A First-Order Equation Operator is Degenerate Elliptic and Its $\delta$-Shifts Ignore the Form Argument

In the setting of Hilbert Triples: Standing Notation and Background, let $U\subseteq H$ be open in $H$, with $W=D(A)\cap U$ as in Hilbert Triples: Standing Notation and Background (v), let $\mathrm{Sym}(V)$ and $\mathrm{Sym}(H)$ be as in Hilbert Triples: Standing Notation and Background (vi), and let $F$ be a second-order equation operator on $U$ relative to $(H,V,A)$ that is first order, with $\delta$-shifts $F^{-}_{\delta}$ and $F^{+}_{\delta}$. Let $\delta\in\mathbb{R}$ be positive. Then the following hold.

1. (Degenerate ellipticity)(i) The operator $F$ is degenerate elliptic.

2. (The shifts ignore the form argument)(ii) For every $x\in W$, every $r\in\mathbb{R}$, every $p\in H$ and all $Y,Y'\in\mathrm{Sym}(H)$,

$$F^{-}_{\delta}(x,r,p,Y)=F^{-}_{\delta}(x,r,p,Y'),\qquad F^{+}_{\delta}(x,r,p,Y)=F^{+}_{\delta}(x,r,p,Y').$$