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

diff --git a/matita/matita/contribs/lambda/labelled_hap_computation.ma b/matita/matita/contribs/lambda/labelled_hap_computation.ma
index 70cc06b79beab9f70f686e60a83c675aa64542cd..4441961e1319391ec6d0cae55ff69827014f3efa 100644 (file)
--- a/matita/matita/contribs/lambda/labelled_hap_computation.ma
+++ b/matita/matita/contribs/lambda/labelled_hap_computation.ma
@@ -29,7 +29,7 @@ notation "hvbox( M break ⓗ⇀* [ term 46 p ] break term 46 N )"
    non associative with precedence 45
    for @{ 'HApStar $M $p $N }.
 
-lemma lhap1_lhap: ∀p,M1,M2. M1 ⓗ⇀[p] M2 → M1 ⓗ⇀*[p::◊] M2.
+lemma lhap_step_rc: ∀p,M1,M2. M1 ⓗ⇀[p] M2 → M1 ⓗ⇀*[p::◊] M2.
 /2 width=1/
 qed.
 
@@ -42,10 +42,19 @@ lemma lhap_inv_cons: ∀s,M1,M2. M1 ⓗ⇀*[s] M2 → ∀q,r. q::r = s →
 /2 width=3 by lstar_inv_cons/
 qed-.
 
-lemma lhap_inv_lhap1: ∀p,M1,M2. M1 ⓗ⇀*[p::◊] M2 → M1 ⓗ⇀[p] M2.
+lemma lhap_inv_step_rc: ∀p,M1,M2. M1 ⓗ⇀*[p::◊] M2 → M1 ⓗ⇀[p] M2.
 /2 width=1 by lstar_inv_step/
 qed-.
 
+lemma lhap_inv_pos: ∀s,M1,M2. M1 ⓗ⇀*[s] M2 → 0 < |s| →
+                    ∃∃p,r,M. p::r = s & M1 ⓗ⇀[p] M & M ⓗ⇀*[r] M2.
+/2 width=1 by lstar_inv_pos/
+qed-.
+
+lemma lhap_compatible_dx: ho_compatible_dx lhap.
+/3 width=1/
+qed.
+
 lemma lhap_lift: ∀s. liftable (lhap s).
 /2 width=1/
 qed.
@@ -62,14 +71,15 @@ theorem lhap_mono: ∀s. singlevalued … (lhap s).
 /3 width=7 by lstar_singlevalued, lhap1_mono/
 qed-.
 
-theorem lhap_trans: ∀s1,M1,M. M1 ⓗ⇀*[s1] M →
-                    ∀s2,M2. M ⓗ⇀*[s2] M2 → M1 ⓗ⇀*[s1@s2] M2.
-/2 width=3 by lstar_trans/
+theorem lhap_trans: ltransitive … lhap.
+/2 width=3 by lstar_ltransitive/
 qed-.
 
-lemma lhap_appl: ∀s,B,A1,A2. A1 ⓗ⇀*[s] A2 → @B.A1 ⓗ⇀*[dx:::s] @B.A2.
-#s #B #A1 #A2 #H @(lstar_ind_l ????????? H) -s -A1 // /3 width=3/
-qed.
+lemma lhap_step_dx: ∀s,M1,M. M1 ⓗ⇀*[s] M →
+                    ∀p,M2. M ⓗ⇀[p] M2 → M1 ⓗ⇀*[s@p::◊] M2.
+#s #M1 #M #HM1 #p #M2 #HM2
+@(lhap_trans … HM1) /2 width=1/
+qed-.
 
 lemma head_lsreds_lhap: ∀s,M1,M2. M1 ⇀*[s] M2 → is_head s → M1 ⓗ⇀*[s] M2.
 #s #M1 #M2 #H @(lstar_ind_l ????????? H) -s -M1 //
@@ -87,12 +97,3 @@ lemma lhap_inv_lsreds: ∀s,M1,M2. M1 ⓗ⇀*[s] M2 → M1 ⇀*[s] M2.
 #p #s #M1 #M #HM1 #_ #IHM2
 lapply (lhap1_inv_lsred … HM1) -HM1 /2 width=3/
 qed-.
-
-lemma lhap_fwd_le: ∀s,M1,M2. M1 ⓗ⇀*[s] M2 → is_le s.
-#s #M1 #M2 #H @(lstar_ind_l ????????? H) -s -M1 /3 width=3/
-#a1 #s #M1 #M #HM1 #IHM1
-generalize in match HM1; -HM1
-cases IHM1 -s -M -M2 //
-#a #M0 #M #HM0 #s #M2 #_ #HM10 #H -M2
-lapply (lhap1_fwd_le … HM10 … HM0) -M -M0 -M1 /2 width=1/
-qed-.