partial commit: just the components before "static" ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / yprs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/yprs.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/yprs.ma
index 30c90c43e003f1418cde79b01e33eb6f57a101b7..a8be72e7255ef2700b301c6d5aba8e3781f2e044 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/yprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/yprs.ma
@@ -12,7 +12,9 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/ltprs.ma".
+include "basic_2/notation/relations/btpredstar_6.ma".
+include "basic_2/substitution/fsupp.ma".
+include "basic_2/computation/lprs.ma".
 include "basic_2/dynamic/ypr.ma".
 
 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
@@ -26,13 +28,13 @@ interpretation "'big tree' parallel computation (closure)"
 (* Basic eliminators ********************************************************)
 
 lemma yprs_ind: ∀h,g,L1,T1. ∀R:relation2 lenv term. R L1 T1 →
-                (∀L,L2,T,T2. h ⊢ ⦃L1, T1⦄ ≥[g] ⦃L, T⦄ → h ⊢ ⦃L, T⦄ ≽[g] ⦃L2, T2⦄ → R L T → R L2 T2) →
-                ∀L2,T2. h ⊢ ⦃L1, T1⦄ ≥[g] ⦃L2, T2⦄ → R L2 T2.
+                (∀L,L2,T,T2. h ⊢ ⦃L1, T1⦄ ≥[h, g] ⦃L, T⦄ → h ⊢ ⦃L, T⦄ ≽[h, g] ⦃L2, T2⦄ → R L T → R L2 T2) →
+                ∀L2,T2. h ⊢ ⦃L1, T1⦄ ≥[h, g] ⦃L2, T2⦄ → R L2 T2.
 /3 width=7 by bi_TC_star_ind/ qed-.
 
 lemma yprs_ind_dx: ∀h,g,L2,T2. ∀R:relation2 lenv term. R L2 T2 →
-                   (∀L1,L,T1,T. h ⊢ ⦃L1, T1⦄ ≽[g] ⦃L, T⦄ → h ⊢ ⦃L, T⦄ ≥[g] ⦃L2, T2⦄ → R L T → R L1 T1) →
-                   ∀L1,T1. h ⊢ ⦃L1, T1⦄ ≥[g] ⦃L2, T2⦄ → R L1 T1.
+                   (∀L1,L,T1,T. h ⊢ ⦃L1, T1⦄ ≽[h, g] ⦃L, T⦄ → h ⊢ ⦃L, T⦄ ≥[h, g] ⦃L2, T2⦄ → R L T → R L1 T1) →
+                   ∀L1,T1. h ⊢ ⦃L1, T1⦄ ≥[h, g] ⦃L2, T2⦄ → R L1 T1.
 /3 width=7 by bi_TC_star_ind_dx/ qed-.
 
 (* Basic properties *********************************************************)
@@ -40,39 +42,41 @@ lemma yprs_ind_dx: ∀h,g,L2,T2. ∀R:relation2 lenv term. R L2 T2 →
 lemma yprs_refl: ∀h,g. bi_reflexive … (yprs h g).
 /2 width=1/ qed.
 
-lemma ypr_yprs: ∀h,g,L1,L2,T1,T2. h ⊢ ⦃L1, T1⦄ ≽[g] ⦃L2, T2⦄ →
-                h ⊢ ⦃L1, T1⦄ ≥[g] ⦃L2, T2⦄.
+lemma ypr_yprs: ∀h,g,L1,L2,T1,T2. h ⊢ ⦃L1, T1⦄ ≽[h, g] ⦃L2, T2⦄ →
+                h ⊢ ⦃L1, T1⦄ ≥[h, g] ⦃L2, T2⦄.
 /2 width=1/ qed.
 
-lemma yprs_strap1: ∀h,g,L1,L,L2,T1,T,T2. h ⊢ ⦃L1, T1⦄ ≥[g] ⦃L, T⦄ →
-                   h ⊢ ⦃L, T⦄ ≽[g] ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ ≥[g] ⦃L2, T2⦄.
+lemma yprs_strap1: ∀h,g,L1,L,L2,T1,T,T2. h ⊢ ⦃L1, T1⦄ ≥[h, g] ⦃L, T⦄ →
+                   h ⊢ ⦃L, T⦄ ≽[h, g] ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ ≥[h, g] ⦃L2, T2⦄.
 /2 width=4/ qed-.
 
