Write down statements … for source-free fields … in three dimensions

Write down statements $\mathbf{E}-\mathbf{F}-\mathbf{G}-\mathbf{H}$ for source-free fields $\mathbf{F}(x,y,z)$ in three dimensions. In statement $\mathbf{F}$, paths sharing the same endpoint become surfaces sharing the same boundary curve. In G, the stream function becomes a vector field such that $\mathbf{F}=\mathrm{curl}\mathbf{g}$.

Its source prints no answer for this problem, so there's nothing to check against.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §15.5 The Divergence Theorem, #28