from DAkkaDakka forum:
Here I'm going to have to point out that yes, if the Nob has a Slugga and a Choppa, and the entire unit exchanges Slugga and Choppa for a Shoota, then the Nob makes the exchange and now has a Slugga. However, as you will notice it does not contradict the original schema showing how a Nob that has exchanged its Choppa for a Power Klaw does not have a Slugga and Choppa and thus does not exhange his Slugga and Choppa for a Shoota when the Shoota upgrade is applied.
Rule: The Nob may exchange Choppa for Power Klaw
A1. If B then D
Rule: All models with a Slugga and Choppa may exchange Slugga and Choppa for a Shoota:
A2. If (A & B) then C
Condition: All models in the unit, Boyz and Nobz, initially have a Slugga and Choppa
A3. A & B
Condition: The Nob has a Choppa since all models in the unit have one.
4. B (3. Simplification)
Consequence: The Nob has a Slugga and Power Klaw
5. D (1 & 4, Modus Ponens)
Consequence: The Boyz have Shootas
6. C (2 & 3, Modus Ponens)
If you really want to be rigorous about it then you need to add in the modal operators to cover "may" (<> for 'it is possible that', [] for 'it is actually the case that') and the quantifiers to cover the difference between the entire mob (U for univeral or entire) and one model in the mob (the Nob, E for existential or not entire).
A1. <>(Ex)(Nm & Bx) → [](Ex)(Nb & Dx)
A2. <>(Ux)(Uy)(My & (Ax & Bx)) → [](Ex)(Ey)(My & Cx)
A3. [](Ux)(Uy)(My & (Ax & Bx))
4a. [](Ux)(Uy)(My & (Ax & Bx)) (3, Commutation)
4b. [](Ux)(Uy)((My & Bx) & Ax) (4a, Association)
4c. [](Ux)((Nm & Bx) & Ax) (4b, Universal Instantiation)
4d. [](Ux)(Nm & Bx) (4c, Simplification)
4e. [](Ex)(Nm & Bx) (4d, Universal Weakening)
4f. <>(Ex)(Nm & Bx) (4e, Modal Weakening)
5. [](Ex)(Nb & Dx) (1 & 4, Modus Ponens)
6a. <>(Ux)(Uy)(My & (Ax & Bx)) (3, Modal Weakening)
6b. [](Ex)(Uy)(My & Cx) (2 & 3, Modus Ponens)
6c. [](Ex)(Bm & Cx) (6b, Universal Instantiation)
Since we know that Nobz are not Boyz we know that:
Boyz models are not Nobz models
A7. Bm ≠ Nm
And that if a Nob has a Power Klaw then it is not a Boy and does not have a Shoota
8. [](Ex)(Nb & Dx) → ~[](Ex)(Bm & Cx)
Astute readers will notice that how this argument works is a classic feature of linear logics, the consumption of material. Since the upgrade to the Nob happens first, the Nob is not upgraded when the entire mob is upgraded. Conversely had we applied the upgrade to the entire mob first, then the Nob would have been upgraded to a Shoota instead of a Power Klaw (or Big Choppa). Since the order to upgrades is Characters first (since "...additional options depending on whether an associated character is taken" applies to the associated character, the Nob, taken) and upgrades may only be given to models that have it available (the upgrades apply to the model and not exclusive of each other like Mega-Armour and Bikes) where the Nob is upgraded first it does not meet the conditions for upgrading to a Shoota when the entire mob does.