- we introduced the pointer_step rc in the perspective of proving

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / substitution / tps.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/substitution/tps.ma b/matita/matita/contribs/lambda_delta/basic_2/substitution/tps.ma
index db116f77e63b526eb2dc408ec50dfb645a0b9327..ab11536bdf4db831547641e2ffadce07e5338283 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/substitution/tps.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/substitution/tps.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/substitution/ldrop.ma".
+include "basic_2/substitution/ldrop_append.ma".
 
 (* PARALLEL SUBSTITUTION ON TERMS *******************************************)
 
@@ -144,6 +144,15 @@ lemma tps_split_down: ∀L,T1,T2,d,e. L ⊢ T1 ▶ [d, e] T2 →
 ]
 qed.
 
+lemma tps_append: ∀K,T1,T2,d,e. K ⊢ T1 ▶ [d, e] T2 →
+                  ∀L. L @@ K ⊢ T1 ▶ [d, e] T2.
+#K #T1 #T2 #d #e #H elim H -K -T1 -T2 -d -e // /2 width=1/
+#K #K0 #V #W #i #d #e #Hdi #Hide #HK0 #HVW #L
+lapply (ldrop_fwd_ldrop2_length … HK0) #H
+@(tps_subst … (L@@K0) … HVW) // (**) (* /3/ does not work *)
+@(ldrop_O1_append_sn_le … HK0) /2 width=2/
+qed.
+
 (* Basic inversion lemmas ***************************************************)
 
 fact tps_inv_atom1_aux: ∀L,T1,T2,d,e. L ⊢ T1 ▶ [d, e] T2 → ∀I. T1 = ⓪{I} →
@@ -250,6 +259,21 @@ lemma tps_fwd_tw: ∀L,T1,T2,d,e. L ⊢ T1 ▶ [d, e] T2 → #{T1} ≤ #{T2}.
 /3 by monotonic_le_plus_l, le_plus/ (**) (* just /3 width=1/ is too slow *)
 qed-.
 
+lemma tps_fwd_shift1: ∀L1,L,T1,T,d,e. L ⊢ L1 @@ T1 ▶[d, e] T →
+                      ∃∃L2,T2. |L1| = |L2| & T = L2 @@ T2.
+#L1 @(lenv_ind_dx … L1) -L1 normalize
+[ #L #T1 #T #d #e #HT1
+  @(ex2_2_intro … (⋆)) // (**) (* explicit constructor *)
+| #I #L1 #V1 #IH #L #T1 #X #d #e
+  >shift_append_assoc normalize #H
+  elim (tps_inv_bind1 … H) -H
+  #V0 #T0 #_ #HT10 #H destruct
+  elim (IH … HT10) -IH -HT10 #L2 #T2 #HL12 #H destruct
+  >append_length >HL12 -HL12
+  @(ex2_2_intro … (⋆.ⓑ{I}V0@@L2) T2) [ >append_length ] // /2 width=3/ (**) (* explicit constructor *)
+]
+qed-.
+
 (* Basic_1: removed theorems 25:
             subst0_gen_sort subst0_gen_lref subst0_gen_head subst0_gen_lift_lt
             subst0_gen_lift_false subst0_gen_lift_ge subst0_refl subst0_trans