Op-amp 1 is topmost in the schematic below. I used the ideal amplifier method (using A until the end and then lim A->infinity) and also the virtual short method.
But I don't know if that's enough to prove negative feedback?
simulate this circuit – Schematic created using CircuitLab
Apply "up-down thinking". This is a way of reasoning about which way quantities like voltages and currents will change if a circuit is disturbed in some particular way.
Assume that there is in fact negative feedback and so the circuit is stable with \$V_i\$ and \$V_o\$ at zero volts (on a dual-voltage supply).
Now, what happens if \$V_i\$ increases slightly? Which way will the output \$V_o\$ move, and how does that propagate through OA2 to influence the + input of OA1? Does the + input move in the same direction as -, or against it?
If + follows -, is that negative feedback or positive feedback?
Look at OA2's circuit in isolation to OA1: -
Regard Vo as an input (because that is what is is) and the junction of R3 and R4 as the output
Can you "show" that the voltage at the junction of R3 and R4 is -Vo * R3/(R3 + R4)
Can you see that OA2's circuit is applying feedback to OA1?
Because the feedback voltage formula has a negative sign (the one in front of Vo above) AND it feeds back to the non-inverting input of OA1, does this tell you that it is negative feedback? It is negative feedback!
Smallprint: As an acedemic exercise to demonstrate negative feedback this is OK but in the real world, at frequencies approaching the unity gain point on the TL082, its inherent phase shift (and most op-amps) approaches 90º and, because one TL082 is applying feedback around the other one, the combined phase shift will be 180º and this then becomes positive feedback and the circuit will likely oscillate: -
