deffunc H₁( Element of NAT ) -> Element of ExtREAL = M . (FSets . $1);
consider IT being sequence of ExtREAL such that
A1: for n being Element of NAT holds IT . n = H₁(n) from FUNCT_2:sch 4();
take IT ; :: thesis: for n being Nat holds IT . n = M . (FSets . n)

hereby :: thesis: verum

let n be Nat; :: thesis: IT . n = M . (FSets . n)
n in NAT by ORDINAL1:def 12;
hence IT . n = M . (FSets . n) by A1; :: thesis: verum

end;