This line, and those below, will be ignored--

[helm.git] / matita / matita / contribs / lambda / pointer_sequence.ma

diff --git a/matita/matita/contribs/lambda/pointer_sequence.ma b/matita/matita/contribs/lambda/pointer_sequence.ma
index 131711426a66e48b68e91377aa309565e86339ac..0a3d3422c37a98cbce8316b4c5c162158f82f19b 100644 (file)
--- a/matita/matita/contribs/lambda/pointer_sequence.ma
+++ b/matita/matita/contribs/lambda/pointer_sequence.ma
@@ -24,3 +24,55 @@ definition is_head: predicate pseq ≝ All … in_head.
 
 (* Note: to us, a "normal" computation contracts redexes in non-decreasing positions *)
 definition is_le: predicate pseq ≝ Allr … ple.
+
+lemma is_le_compatible: ∀c,s. is_le s → is_le (c:::s).
+#c #s elim s -s // #p * //
+#q #s #IHs * /3 width=1/
+qed.
+
+lemma is_le_cons: ∀p,s. is_le s → is_le ((dx::p)::sn:::s).
+#p #s elim s -s // #q1 * /2 width=1/
+#q2 #s #IHs * /4 width=1/
+qed.
+
+lemma is_le_append: ∀r. is_le r → ∀s. is_le s → is_le ((dx:::r)@sn:::s).
+#r elim r -r /3 width=1/ #p * /2 width=1/
+#q #r #IHr * /3 width=1/
+qed.
+
+theorem is_head_is_le: ∀s. is_head s → is_le s.
+#s elim s -s // #p * //
+#q #s #IHs * /3 width=1/
+qed.
+
+lemma is_le_in_head: ∀p. in_head p → ∀s. is_le s → is_le (p::s).
+#p #Hp * // /3 width=1/
+qed.
+
+theorem is_head_is_le_trans: ∀r. is_head r → ∀s. is_le s → is_le (r@s).
+#r elim r -r // #p *
+[ #_ * /2 width=1/
+| #q #r #IHr * /3 width=1/
+]
+qed.
+
+definition ho_compatible_rc: predicate (pseq→relation term) ≝ λR.
+                             ∀s,A1,A2. R s A1 A2 → R (sn:::s) (𝛌.A1) (𝛌.A2).
+
+definition ho_compatible_sn: predicate (pseq→relation term) ≝ λR.
+                             ∀s,B1,B2,A. R s B1 B2 → R (sn:::s) (@B1.A) (@B2.A).
+
+definition ho_compatible_dx: predicate (pseq→relation term) ≝ λR.
+                             ∀s,B,A1,A2. R s A1 A2 → R (dx:::s) (@B.A1) (@B.A2).
+
+lemma lstar_compatible_rc: ∀R. compatible_rc R → ho_compatible_rc (lstar … R).
+#R #HR #s #A1 #A2 #H @(lstar_ind_l ????????? H) -s -A1 // /3 width=3/
+qed.
+
+lemma lstar_compatible_sn: ∀R. compatible_sn R → ho_compatible_sn (lstar … R).
+#R #HR #s #B1 #B2 #A #H @(lstar_ind_l ????????? H) -s -B1 // /3 width=3/
+qed.
+
+lemma lstar_compatible_dx: ∀R. compatible_dx R → ho_compatible_dx (lstar … R).
+#R #HR #s #B #A1 #A2 #H @(lstar_ind_l ????????? H) -s -A1 // /3 width=3/
+qed.