Definition. First Sets in Dependent Lambek Calculus

The first set of a grammar 𝐴 may be captured in Lambek𝙳 via the following proposition:

π‘βˆ‰π–₯π—‚π—‹π—Œπ—(𝐴)≔𝐴&('𝑐'βŠ—βŠ€)⊒βŠ₯

Or perhaps with ones of the grammars

𝐴⇒¬('𝑐'βŠ—βŠ€),'𝑐'βŠ—βŠ€β‡’Β¬π΄
first-set-in-dependent-lambek definition entries/parsing/first-set-in-dependent-lambek.hel