ex f being Function st
( dom f = dom f & ( for x being object st x in dom f holds
f . x = H₁(x) ) ) from FUNCT_1:sch 3();
hence ex b₁ being Function st
( dom b₁ = dom f & ( for x being object st x in dom b₁ holds
b₁ . x = Re (f . x) ) ) ; :: thesis: verum