31. The bone anchor assembly of claim 30 , wherein the insert upright arm uppermost portions protruding laterally extend radially outward near the uppermost top surfaces thereof, with the top surfaces of the radially-outward protruding uppermost portions defining the uppermost top surfaces of the insert.
30. A bone anchor assembly for securing an elongate rod to a bone, the bone anchor assembly comprising: a receiver having a vertical axis, a lower body defining an internal cavity communicating with a bottom surface of the receiver through a bottom opening, and a first pair of upright arms extending upwardly from the lower body to define a first channel opening onto a top thereof for receiving the elongate rod, the first channel having a transverse axis perpendicular to the vertical axis and communicating with the internal cavity to define a through bore centered around the vertical axis, the upright arms having interior surfaces with a discontinuous guide and advancement structure formed therein, the receiver having opposed recesses with downwardly-facing top surfaces located entirely below the discontinuous guide and advancement structure; a bone attachment structure having a body and an upper head portion with a substantially spherical surface above a hemisphere thereof, the body extending through the receiver bottom opening and pivotal with respect to the receiver; and an insert having a body with a second pair of upright arms centered around a vertically-extending midsection of the body and forming a second channel therebetween, the second channel being alignable with the receiver transverse axis to receive the elongate rod, the insert upright arms having uppermost portions protruding laterally at the vertically-extending midsection of the insert body and terminating at uppermost top surfaces, the insert body further including a central through-and-through tool receiving opening and oppositely-directed opposed radial extensions in the direction of the receiver transverse axis to inhibit rotation between the receiver and the insert, wherein top surfaces of the insert opposed radial extensions extend radially outward so as to be underneath a most bottom surface of the elongate rod, and wherein the uppermost top surfaces of the upright arms are snapped under and engaging the downwardly-facing top surfaces of the receiver opposed recesses to prevent upward movement of the insert when the insert is fully disposed within the receiver first channel, so as to prevent the insert from moving back up within the receiver prior to the insert being further pushed down within the receiver into a locked orientation by a closure.