X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Fcpx.ma;h=9532929a54c81e954c0b18eb09855c8f89ec7375;hb=d8d00d6f6694155be5be486a8239f5953efe28b7;hp=005c4335504d9dbf4d79f963c654bb888b4461db;hpb=5b5dca0c118dfbe3ba8f0514ef07549544eb7810;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx.ma
index 005c43355..9532929a5 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx.ma
@@ -12,6 +12,13 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground_2/xoa/ex_3_4.ma".
+include "ground_2/xoa/ex_4_1.ma".
+include "ground_2/xoa/ex_5_6.ma".
+include "ground_2/xoa/ex_6_6.ma".
+include "ground_2/xoa/ex_6_7.ma".
+include "ground_2/xoa/ex_7_7.ma".
+include "ground_2/xoa/or_4.ma".
 include "basic_2/notation/relations/predty_5.ma".
 include "basic_2/rt_transition/cpg.ma".
 
@@ -31,13 +38,13 @@ lemma cpx_ess: ∀h,G,L,s. ⦃G,L⦄ ⊢ ⋆s ⬈[h] ⋆(⫯[h]s).
 /2 width=2 by cpg_ess, ex_intro/ qed.
 
 lemma cpx_delta: ∀h,I,G,K,V1,V2,W2. ⦃G,K⦄ ⊢ V1 ⬈[h] V2 →
-                 ⬆*[1] V2 ≘ W2 → ⦃G,K.ⓑ{I}V1⦄ ⊢ #0 ⬈[h] W2.
+                 ⇧*[1] V2 ≘ W2 → ⦃G,K.ⓑ{I}V1⦄ ⊢ #0 ⬈[h] W2.
 #h * #G #K #V1 #V2 #W2 *
 /3 width=4 by cpg_delta, cpg_ell, ex_intro/
 qed.
 
 lemma cpx_lref: ∀h,I,G,K,T,U,i. ⦃G,K⦄ ⊢ #i ⬈[h] T →
-                ⬆*[1] T ≘ U → ⦃G,K.ⓘ{I}⦄ ⊢ #↑i ⬈[h] U.
+                ⇧*[1] T ≘ U → ⦃G,K.ⓘ{I}⦄ ⊢ #↑i ⬈[h] U.
 #h #I #G #K #T #U #i *
 /3 width=4 by cpg_lref, ex_intro/
 qed.
@@ -57,7 +64,7 @@ lemma cpx_flat: ∀h,I,G,L,V1,V2,T1,T2.
 qed.
 
 lemma cpx_zeta (h) (G) (L):
-               ∀T1,T. ⬆*[1] T ≘ T1 → ∀T2. ⦃G,L⦄ ⊢ T ⬈[h] T2 →
+               ∀T1,T. ⇧*[1] T ≘ T1 → ∀T2. ⦃G,L⦄ ⊢ T ⬈[h] T2 →
                ∀V. ⦃G,L⦄ ⊢ +ⓓV.T1 ⬈[h] T2.
 #h #G #L #T1 #T #HT1 #T2 *
 /3 width=4 by cpg_zeta, ex_intro/
@@ -77,15 +84,15 @@ qed.
 lemma cpx_beta: ∀h,p,G,L,V1,V2,W1,W2,T1,T2.
                 ⦃G,L⦄ ⊢ V1 ⬈[h] V2 → ⦃G,L⦄ ⊢ W1 ⬈[h] W2 → ⦃G,L.ⓛW1⦄ ⊢ T1 ⬈[h] T2 →
                 ⦃G,L⦄ ⊢ ⓐV1.ⓛ{p}W1.T1 ⬈[h] ⓓ{p}ⓝW2.V2.T2.
-#h #p #G #L #V1 #V2 #W1 #W2 #T1 #T2 * #cV #HV12 * #cW #HW12 * 
+#h #p #G #L #V1 #V2 #W1 #W2 #T1 #T2 * #cV #HV12 * #cW #HW12 *
 /3 width=2 by cpg_beta, ex_intro/
 qed.
 
 lemma cpx_theta: ∀h,p,G,L,V1,V,V2,W1,W2,T1,T2.
-                 ⦃G,L⦄ ⊢ V1 ⬈[h] V → ⬆*[1] V ≘ V2 → ⦃G,L⦄ ⊢ W1 ⬈[h] W2 →
+                 ⦃G,L⦄ ⊢ V1 ⬈[h] V → ⇧*[1] V ≘ V2 → ⦃G,L⦄ ⊢ W1 ⬈[h] W2 →
                  ⦃G,L.ⓓW1⦄ ⊢ T1 ⬈[h] T2 →
                  ⦃G,L⦄ ⊢ ⓐV1.ⓓ{p}W1.T1 ⬈[h] ⓓ{p}W2.ⓐV2.T2.
-#h #p #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 * #cV #HV1 #HV2 * #cW #HW12 * 
+#h #p #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 * #cV #HV1 #HV2 * #cW #HW12 *
 /3 width=4 by cpg_theta, ex_intro/
 qed.
 
