A Current Source Circuit from AoE-X

H&H show a clever current source circuit and challenge readers to prove the circuit works especially without using two of the constraints.

It is a circuit of an opamp driving a bipolar transistor.  The base current of the bipolar transistor would normally cause an error.  Here the error is compensated.  The base current is sensed with the base resistor kR1; the emitter voltage is Vin with the differential voltage added using a circuit configuration resembling a difference amplifier.

Note that the current through R1 is the sum of the collector current, the base current and the current through R2, which the last two are the current through kR1.  The derivation makes no use of the constraints on the resistors.  The base current compensation is strictly accurate (assuming ideal opamp).