deffunc H_{1}( 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 = H_{1}(n)
from FUNCT_2:sch 4();

take IT ; :: thesis: for n being Nat holds IT . n = M . (FSets . n)

consider IT being sequence of ExtREAL such that

A1: for n being Element of NAT holds IT . n = H

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;n in NAT by ORDINAL1:def 12;

hence IT . n = M . (FSets . n) by A1; :: thesis: verum