update in basic_2

[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 05292539f92f0fb191b3e266cd2189ea700e756e..2e477082b0541abeb609e152e61899d0b9e096d7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground_2/xoa/ex_4_3.ma".
 include "basic_2/notation/relations/topredtysnstrong_4.ma".
 include "basic_2/rt_computation/rsx.ma".
 
@@ -22,9 +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 ⊢ ⬈*[h,V] 𝐒⦃K2⦄ → jsx h G (K1.ⓑ{I}V) (K2.ⓧ)
+            G ⊢ ⬈*𝐒[h,V] K2 → jsx h G (K1.ⓑ[I]V) (K2.ⓧ)
 .
 
 interpretation
@@ -42,14 +43,15 @@ fact jsx_inv_atom_sn_aux (h) (G):
 ]
 qed-.
 
-lemma jsx_inv_atom_sn (h) (G): ∀L2. G ⊢ ⋆ ⊒[h] L2 → L2 = ⋆.
+lemma jsx_inv_atom_sn (h) (G):
+      ∀L2. G ⊢ ⋆ ⊒[h] L2 → L2 = ⋆.
 /2 width=5 by jsx_inv_atom_sn_aux/ qed-.
 
 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}
-      | ∃∃J,K2,V. G ⊢ K1 ⊒[h] K2 & G ⊢ ⬈*[h,V] 𝐒⦃K2⦄  & I = BPair J V & L2 = K2.ⓧ.
+     ∀I,K1. L1 = K1.ⓘ[I] →
+     ∨∨ ∃∃K2. G ⊢ K1 ⊒[h] K2 & L2 = K2.ⓘ[I]
+      | ∃∃J,K2,V. G ⊢ K1 ⊒[h] K2 & G ⊢ ⬈*𝐒[h,V] K2 & 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/
@@ -58,18 +60,18 @@ 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}
-      | ∃∃J,K2,V. G ⊢ K1 ⊒[h] K2 & G ⊢ ⬈*[h,V] 𝐒⦃K2⦄  & I = BPair J V & L2 = K2.ⓧ.
+     ∀I,K1,L2. G ⊢ K1.ⓘ[I] ⊒[h] L2 →
+     ∨∨ ∃∃K2. G ⊢ K1 ⊒[h] K2 & L2 = K2.ⓘ[I]
+      | ∃∃J,K2,V. G ⊢ K1 ⊒[h] K2 & G ⊢ ⬈*𝐒[h,V] K2 & 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
-       | ∃∃K2. G ⊢ K1 ⊒[h] K2 & G ⊢ ⬈*[h,V] 𝐒⦃K2⦄ & L2 = K2.ⓧ.
+      ∀I,K1,L2,V. G ⊢ K1.ⓑ[I]V ⊒[h] L2 →
+      ∨∨ ∃∃K2. G ⊢ K1 ⊒[h] K2 & L2 = K2.ⓑ[I]V
+       | ∃∃K2. G ⊢ K1 ⊒[h] K2 & G ⊢ ⬈*𝐒[h,V] K2 & 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/
@@ -86,8 +88,8 @@ 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-.