Unified-Sub: lift_comm completed

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

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/fun.ma b/helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/fun.ma
index fd794fe9ba18ad784e24a589c2f57e1fde240c6a..cfddffd3df932e642cf204106e1e14e2f7107e34 100644 (file)
--- a/helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/fun.ma
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/fun.ma
@@ -17,18 +17,26 @@ 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;
- [ 
-*)
+ [ auto
+ | lapply (nle_gt_or_le n i). decompose;
+   [ auto
+   | lapply (nplus_total l n). decompose. auto
+   ]
+ | lapply (H i1). lapply (H1 (succ i1)). decompose. auto
+ | lapply (H i1). lapply (H1 i1). decompose. auto  
+ ].
+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.
@@ -40,9 +48,9 @@ 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.