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1 (**************************************************************************)
2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
5 (*      ||T||                                                             *)
6 (*      ||I||       Developers:                                           *)
7 (*      ||T||         The HELM team.                                      *)
8 (*      ||A||         http://helm.cs.unibo.it                             *)
9 (*      \   /                                                             *)
10 (*       \ /        This file is distributed under the terms of the       *)
11 (*        v         GNU General Public License Version 2                  *)
12 (*                                                                        *)
13 (**************************************************************************)
14
15 include "CC2FO_K.ma".
16 include "cube.ma".
17 include "inversion.ma".
18
19 (* The K interpretation in the λ-Cube *****************************************)
20
21 lemma ki_type: ∀G,t,u. G ⊢_{CC} t : u → u = Sort 1 → 𝕂{G} ⊢_{FO} 𝕂{t}_[G] : u.
22 #G #t #u #H elim H -H G t u
23 [ #i #j * #_ @ax //
24 | #G #A #i #HA #IHA #Heq