Methyl esters $\left(\mathrm{RCO}_{2} \mathrm{CH}_{3}\right)$ undergo a cleavage reaction to yield carboxylate ions plus iodomethane on heating with LiI in dimethylformamide:
The following evidence has been obtained: (1) The reaction occurs much faster in DMF than in ethanol. (2) The corresponding ethyl ester $\left(\mathrm{RCO}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\right)$ cleaves approximately 10 times more slowly than the methyl ester. Propose a mechanism for the reaction. What other kinds of experimental evidence could you gather to support your hypothesis?