colength and identity relocation

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / relocation / trace_sor.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/trace_sor.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/trace_sor.ma
index f4e79a6ce25f44ea770e2c07784f33b91c684aeb..65aba02ac4da17fa88f8b24b11aa8e701c892653 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/trace_sor.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/trace_sor.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "ground_2/notation/relations/runion_3.ma".
-include "ground_2/relocation/trace.ma".
+include "ground_2/relocation/trace_isid.ma".
 
 (* RELOCATION TRACE *********************************************************)
 
@@ -28,6 +28,35 @@ interpretation
 
 (* Basic properties *********************************************************)
 
+lemma sor_length: ∀cs1,cs2. |cs1| = |cs2| →
+                  ∃∃cs. cs2 ⋓ cs1 ≡ cs & |cs| = |cs1| & |cs| = |cs2|.
+#cs1 elim cs1 -cs1
+[ #cs2 #H >(length_inv_zero_sn … H) -H /2 width=4 by sor_empty, ex3_intro/
+| #b1 #cs1 #IH #x #H elim (length_inv_succ_sn … H) -H
+  #cs2 #b2 #H12 #H destruct elim (IH … H12) -IH -H12
+  #cs #H12 #H1 #H2 @(ex3_intro … ((b1 ∨ b2) @ cs)) /2 width=1 by sor_inh/ (**) (* explicit constructor *)
+]
+qed-.
+
 lemma sor_sym: ∀cs1,cs2,cs. cs1 ⋓ cs2 ≡ cs → cs2 ⋓ cs1 ≡ cs.
 #cs1 #cs2 #cs #H elim H -cs1 -cs2 -cs /2 width=1 by sor_inh/
 qed-.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma sor_inv_length: ∀cs1,cs2,cs. cs2 ⋓ cs1 ≡ cs →
+                      ∧∧ |cs1| = |cs2| & |cs| = |cs1| & |cs| = |cs2|.
+#cs1 #cs2 #cs #H elim H -cs1 -cs2 -cs /2 width=1 by and3_intro/
+#cs1 #cs2 #cs #_ #b1 #b2 * /2 width=1 by and3_intro/
+qed-.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma sor_fwd_isid_sn: ∀cs1,cs2,cs. cs1 ⋓ cs2 ≡ cs → 𝐈⦃cs1⦄ → 𝐈⦃cs⦄.
+#cs1 #cs2 #cs #H elim H -cs1 -cs2 -cs //
+#cs1 #cs2 #cs #_ #b1 #b2 #IH #H elim (isid_inv_cons … H) -H
+/3 width=1 by isid_true/
+qed-.
+
+lemma sor_fwd_isid_dx: ∀cs1,cs2,cs. cs1 ⋓ cs2 ≡ cs → 𝐈⦃cs2⦄ → 𝐈⦃cs⦄.
+/3 width=4 by sor_fwd_isid_sn, sor_sym/ qed-.