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