deffunc H₂( Nat) -> Element of NAT = H₁(m,$1);
consider f being Function of NAT,NAT such that
A1: for x being Element of NAT holds f . x = H₂(x) from FUNCT_2:sch 4();
take f ; :: thesis: for n being Nat holds f . n = Ackermann (m,n)
let n be Nat; :: thesis: f . n = Ackermann (m,n)
n in NAT by ORDINAL1:def 12;
hence f . n = Ackermann (m,n) by A1; :: thesis: verum