deffunc H_{1}( Nat) -> Element of the carrier of X = (S . $1) * a;

consider S being sequence of X such that

A4: for n being Element of NAT holds S . n = H_{1}(n)
from FUNCT_2:sch 4();

take S ; :: thesis: for n being Nat holds S . n = (S . n) * a

let n be Nat; :: thesis: S . n = (S . n) * a

n in NAT by ORDINAL1:def 12;

hence S . n = (S . n) * a by A4; :: thesis: verum

consider S being sequence of X such that

A4: for n being Element of NAT holds S . n = H

take S ; :: thesis: for n being Nat holds S . n = (S . n) * a

let n be Nat; :: thesis: S . n = (S . n) * a

n in NAT by ORDINAL1:def 12;

hence S . n = (S . n) * a by A4; :: thesis: verum