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

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/ygt.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/ygt.ma
index b593d637de03bb4cb7676417d5716a902a0920a8..7b50bfdcfd08da392bfebb3c24325068815fa8d6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/ygt.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/ygt.ma
@@ -19,9 +19,9 @@ include "basic_2/dynamic/yprs.ma".
 (* "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **********************)
 
 inductive ygt (h) (g) (L1) (T1): relation2 lenv term ≝
-| ygt_inj : ∀L,L2,T,T2. h ⊢ ⦃L1, T1⦄ ≥[g] ⦃L, T⦄ → h ⊢ ⦃L, T⦄ ≻[g] ⦃L2, T2⦄ →
+| ygt_inj : ∀L,L2,T,T2. h ⊢ ⦃L1, T1⦄ ≥[h, g] ⦃L, T⦄ → h ⊢ ⦃L, T⦄ ≻[h, g] ⦃L2, T2⦄ →
             ygt h g L1 T1 L2 T2
-| ygt_step: ∀L,L2,T. ygt h g L1 T1 L T → L ⊢ ➡ L2 → ygt h g L1 T1 L2 T
+| ygt_step: ∀L,L2,T. ygt h g L1 T1 L T → ⦃G, L⦄ ⊢ ➡ L2 → ygt h g L1 T1 L2 T
 .
 
 interpretation "'big tree' proper parallel computation (closure)"
@@ -29,49 +29,49 @@ interpretation "'big tree' proper parallel computation (closure)"
 
 (* Basic forvard lemmas *****************************************************)
 
-lemma ygt_fwd_yprs: ∀h,g,L1,L2,T1,T2. h ⊢ ⦃L1, T1⦄ >[g] ⦃L2, T2⦄ →
-                    h ⊢ ⦃L1, T1⦄ ≥[g] ⦃L2, T2⦄.
+lemma ygt_fwd_yprs: ∀h,g,L1,L2,T1,T2. h ⊢ ⦃L1, T1⦄ >[h, g] ⦃L2, T2⦄ →
+                    h ⊢ ⦃L1, T1⦄ ≥[h, g] ⦃L2, T2⦄.
 #h #g #L1 #L2 #T1 #T2 #H elim H -L2 -T2
 /3 width=4 by yprs_strap1, ysc_ypr, ypr_lpr/
 qed-.
 
 (* Basic properties *********************************************************)
 
-lemma ysc_ygt: ∀h,g,L1,L2,T1,T2. h ⊢ ⦃L1, T1⦄ ≻[g] ⦃L2, T2⦄ →
-               h ⊢ ⦃L1, T1⦄ >[g] ⦃L2, T2⦄.
+lemma ysc_ygt: ∀h,g,L1,L2,T1,T2. h ⊢ ⦃L1, T1⦄ ≻[h, g] ⦃L2, T2⦄ →
+               h ⊢ ⦃L1, T1⦄ >[h, g] ⦃L2, T2⦄.
 /3 width=4/ qed.
 
-lemma ygt_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 ygt_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⦄.
 #h #g #L1 #L #L2 #T1 #T #T2 #H1 #H2
 lapply (ygt_fwd_yprs … H1) #H0
 elim (ypr_inv_ysc … H2) -H2 [| * #HL2 #H destruct ] /2 width=4/
 qed-.
 
-lemma ygt_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 ygt_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⦄.
 #h #g #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim H2 -L2 -T2
 [ /3 width=4 by ygt_inj, yprs_strap2/ | /2 width=3/ ]
 qed-.
 
-lemma ygt_yprs_trans: ∀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 ygt_yprs_trans: ∀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⦄.
 #h #g #L1 #L #L2 #T1 #T #T2 #HT1 #HT2 @(yprs_ind … HT2) -L2 -T2 //
 /2 width=4 by ygt_strap1/
 qed-.
 
-lemma yprs_ygt_trans: ∀h,g,L1,L,T1,T. h ⊢ ⦃L1, T1⦄ ≥[g] ⦃L, T⦄ →
-                      ∀L2,T2. h ⊢ ⦃L, T⦄ >[g] ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ >[g] ⦃L2, T2⦄.
+lemma yprs_ygt_trans: ∀h,g,L1,L,T1,T. h ⊢ ⦃L1, T1⦄ ≥[h, g] ⦃L, T⦄ →
+                      ∀L2,T2. h ⊢ ⦃L, T⦄ >[h, g] ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ >[h, g] ⦃L2, T2⦄.
 #h #g #L1 #L #T1 #T #HT1 @(yprs_ind … HT1) -L -T //
 /3 width=4 by ygt_strap2/
 qed-.
 
-lemma fsupp_ygt: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ ⊃+ ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ >[g] ⦃L2, T2⦄.
+lemma fsupp_ygt: ∀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_ygt: ∀h,g,L,T1,T2. L ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) →
-                h ⊢ ⦃L, T1⦄ >[g] ⦃L, T2⦄.
+lemma cprs_ygt: ∀h,g,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) →
+                h ⊢ ⦃L, T1⦄ >[h, g] ⦃L, T2⦄.
 #h #g #L #T1 #T2 #H @(cprs_ind … H) -T2
 [ #H elim H //
 | #T #T2 #_ #HT2 #IHT1 #HT12
@@ -83,8 +83,8 @@ lemma cprs_ygt: ∀h,g,L,T1,T2. L ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) →
 ]
 qed.
 
-lemma sstas_ygt: ∀h,g,L,T1,T2. ⦃h, L⦄ ⊢ T1 •*[g] T2 → (T1 = T2 → ⊥) →
-                 h ⊢ ⦃L, T1⦄ >[g] ⦃L, T2⦄.
+lemma sstas_ygt: ∀h,g,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*[h, g] T2 → (T1 = T2 → ⊥) →
+                 h ⊢ ⦃L, T1⦄ >[h, g] ⦃L, T2⦄.
 #h #g #L #T1 #T2 #H @(sstas_ind … H) -T2
 [ #H elim H //
 | #T #T2 #l #_ #HT2 #IHT1 #HT12 -HT12
@@ -96,6 +96,6 @@ lemma sstas_ygt: ∀h,g,L,T1,T2. ⦃h, L⦄ ⊢ T1 •*[g] T2 → (T1 = T2 → 
 ]
 qed.
 
-lemma lsubsv_ygt: ∀h,g,L1,L2,T. h ⊢ L2 ¡⊑[g] L1 → (L1 = L2 → ⊥) →
-                  h ⊢ ⦃L1, T⦄ >[g] ⦃L2, T⦄.
+lemma lsubsv_ygt: ∀h,g,L1,L2,T. h ⊢ L2 ¡⊑[h, g] L1 → (L1 = L2 → ⊥) →
+                  h ⊢ ⦃L1, T⦄ >[h, g] ⦃L2, T⦄.
 /4 width=1/ qed.