@@ -111,9 +118,9 @@ qed.
 lemma cpx_inv_atom1: ∀h,J,G,L,T2. ⦃G,L⦄ ⊢ ⓪{J} ⬈[h] T2 →
                      ∨∨ T2 = ⓪{J}
                       | ∃∃s. T2 = ⋆(⫯[h]s) & J = Sort s
-                      | ∃∃I,K,V1,V2. ⦃G,K⦄ ⊢ V1 ⬈[h] V2 & ⬆*[1] V2 ≘ T2 &
+                      | ∃∃I,K,V1,V2. ⦃G,K⦄ ⊢ V1 ⬈[h] V2 & ⇧*[1] V2 ≘ T2 &
                                      L = K.ⓑ{I}V1 & J = LRef 0
-                      | ∃∃I,K,T,i. ⦃G,K⦄ ⊢ #i ⬈[h] T & ⬆*[1] T ≘ T2 &
+                      | ∃∃I,K,T,i. ⦃G,K⦄ ⊢ #i ⬈[h] T & ⇧*[1] T ≘ T2 &
                                    L = K.ⓘ{I} & J = LRef (↑i).
 #h #J #G #L #T2 * #c #H elim (cpg_inv_atom1 … H) -H *
 /4 width=8 by or4_intro0, or4_intro1, or4_intro2, or4_intro3, ex4_4_intro, ex2_intro, ex_intro/
@@ -127,7 +134,7 @@ qed-.
 
 lemma cpx_inv_zero1: ∀h,G,L,T2. ⦃G,L⦄ ⊢ #0 ⬈[h] T2 →
                      ∨∨ T2 = #0
-                      | ∃∃I,K,V1,V2. ⦃G,K⦄ ⊢ V1 ⬈[h] V2 & ⬆*[1] V2 ≘ T2 &
+                      | ∃∃I,K,V1,V2. ⦃G,K⦄ ⊢ V1 ⬈[h] V2 & ⇧*[1] V2 ≘ T2 &
                                      L = K.ⓑ{I}V1.
 #h #G #L #T2 * #c #H elim (cpg_inv_zero1 … H) -H *
 /4 width=7 by ex3_4_intro, ex_intro, or_introl, or_intror/
@@ -135,7 +142,7 @@ qed-.
 
 lemma cpx_inv_lref1: ∀h,G,L,T2,i. ⦃G,L⦄ ⊢ #↑i ⬈[h] T2 →
                      ∨∨ T2 = #(↑i)
-                      | ∃∃I,K,T. ⦃G,K⦄ ⊢ #i ⬈[h] T & ⬆*[1] T ≘ T2 & L = K.ⓘ{I}.
+                      | ∃∃I,K,T. ⦃G,K⦄ ⊢ #i ⬈[h] T & ⇧*[1] T ≘ T2 & L = K.ⓘ{I}.
 #h #G #L #T2 #i * #c #H elim (cpg_inv_lref1 … H) -H *
 /4 width=6 by ex3_3_intro, ex_intro, or_introl, or_intror/
 qed-.
@@ -147,7 +154,7 @@ qed-.
 lemma cpx_inv_bind1: ∀h,p,I,G,L,V1,T1,U2. ⦃G,L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈[h] U2 →
                      ∨∨ ∃∃V2,T2. ⦃G,L⦄ ⊢ V1 ⬈[h] V2 & ⦃G,L.ⓑ{I}V1⦄ ⊢ T1 ⬈[h] T2 &
                                  U2 = ⓑ{p,I}V2.T2
-                      | ∃∃T. ⬆*[1] T ≘ T1 & ⦃G,L⦄ ⊢ T ⬈[h] U2 & 
+                      | ∃∃T. ⇧*[1] T ≘ T1 & ⦃G,L⦄ ⊢ T ⬈[h] U2 &
                              p = true & I = Abbr.
 #h #p #I #G #L #V1 #T1 #U2 * #c #H elim (cpg_inv_bind1 … H) -H *
 /4 width=5 by ex4_intro, ex3_2_intro, ex_intro, or_introl, or_intror/
@@ -156,7 +163,7 @@ qed-.
 lemma cpx_inv_abbr1: ∀h,p,G,L,V1,T1,U2. ⦃G,L⦄ ⊢ ⓓ{p}V1.T1 ⬈[h] U2 →
                      ∨∨ ∃∃V2,T2. ⦃G,L⦄ ⊢ V1 ⬈[h] V2 & ⦃G,L.ⓓV1⦄ ⊢ T1 ⬈[h] T2 &
                                  U2 = ⓓ{p}V2.T2
-                      | ∃∃T. ⬆*[1] T ≘ T1 & ⦃G,L⦄ ⊢ T ⬈[h] U2 & p = true.
+                      | ∃∃T. ⇧*[1] T ≘ T1 & ⦃G,L⦄ ⊢ T ⬈[h] U2 & p = true.
 #h #p #G #L #V1 #T1 #U2 * #c #H elim (cpg_inv_abbr1 … H) -H *
 /4 width=5 by ex3_2_intro, ex3_intro, ex_intro, or_introl, or_intror/
 qed-.
@@ -174,7 +181,7 @@ lemma cpx_inv_appl1: ∀h,G,L,V1,U1,U2. ⦃G,L⦄ ⊢ ⓐ V1.U1 ⬈[h] U2 →
                       | ∃∃p,V2,W1,W2,T1,T2. ⦃G,L⦄ ⊢ V1 ⬈[h] V2 & ⦃G,L⦄ ⊢ W1 ⬈[h] W2 &
                                             ⦃G,L.ⓛW1⦄ ⊢ T1 ⬈[h] T2 &
                                             U1 = ⓛ{p}W1.T1 & U2 = ⓓ{p}ⓝW2.V2.T2
-                      | ∃∃p,V,V2,W1,W2,T1,T2. ⦃G,L⦄ ⊢ V1 ⬈[h] V & ⬆*[1] V ≘ V2 &
+                      | ∃∃p,V,V2,W1,W2,T1,T2. ⦃G,L⦄ ⊢ V1 ⬈[h] V & ⇧*[1] V ≘ V2 &
                                               ⦃G,L⦄ ⊢ W1 ⬈[h] W2 & ⦃G,L.ⓓW1⦄ ⊢ T1 ⬈[h] T2 &
                                               U1 = ⓓ{p}W1.T1 & U2 = ⓓ{p}W2.ⓐV2.T2.
 #h #G #L #V1 #U1 #U2 * #c #H elim (cpg_inv_appl1 … H) -H *
@@ -194,14 +201,14 @@ qed-.
 
