of strong bundle $\pi: E(Q,\omega, J)\to B(Q,\omega)$. Although it is a section between spaces of varying dimensions, near every smooth point, we can locally fill $f:r(U)\to R(U\triangleleft F)$ into the graph $\text{gr}(h)$ for some **filling** ([@Polyfoldanalysis] 1.35) $h: U\to F$ between sc-Banach spaces without changing its zero set and kernel and cokernel of its linearization at zeros and thus in essence has the same[^7] Fredholm behavior. $h$ has linear sc-Fredholm linearizations but implicit function theorem does not hold for general sc-smooth maps with linear sc-Fredholm linearizations, because $x\mapsto Dh(x), E_1\mapsto L(E_0, F_0)$ is not continuous, which is used in the usual argument. We have to restrict to a special class of maps, called basic class, where a version of implicit function theorem holds. First, let us define an open germ around $0$ in $E$, namely, $\mathcal{O}(E,0):=(V_m)_{m\in \mathbb{N}_0}$ is an **open germ** around $0$ in $E$ if $V_m$ is open in $E_m$ and contains 0, and $V_{m+1}\subset V_m$[^8]). A map germ mapping from $\mathcal{O}(E,0)$ is also denoted by $[f,0]$. A map germ $h: \mathcal{O}({\mathbb{R}}^m\oplus W,0)\mapsto (W\oplus {\mathbb{R}}^N,0)$ is **of basic class** if it is of the form $(v,x)\mapsto (x-B(v,x), C(v,x))$ such that $B(v,\cdot)$ between each level of the same regularity is 