set_of_l1ComplexSequences holds
f . x = H₁(x) from FUNCT_2:sch 2(A1);
hence ex NORM being Function of the_set_of_l1ComplexSequences ,REAL st
for x being set st x in the_set_of_l1ComplexSequences holds
NORM . x = Sum |.(seq_id x).| ; :: thesis: verum