(* MATTER CONCERNING STRONG NORMALIZATION TO BE PUT ELSEWHERE *****************)
-(* terms **********************************************************************)
-
-(* FG: not needed for now
-(* nautral terms *)
-inductive neutral: T → Prop ≝
- | neutral_sort: ∀n.neutral (Sort n)
- | neutral_rel: ∀i.neutral (Rel i)
- | neutral_app: ∀M,N.neutral (App M N)
-.
-*)
-
(* substitution ***************************************************************)
-
+(*
+axiom is_dummy_lift: ∀p,t,k. is_dummy (lift t k p) = is_dummy t.
+*)
(* FG: do we need this?
definition lift0 ≝ λp,k,M . lift M p k. (**) (* remove definition *)
#p #k #l (elim l) -l /2/ #A #D #IHl #F >IHl //
qed.
*)
-
+(*
lemma lift_rel_lt: ∀i,p,k. (S i) ≤ k → lift (Rel i) k p = Rel i.
#i #p #k #Hik normalize >(le_to_leb_true … Hik) //
qed.
-
-lemma lift_rel_ge: ∀i,p,k. (S i) ≰ k → lift (Rel i) k p = Rel (i+p).
+*)
+lemma lift_rel_not_le: ∀i,p,k. (S i) ≰ k → lift (Rel i) k p = Rel (i+p).
#i #p #k #Hik normalize >(lt_to_leb_false (S i) k) /2/
qed.