X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Flprs.ma;h=6e8431959463f9f3410b36dd3c01d78786c91c14;hb=ab0d181f9a89f461a9c280f42a949a2dc2abe44c;hp=2e6a2516770cd559b84b8006c1639ddec5d14596;hpb=29973426e0227ee48368d1c24dc0c17bf2baef77;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lprs.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lprs.ma
index 2e6a25167..6e8431959 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lprs.ma
@@ -12,59 +12,60 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predsnstar_2.ma".
+include "basic_2/notation/relations/predsnstar_3.ma".
 include "basic_2/grammar/lpx_sn_tc.ma".
 include "basic_2/reduction/lpr.ma".
 
 (* SN PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS ****************************)
 
-definition lprs: relation lenv ≝ TC … lpr.
+definition lprs: relation3 genv lenv lenv ≝
+                 λG. TC … (lpr G).
 
 interpretation "parallel computation (local environment, sn variant)"
-   'PRedSnStar L1 L2 = (lprs L1 L2).
+   'PRedSnStar G L1 L2 = (lprs G L1 L2).
 
 (* Basic eliminators ********************************************************)
 
-lemma lprs_ind: ∀L1. ∀R:predicate lenv. R L1 →
-                (∀L,L2. L1 ⊢ ➡* L → ⦃G, L⦄ ⊢ ➡ L2 → R L → R L2) →
-                ∀L2. L1 ⊢ ➡* L2 → R L2.
-#L1 #R #HL1 #IHL1 #L2 #HL12
+lemma lprs_ind: ∀G,L1. ∀R:predicate lenv. R L1 →
+                (∀L,L2. ⦃G, L1⦄ ⊢ ➡* L → ⦃G, L⦄ ⊢ ➡ L2 → R L → R L2) →
+                ∀L2. ⦃G, L1⦄ ⊢ ➡* L2 → R L2.
+#G #L1 #R #HL1 #IHL1 #L2 #HL12
 @(TC_star_ind … HL1 IHL1 … HL12) //
 qed-.
 
-lemma lprs_ind_dx: ∀L2. ∀R:predicate lenv. R L2 →
-                   (∀L1,L. L1 ⊢ ➡ L → ⦃G, L⦄ ⊢ ➡* L2 → R L → R L1) →
-                   ∀L1. L1 ⊢ ➡* L2 → R L1.
-#L2 #R #HL2 #IHL2 #L1 #HL12
+lemma lprs_ind_dx: ∀G,L2. ∀R:predicate lenv. R L2 →
+                   (∀L1,L. ⦃G, L1⦄ ⊢ ➡ L → ⦃G, L⦄ ⊢ ➡* L2 → R L → R L1) →
+                   ∀L1. ⦃G, L1⦄ ⊢ ➡* L2 → R L1.
+#G #L2 #R #HL2 #IHL2 #L1 #HL12
 @(TC_star_ind_dx … HL2 IHL2 … HL12) //
 qed-.
 
 (* Basic properties *********************************************************)
 
-lemma lpr_lprs: ∀L1,L2. L1 ⊢ ➡ L2 → L1 ⊢ ➡* L2.
+lemma lpr_lprs: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L1⦄ ⊢ ➡* L2.
 /2 width=1/ qed.
 
-lemma lprs_refl: ∀L. ⦃G, L⦄ ⊢ ➡* L.
+lemma lprs_refl: ∀G,L. ⦃G, L⦄ ⊢ ➡* L.
 /2 width=1/ qed.
 
-lemma lprs_strap1: ∀L1,L,L2. L1 ⊢ ➡* L → ⦃G, L⦄ ⊢ ➡ L2 → L1 ⊢ ➡* L2.
+lemma lprs_strap1: ∀G,L1,L,L2. ⦃G, L1⦄ ⊢ ➡* L → ⦃G, L⦄ ⊢ ➡ L2 → ⦃G, L1⦄ ⊢ ➡* L2.
 /2 width=3/ qed.
 
-lemma lprs_strap2: ∀L1,L,L2. L1 ⊢ ➡ L → ⦃G, L⦄ ⊢ ➡* L2 → L1 ⊢ ➡* L2.
+lemma lprs_strap2: ∀G,L1,L,L2. ⦃G, L1⦄ ⊢ ➡ L → ⦃G, L⦄ ⊢ ➡* L2 → ⦃G, L1⦄ ⊢ ➡* L2.
 /2 width=3/ qed.
 
-lemma lprs_pair_refl: ∀L1,L2. L1 ⊢ ➡* L2 → ∀I,V. L1. ⓑ{I} V ⊢ ➡* L2. ⓑ{I} V.
+lemma lprs_pair_refl: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡* L2 → ∀I,V. ⦃G, L1.ⓑ{I}V⦄ ⊢ ➡* L2.ⓑ{I}V.
 /2 width=1 by TC_lpx_sn_pair_refl/ qed.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma lprs_inv_atom1: ∀L2. ⋆ ⊢ ➡* L2 → L2 = ⋆.
+lemma lprs_inv_atom1: ∀G,L2. ⦃G, ⋆⦄ ⊢ ➡* L2 → L2 = ⋆.
 /2 width=2 by TC_lpx_sn_inv_atom1/ qed-.
 
-lemma lprs_inv_atom2: ∀L1. L1 ⊢ ➡* ⋆ → L1 = ⋆.
+lemma lprs_inv_atom2: ∀G,L1. ⦃G, L1⦄ ⊢ ➡* ⋆ → L1 = ⋆.
 /2 width=2 by TC_lpx_sn_inv_atom2/ qed-.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma lprs_fwd_length: ∀L1,L2. L1 ⊢ ➡* L2 → |L1| = |L2|.
+lemma lprs_fwd_length: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡* L2 → |L1| = |L2|.
 /2 width=2 by TC_lpx_sn_fwd_length/ qed-.