(* *)
(**************************************************************************)
-include "basic_2/computation/ltprs.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 *****************************)
h ⊢ ⦃L, T⦄ ≥[g] ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ ≥[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⦄ ≥[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⦄.
#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⦄ ≥[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 #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 ¡⊑[g] L1 → h ⊢ ⦃L1, T⦄ ≥[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⦄ ≥[g] ⦃L2, T2⦄.
+/3 width=4 by yprs_strap1, ypr_lpr, cprs_yprs/
qed.