(* *)
(**************************************************************************)
-set "baseuri" "cic:/matita/LAMBDA-TYPES/Unified-Sub/Lift/fun".
-
-include "Lift/inv.ma".
+include "Unified-Sub/Lift/inv.ma".
(* Functional properties ****************************************************)
-(*
+
theorem lift_total: \forall l, t, i. \exists u. Lift l i t u.
intros 2. elim t; clear t;
- [
-*)
+ [ autobatch
+ | lapply (nle_gt_or_le n i). decompose;
+ [ autobatch
+ | lapply (nplus_total l n). decompose. autobatch
+ ]
+ | lapply (H i1). lapply (H1 (succ i1)). decompose. autobatch
+ | lapply (H i1). lapply (H1 i1). decompose. autobatch
+ ].
+qed.
+
theorem lift_mono: \forall l,i,t,t1. Lift l i t t1 \to
\forall t2. Lift l i t t2 \to
t1 = t2.
intros 5. elim H; clear H i t t1;
[ lapply linear lift_inv_sort_1 to H1
| lapply linear lift_inv_lref_1_gt to H2, H1
- | lapply linear lift_inv_lref_1_le to H3, H1, H2
+ | lapply linear lift_inv_lref_1_le_nplus to H3, H1, H2
| lapply linear lift_inv_bind_1 to H5. decompose
| lapply linear lift_inv_flat_1 to H5. decompose
- ]; subst; auto.
+ ]; destruct; autobatch.
qed.
theorem lift_inj: \forall l,i,t1,t. Lift l i t1 t \to
intros 5. elim H; clear H i t1 t;
[ lapply linear lift_inv_sort_2 to H1
| lapply linear lift_inv_lref_2_gt to H2, H1
- | lapply nle_nplus to H2 as H. (**)
+ | lapply nle_nplus to H2 as H.
lapply linear nle_trans to H1, H as H0.
- lapply lift_inv_lref_2_le to H3, H0, H2
+ lapply lift_inv_lref_2_le_nplus to H3, H0, H2
| lapply linear lift_inv_bind_2 to H5. decompose
| lapply linear lift_inv_flat_2 to H5. decompose
- ]; subst; auto.
+ ]; destruct; autobatch.
qed.