Taurus Trace (timing query)

So, here's a bit of a doozy for me, that I'd appreciate some light shed on. Firstly, for context, Taurus' subroutine reads: Trace2 – If successful, trash 1 piece of hardware. If your trace strength is 5 or greater, trash 1 piece of hardware. For those that need the visual refresher, this is the card in question: http://www.cardgamedb.com/forums/uploads/an/taurus-upstalk-9.png

Let us assume that the Runner, upon encountering Taurus, does not break the subroutine. If the Corp then spends 3 credits to boost said trace's strength to 5, would the Corp then trash a piece of hardware immediately upon satisfying the 'If your trace strength is 5 or greater' condition? Or would the Corp's trashing window involve waiting until the Runner has boosted their link strength accordingly?

Now, I realize this might seem largely irrelevant (5-strength trace means 'at least 1 hardware trashed' regardless of when it occurs). However, if the Runner has a Toolbox or Rabbit Hole installed, i.e. hardware that increases base link strength, then the timing of when the 'If your trace strength is 5 or greater' clause is considered fulfilled would affect how much the Runner is required to spend in order to prevent the trace from being successful.

For example, if a piece of hardware is determined to be trashed immediately after the Corp increases trace strength to 5, the Corp could choose to trash the Runner's Toolbox, removing the 2 links it adds, and the Runner would then be required to pay 2 more credits in order to beat the trace.

Personally, I would think that as soon as the Corp increases the trace strength to 5, they get to trash a piece of hardware, prior to the Runner's opportunity to increase their link strength. Given that Taurus is the first card to initiate a trace with an effect independent of whether it is successful or not, however, there is no established precedent.