User blog comment:Upquark11111/An Explanation of Loader's Number/@comment-11227630-20171210002438/@comment-11227630-20171210101141

Why can't we get, for example, $$0:\text{nat}$$ (i.e. $$(\lambda A:*.\lambda f:(\Pi y:A.A).\lambda x:A.x):(\Pi A:*.\Pi x:(\Pi y:A.A).\Pi y:A.A)$$)? The only difference between λ-cube version of λ→ and λPω is the "pi rule", which is used only when we infer $$*\vdash(\Pi0.1):*$$ from $$*,0\vdash1:*$$.

Or do you mean that we can't infer the type of $$\Pi A:*.\Pi x:(\Pi y:A.A).\Pi y:A.A$$ in λ→?