Chapter 71: The Meta-Logical Toolkit

Book I’s sixty-seven chapters build Category τ from five generators and seven axioms. Every object, operation, and theorem is earned. But the proofs themselves were written in Lean 4’s Calculus of Inductive Constructions (CIC) — a logical substrate that was imported, not derived from K0–K6. This chapter takes inventory: what CIC provides, what Book I actually used, and where the earned-vs-imported boundary lies. The structural rules of contraction and weakening — free in CIC, refused by K5 at the object level — point toward a deep correspondence that the next chapter will make precise.