Scope of da'i in counterfactual implications

I am currently working on the BPFK section containing da'i.

da'i is a UI, so it should follow the same left-influencing behaviour as any other free modifier, right?

Now, consider what is going on here, in the CLL's sole example of da'i:

ganai da'i do viska le mi citno mensi gi ju'o do djuno le du'u ri pazvau

The camxes parse tree is as follows:

text
   gekSentence
   |- gek
   |  |- CMAVO
   |  |     GA: ga
   |  |- NAIClause
   |     |- CMAVO
   |     |     NAI: nai
   |     |- CMAVO
   |           UI: da'i
   |- sentence
   |  |- CMAVO
   |  |     KOhA: do
   |  |- bridiTail3
   |     |- BRIVLA
   |     |     gismu: viska
   |     |- sumti6
   |        |- CMAVO
   |        |     LE: le
   |        |- sumtiTail
   |           |- CMAVO
   |           |     KOhA: mi
   |           |- selbri3
   |              |- BRIVLA
   |              |     gismu: citno
   |              |- BRIVLA
   |                    gismu: mensi
   |- GIClause
   |  |- CMAVO
   |  |     GI: gi
   |  |- CMAVO
   |        UI: ju'o
   |- sentence
      |- CMAVO
      |     KOhA: do
      |- bridiTail3
         |- BRIVLA
         |     gismu: djuno
         |- sumti6
            |- CMAVO
            |     LE: le
            |- tanruUnit2
               |- CMAVO
               |     NU: du'u
               |- sentence
                  |- CMAVO
                  |     KOhA: ri
                  |- BRIVLA
                        lujvo: pazvau

See where the da'i ends up in the tree?

Now, even assuming that the semantic effect of da'i can reach back through both the NAIClause and the gek (which is quite a stretch), what is it supposed to be doing to the gekSentence? I thought it was the _antecedent_ that was supposed to be marked as counterfactual, not the implication in its entirety!

-- 
Arnt Richard Johansen                                http://arj.nvg.org/
<JohnCowan> Can someone poke Shawn?
<JayKominek> next meeting, electroshock devices go under everyone's chairs.
<MarkShoulson> Just send an EOU to their terminal (end of user.  Makes
terminal explode)


 
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