-lemma yprs_strap2: ∀h,g,L1,L,L2,T1,T,T2. h ⊢ ⦃L1, T1⦄ ≽[g] ⦃L, T⦄ →
-                   h ⊢ ⦃L, T⦄ ≥[g] ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ ≥[g] ⦃L2, T2⦄.
+lemma yprs_strap2: ∀h,g,L1,L,L2,T1,T,T2. h ⊢ ⦃L1, T1⦄ ≽[h, g] ⦃L, T⦄ →
+                   h ⊢ ⦃L, T⦄ ≥[h, g] ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ ≥[h, g] ⦃L2, T2⦄.
 /2 width=4/ qed-.
 
-lemma fw_yprs: ∀h,g,L1,L2,T1,T2. ♯{L2, T2} < ♯{L1, T1} →
-               h ⊢ ⦃L1, T1⦄ ≥[g] ⦃L2, T2⦄.
-/3 width=1/ qed.
+(* Note: this is a general property of bi_TC *)
+lemma fsupp_yprs: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ ⊃+ ⦃L2, T2⦄ →
+                  h ⊢ ⦃L1, T1⦄ ≥[h, g] ⦃L2, T2⦄.
+#h #g #L1 #L2 #T1 #T2 #H @(fsupp_ind … L2 T2 H) -L2 -T2 /3 width=1/ /3 width=4/
+qed.
 
-lemma cprs_yprs: ∀h,g,L,T1,T2. L ⊢ T1 ➡* T2 → h ⊢ ⦃L, T1⦄ ≥[g] ⦃L, T2⦄.
+lemma cprs_yprs: ∀h,g,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → h ⊢ ⦃L, T1⦄ ≥[h, g] ⦃L, T2⦄.
 #h #g #L #T1 #T2 #H @(cprs_ind … H) -T2 // /3 width=4 by ypr_cpr, yprs_strap1/
 qed.
 
-lemma ltprs_yprs: ∀h,g,L1,L2,T. L1 ➡* L2 → h ⊢ ⦃L1, T⦄ ≥[g] ⦃L2, T⦄.
-#h #g #L1 #L2 #T #H @(ltprs_ind … H) -L2 // /3 width=4 by ypr_ltpr, yprs_strap1/
+lemma lprs_yprs: ∀h,g,L1,L2,T. L1 ⊢ ➡* L2 → h ⊢ ⦃L1, T⦄ ≥[h, g] ⦃L2, T⦄.
+#h #g #L1 #L2 #T #H @(lprs_ind … H) -L2 // /3 width=4 by ypr_lpr, yprs_strap1/
 qed.
 
-lemma sstas_yprs: ∀h,g,L,T1,T2. ⦃h, L⦄ ⊢ T1 •*[g] T2 →
-                  h ⊢ ⦃L, T1⦄ ≥[g] ⦃L, T2⦄.
+lemma sstas_yprs: ∀h,g,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*[h, g] T2 →
+                  h ⊢ ⦃L, T1⦄ ≥[h, g] ⦃L, T2⦄.
 #h #g #L #T1 #T2 #H @(sstas_ind … H) -T2 // /3 width=4 by ypr_ssta, yprs_strap1/
 qed.
 
-lemma lsubsv_yprs: ∀h,g,L1,L2,T. h ⊢ L2 ⊩:⊑[g] L1 → h ⊢ ⦃L1, T⦄ ≥[g] ⦃L2, T⦄.
+lemma lsubsv_yprs: ∀h,g,L1,L2,T. h ⊢ L2 ¡⊑[h, g] L1 → h ⊢ ⦃L1, T⦄ ≥[h, g] ⦃L2, T⦄.
 /3 width=1/ qed.
 
-lemma ltpr_cprs_yprs: ∀h,g,L1,L2,T1,T2. L1 ➡ L2 → L2 ⊢ T1 ➡* T2 →
-                      h ⊢ ⦃L1, T1⦄ ≥[g] ⦃L2, T2⦄.
-/3 width=4 by yprs_strap2, ypr_ltpr, cprs_yprs/
+lemma cprs_lpr_yprs: ∀h,g,L1,L2,T1,T2. L1 ⊢ T1 ➡* T2 → L1 ⊢ ➡ L2 →
+                     h ⊢ ⦃L1, T1⦄ ≥[h, g] ⦃L2, T2⦄.
+/3 width=4 by yprs_strap1, ypr_lpr, cprs_yprs/
 qed.