This article shows that achieving capacity region of a 2-users weak Gaussian Interference Channel (GIC) is equivalent to enlarging the core in a nested set of Polymatroids (each equivalent to capacity region of a multiple-access channel) through maximizing a minimum rate, then projecting along its orthogonal span and continuing recursively. This formulation relies on defining dummy private messages to capture the effect of interference in GIC. It follows that relying on independent Gaussian random code-books is optimum, and the corresponding solution corresponds to achieving the boundary in HK constraints.