We study hypoellopticity, in the sense of C∞ local hypoellipticity, which is defined as follows. If E is a partial differential operator on Rn, if P∈Rn, then E is hypoelliptic at P if whenever u is a distribution such that the restriction of u to U is in C∞(U) then the restriction of Eu to U is in C∞(U). We say that E gains s1​ derivatives in the Sobolev at P if for every distribution u with the property that $Eu\$