deffunc H_{1}( 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 = H_{1}(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 = H_{1}(n)
by A1;

hence f . n = IFGT (n,(n1 + 1),(n + n2),n) ; :: thesis: verum

consider f being sequence of NAT such that

A1: for n being Element of NAT holds f . n = H

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 = H

hence f . n = IFGT (n,(n1 + 1),(n + n2),n) ; :: thesis: verum