Can anyone give me a link to a proof of strongly or weakly normalization of Calculus of Inductive Constructions (CIC) and a proof of consistency strength of CIC?
I use the word “CIC” as the system presented in “Inductively defined types” by Coquand, Paulin in 1990.
Similar questions are at https://coq-club.inria.narkive.com/jHBce3xb/proof-on-strong-normalization-of-cic
According to them, Werner proved strong normalization of “λP2 + Inductive Types” in 1994. Altenkirch proved but did not cover general inductive types. Werner proved the upper bound of consistency strength of CIC is ZFC+ω inaccessible cardinals in 1997. Miquel proved the lower bound is Z + ω Zermelo universes.
Is there a proof on strongly or weakly normalization of Coquand’s CIC? Are there tighter bounds of its consistency strength?
Thanks for any hint.