deffunc H₁( 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 = H₁(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