- lambda: first half of the standardization theorem is proved!

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

diff --git a/matita/matita/contribs/lambda/labelled_sequential_computation.ma b/matita/matita/contribs/lambda/labelled_sequential_computation.ma
index 52fef251405d9000fe9f9ff45b3a388d257f693d..4a7392a7646eaff25e913ebfc1e9919f28e5d69b 100644 (file)
--- a/matita/matita/contribs/lambda/labelled_sequential_computation.ma
+++ b/matita/matita/contribs/lambda/labelled_sequential_computation.ma
@@ -12,12 +12,12 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "redex_pointer_sequence.ma".
+include "pointer_sequence.ma".
 include "labelled_sequential_reduction.ma".
 
 (* LABELLED SEQUENTIAL COMPUTATION (MULTISTEP) ******************************)
 
-definition lsreds: rpseq → relation term ≝ lstar … lsred.
+definition lsreds: pseq → relation term ≝ lstar … lsred.
 
 interpretation "labelled sequential computation"
    'SeqRedStar M s N = (lsreds s M N).
@@ -26,7 +26,7 @@ notation "hvbox( M break ⇀* [ term 46 s ] break term 46 N )"
    non associative with precedence 45
    for @{ 'SeqRedStar $M $s $N }.
 
-lemma lsred_lsreds: ∀p,M1,M2. M1 ⇀[p] M2 → M1 ⇀*[p::◊] M2.
+lemma lsreds_step_rc: ∀p,M1,M2. M1 ⇀[p] M2 → M1 ⇀*[p::◊] M2.
 /2 width=1/
 qed.
 
@@ -39,10 +39,22 @@ lemma lsreds_inv_cons: ∀s,M1,M2. M1 ⇀*[s] M2 → ∀q,r. q::r = s →
 /2 width=3 by lstar_inv_cons/
 qed-.
 
-lemma lsreds_inv_lsred: ∀p,M1,M2. M1 ⇀*[p::◊] M2 → M1 ⇀[p] M2.
+lemma lsreds_inv_step_rc: ∀p,M1,M2. M1 ⇀*[p::◊] M2 → M1 ⇀[p] M2.
 /2 width=1 by lstar_inv_step/
 qed-.
 
+lemma lsred_compatible_rc: ho_compatible_rc lsreds.
+/3 width=1/
+qed.
+
+lemma lsred_compatible_sn: ho_compatible_sn lsreds.
+/3 width=1/
+qed.
+
+lemma lsred_compatible_dx: ho_compatible_dx lsreds.
+/3 width=1/
+qed.
+
 lemma lsreds_lift: ∀s. liftable (lsreds s).
 /2 width=1/
 qed.
@@ -59,15 +71,14 @@ theorem lsreds_mono: ∀s. singlevalued … (lsreds s).
 /3 width=7 by lstar_singlevalued, lsred_mono/
 qed-.
 
-theorem lsreds_trans: ∀s1,M1,M. M1 ⇀*[s1] M →
-                      ∀s2,M2. M ⇀*[s2] M2 → M1 ⇀*[s1@s2] M2.
-/2 width=3 by lstar_trans/
+theorem lsreds_trans: ltransitive … lsreds.
+/2 width=3 by lstar_ltransitive/
 qed-.
 
 (* Note: "|s|" should be unparetesized *)
 lemma lsreds_fwd_mult: ∀s,M1,M2. M1 ⇀*[s] M2 → #{M2} ≤ #{M1} ^ (2 ^ (|s|)).
-#s #M1 #M2 #H elim H -s -M1 -M2 normalize //
-#p #M1 #M #HM1 #s #M2 #_ #IHM2
+#s #M1 #M2 #H @(lstar_ind_l ????????? H) -s -M1 normalize //
+#p #s #M1 #M #HM1 #_ #IHM2
 lapply (lsred_fwd_mult … HM1) -p #HM1
 @(transitive_le … IHM2) -M2
 /3 width=1 by le_exp1, lt_O_exp, lt_to_le/ (**) (* auto: slow without trace *)