deffunc H₁( Nat) -> set = (S . $1) - x;
consider S being Real_Sequence such that
A1: for n being Nat holds S . n = H₁(n) from SEQ_1:sch 1();
take S ; :: thesis: for n being Nat holds S . n = (S . n) - x
let n be Nat; :: thesis: S . n = (S . n) - x
thus S . n = (S . n) - x by A1; :: thesis: verum