I am going through the Pinocchio protocol paper and I need 2 clarifications in the section Protocol 1 (Verifiable Computation from strong QAP). The part that explains the Verify process, which contains this expression: $$e(g^{v_0}.g^{v_{io}}.g^{v(s)}, g^{w_0}.g^{w(s)})/e(g^{y_0}.g^{y(s)},g) = e(g^{h(s)},g^{t(s)})$$.
since $e:G \times G \to G_T$, what is the definition of the division operation as shown in the expression above, wrt $G_T$?
If my understanding is correct, the first term in the first pairing should be $g^{v_0}.g^{v_{io}}.g^{v_{mid}(s)}$ instead of $g^{v_0}.g^{v_{io}}.g^{v(s)}$