deffunc H₁( Element of NAT ) -> Element of the carrier of RNS = (a . $1) * (S . $1);
consider S being sequence of RNS such that
A1: 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 = (a . n) * (S . n)
let n be Nat; :: thesis: S . n = (a . n) * (S . n)
n in NAT by ORDINAL1:def 12;
hence S . n = (a . n) * (S . n) by A1; :: thesis: verum