deffunc H₁( Nat) -> Element of NAT = In ((IFGT ($1,(n1 + 1),($1 + n2),$1)),NAT);
consider f being sequence of NAT such that
A1: for n being Element of NAT holds f . n = H₁(n) from FUNCT_2:sch 4();
take f ; :: thesis: for n being Nat holds f . n = IFGT (n,(n1 + 1),(n + n2),n)
let n be Nat; :: thesis: f . n = IFGT (n,(n1 + 1),(n + n2),n)
n in NAT by ORDINAL1:def 12;
then f . n = H₁(n) by A1;
hence f . n = IFGT (n,(n1 + 1),(n + n2),n) ; :: thesis: verum