old subst tactics removed. New destruct tactic used instead

[helm.git] / matita / contribs / LAMBDA-TYPES / Unified-Sub / Lift / fun.ma

diff --git a/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/fun.ma b/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/fun.ma
index fd794fe9ba18ad784e24a589c2f57e1fde240c6a..86e8031b41d947562fdac57d32022d38680d896d 100644 (file)
--- a/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/fun.ma
+++ b/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/fun.ma
@@ -17,21 +17,29 @@ set "baseuri" "cic:/matita/LAMBDA-TYPES/Unified-Sub/Lift/fun".
 include "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
@@ -40,10 +48,10 @@ 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.