- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / append / cpx.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/append/cpx.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/append/cpx.etc
new file mode 100644 (file)
index 0000000..5f8bf52
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/append/cpx.etc
@@ -0,0 +1,25 @@
+lemma cpx_append: ∀h,g,G. l_appendable_sn … (cpx h g G).
+#h #g #G #K #T1 #T2 #H elim H -G -K -T1 -T2
+/2 width=3 by cpx_sort, cpx_bind, cpx_flat, cpx_zeta, cpx_tau, cpx_ti, cpx_beta, cpx_theta/
+#I #G #K #K0 #V1 #V2 #W2 #i #HK0 #_ #HVW2 #IHV12 #L
+lapply (ldrop_fwd_length_lt2 … HK0) #H
+@(cpx_delta … I … (L@@K0) V1 … HVW2) // 
+@(ldrop_O1_append_sn_le … HK0) /2 width=2 by lt_to_le/ (**) (* /3/ does not work *)
+qed.
+
+lemma cpx_fwd_shift1: ∀h,g,G,L1,L,T1,T. ⦃G, L⦄ ⊢ L1 @@ T1 ➡[h, g] T →
+                      ∃∃L2,T2. |L1| = |L2| & T = L2 @@ T2.
+#h #g #G #L1 @(lenv_ind_dx … L1) -L1 normalize
+[ #L #T1 #T #HT1
+  @(ex2_2_intro … (⋆)) // (**) (* explicit constructor *)
+| #I #L1 #V1 #IH #L #T1 #X
+  >shift_append_assoc normalize #H
+  elim (cpx_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 by refl, trans_eq/ (**) (* explicit constructor *)
+  | #T #_ #_ #H destruct
+  ]
+]
+qed-.