update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / jsx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx.ma
index 685ff2a369facfe57b60b680c1a4adde330634ec..a318423b5b1ab82ccd979a4a90b1cd5a498e7888 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx.ma
@@ -23,9 +23,9 @@ include "basic_2/rt_computation/rsx.ma".
 inductive jsx (h) (G): relation lenv ≝
 | jsx_atom: jsx h G (⋆) (⋆)
 | jsx_bind: ∀I,K1,K2. jsx h G K1 K2 →
-            jsx h G (K1.ⓘ{I}) (K2.ⓘ{I})
+            jsx h G (K1.ⓘ[I]) (K2.ⓘ[I])
 | jsx_pair: ∀I,K1,K2,V. jsx h G K1 K2 →
-            G â\8a¢ â¬\88*[h,V] ð\9d\90\92â¦\83K2â¦\84 â\86\92 jsx h G (K1.â\93\91{I}V) (K2.ⓧ)
+            G â\8a¢ â¬\88*[h,V] ð\9d\90\92â\9dªK2â\9d« â\86\92 jsx h G (K1.â\93\91[I]V) (K2.ⓧ)
 .
 
 interpretation
@@ -48,9 +48,9 @@ lemma jsx_inv_atom_sn (h) (G): ∀L2. G ⊢ ⋆ ⊒[h] L2 → L2 = ⋆.
 
 fact jsx_inv_bind_sn_aux (h) (G):
      ∀L1,L2. G ⊢ L1 ⊒[h] L2 →
-     ∀I,K1. L1 = K1.ⓘ{I} →
-     ∨∨ ∃∃K2. G ⊢ K1 ⊒[h] K2 & L2 = K2.ⓘ{I}
-      | â\88\83â\88\83J,K2,V. G â\8a¢ K1 â\8a\92[h] K2 & G â\8a¢ â¬\88*[h,V] ð\9d\90\92â¦\83K2â¦\84  & I = BPair J V & L2 = K2.ⓧ.
+     ∀I,K1. L1 = K1.ⓘ[I] →
+     ∨∨ ∃∃K2. G ⊢ K1 ⊒[h] K2 & L2 = K2.ⓘ[I]
+      | â\88\83â\88\83J,K2,V. G â\8a¢ K1 â\8a\92[h] K2 & G â\8a¢ â¬\88*[h,V] ð\9d\90\92â\9dªK2â\9d«  & I = BPair J V & L2 = K2.ⓧ.
 #h #G #L1 #L2 * -L1 -L2
 [ #J #L1 #H destruct
 | #I #K1 #K2 #HK12 #J #L1 #H destruct /3 width=3 by ex2_intro, or_introl/
@@ -59,18 +59,18 @@ fact jsx_inv_bind_sn_aux (h) (G):
 qed-.
 
 lemma jsx_inv_bind_sn (h) (G):
-     ∀I,K1,L2. G ⊢ K1.ⓘ{I} ⊒[h] L2 →
-     ∨∨ ∃∃K2. G ⊢ K1 ⊒[h] K2 & L2 = K2.ⓘ{I}
-      | â\88\83â\88\83J,K2,V. G â\8a¢ K1 â\8a\92[h] K2 & G â\8a¢ â¬\88*[h,V] ð\9d\90\92â¦\83K2â¦\84  & I = BPair J V & L2 = K2.ⓧ.
+     ∀I,K1,L2. G ⊢ K1.ⓘ[I] ⊒[h] L2 →
+     ∨∨ ∃∃K2. G ⊢ K1 ⊒[h] K2 & L2 = K2.ⓘ[I]
+      | â\88\83â\88\83J,K2,V. G â\8a¢ K1 â\8a\92[h] K2 & G â\8a¢ â¬\88*[h,V] ð\9d\90\92â\9dªK2â\9d«  & I = BPair J V & L2 = K2.ⓧ.
 /2 width=3 by jsx_inv_bind_sn_aux/ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
 (* Basic_2A1: uses: lcosx_inv_pair *)
 lemma jsx_inv_pair_sn (h) (G):
-      ∀I,K1,L2,V. G ⊢ K1.ⓑ{I}V ⊒[h] L2 →
-      ∨∨ ∃∃K2. G ⊢ K1 ⊒[h] K2 & L2 = K2.ⓑ{I}V
-       | â\88\83â\88\83K2. G â\8a¢ K1 â\8a\92[h] K2 & G â\8a¢ â¬\88*[h,V] ð\9d\90\92â¦\83K2â¦\84 & L2 = K2.ⓧ.
+      ∀I,K1,L2,V. G ⊢ K1.ⓑ[I]V ⊒[h] L2 →
+      ∨∨ ∃∃K2. G ⊢ K1 ⊒[h] K2 & L2 = K2.ⓑ[I]V
+       | â\88\83â\88\83K2. G â\8a¢ K1 â\8a\92[h] K2 & G â\8a¢ â¬\88*[h,V] ð\9d\90\92â\9dªK2â\9d« & L2 = K2.ⓧ.
 #h #G #I #K1 #L2 #V #H elim (jsx_inv_bind_sn … H) -H *
 [ /3 width=3 by ex2_intro, or_introl/
 | #J #K2 #X #HK12 #HX #H1 #H2 destruct /3 width=4 by ex3_intro, or_intror/
@@ -87,8 +87,8 @@ qed-.
 (* Advanced forward lemmas **************************************************)
 
 lemma jsx_fwd_bind_sn (h) (G):
-      ∀I1,K1,L2. G ⊢ K1.ⓘ{I1} ⊒[h] L2 →
-      ∃∃I2,K2. G ⊢ K1 ⊒[h] K2 & L2 = K2.ⓘ{I2}.
+      ∀I1,K1,L2. G ⊢ K1.ⓘ[I1] ⊒[h] L2 →
+      ∃∃I2,K2. G ⊢ K1 ⊒[h] K2 & L2 = K2.ⓘ[I2].
 #h #G #I1 #K1 #L2 #H elim (jsx_inv_bind_sn … H) -H *
 /2 width=4 by ex2_2_intro/
 qed-.