//; nqed.
*)
-(*
+(*start: ∀G.∀A.∀i.TJ G A (Sort i) → TJ (A::G) (Rel 0) (lift A 0 1)
+ |
nlemma length_cons: ∀A.∀G. length T (A::G) = length T G + 1.
/2/; nqed.*)
| abs: ∀G.∀A,B,b.∀i.
TJ (A::G) b B → TJ G (Prod A B) (Sort i) → TJ G (Lambda A b) (Prod A B)
| conv: ∀G.∀A,B,C.∀i. conv B C →
- TJ G A B → TJ G B (Sort i) → TJ G A C
+ TJ G A B → TJ G C (Sort i) → TJ G A C
| dummy: ∀G.∀A,B.∀i.
TJ G A B → TJ G B (Sort i) → TJ G (D A) B.
theorem start_lemma2: ∀G.
Glegal G → ∀n. n < |G| → G ⊢ Rel n: lift (nth n T G (Rel O)) 0 (S n).
#G #Gleg (cases Gleg) #A #B #tjAB (elim tjAB) /2/
- [#i #j #axij #p normalize #abs @False_ind @(absurd … abs) //
+ [#i #j #axij #p normalize #abs @(False_ind) @(absurd … abs) //
|#G #A #i #tjA #Hind #m (cases m) /2/
#p #Hle @start_rel // @Hind @le_S_S_to_le @Hle
|#G #A #B #C #i #tjAB #tjC #Hind1 #_ #m (cases m)