# Two Op-Amp Instrumentation Amplifier - Gain derivation

I came across the following appnote(slyt647) which analyses the two op-amp instrumentation amplifier topology.

The gain was found by finding individual gains for each op-amp and adding them in accordance to superposition. I have some hard time understading how $G_{A1V-IN}$ (eq 8) was calculated.

As far as I see it for $G_{A1V-IN}$ we have the following equivalent circuit:

And thus it seems to me that: $$G_{A1V-IN} = -\frac{R_R}{R_G} -\frac{R_R}{R_f}\cdot \left(1+\frac{R_R}{R_f || R_G} \right)$$

Did I go wrong somewhere ?