 lemma cpx_inv_zero1_pair: ∀h,I,G,K,V1,T2. ⦃G,K.ⓑ{I}V1⦄ ⊢ #0 ⬈[h] T2 →
                           ∨∨ T2 = #0
-                           | ∃∃V2. ⦃G,K⦄ ⊢ V1 ⬈[h] V2 & ⬆*[1] V2 ≘ T2.
+                           | ∃∃V2. ⦃G,K⦄ ⊢ V1 ⬈[h] V2 & ⇧*[1] V2 ≘ T2.
 #h #I #G #L #V1 #T2 * #c #H elim (cpg_inv_zero1_pair … H) -H *
 /4 width=3 by ex2_intro, ex_intro, or_intror, or_introl/
 qed-.
 
 lemma cpx_inv_lref1_bind: ∀h,I,G,K,T2,i. ⦃G,K.ⓘ{I}⦄ ⊢ #↑i ⬈[h] T2 →
                           ∨∨ T2 = #(↑i)
-                           | ∃∃T. ⦃G,K⦄ ⊢ #i ⬈[h] T & ⬆*[1] T ≘ T2.
+                           | ∃∃T. ⦃G,K⦄ ⊢ #i ⬈[h] T & ⇧*[1] T ≘ T2.
 #h #I #G #L #T2 #i * #c #H elim (cpg_inv_lref1_bind … H) -H *
 /4 width=3 by ex2_intro, ex_intro, or_introl, or_intror/
 qed-.
@@ -215,7 +222,7 @@ lemma cpx_inv_flat1: ∀h,I,G,L,V1,U1,U2. ⦃G,L⦄ ⊢ ⓕ{I}V1.U1 ⬈[h] U2 
                                             ⦃G,L.ⓛW1⦄ ⊢ T1 ⬈[h] T2 &
                                             U1 = ⓛ{p}W1.T1 &
                                             U2 = ⓓ{p}ⓝW2.V2.T2 & I = Appl
-                      | ∃∃p,V,V2,W1,W2,T1,T2. ⦃G,L⦄ ⊢ V1 ⬈[h] V & ⬆*[1] V ≘ V2 &
+                      | ∃∃p,V,V2,W1,W2,T1,T2. ⦃G,L⦄ ⊢ V1 ⬈[h] V & ⇧*[1] V ≘ V2 &
                                               ⦃G,L⦄ ⊢ W1 ⬈[h] W2 & ⦃G,L.ⓓW1⦄ ⊢ T1 ⬈[h] T2 &
                                               U1 = ⓓ{p}W1.T1 &
                                               U2 = ⓓ{p}W2.ⓐV2.T2 & I = Appl.
@@ -224,7 +231,7 @@ lemma cpx_inv_flat1: ∀h,I,G,L,V1,U1,U2. ⦃G,L⦄ ⊢ ⓕ{I}V1.U1 ⬈[h] U2 
   /3 width=14 by or5_intro0, or5_intro3, or5_intro4, ex7_7_intro, ex6_6_intro, ex3_2_intro/
 | elim (cpx_inv_cast1 … H) -H [ * ]
   /3 width=14 by or5_intro0, or5_intro1, or5_intro2, ex3_2_intro, conj/
-] 
+]
 qed-.
 
 (* Basic forward lemmas *****************************************************)
@@ -242,14 +249,14 @@ lemma cpx_ind: ∀h. ∀Q:relation4 genv lenv term term.
                (∀I,G,L. Q G L (⓪{I}) (⓪{I})) →
                (∀G,L,s. Q G L (⋆s) (⋆(⫯[h]s))) →
                (∀I,G,K,V1,V2,W2. ⦃G,K⦄ ⊢ V1 ⬈[h] V2 → Q G K V1 V2 →
-                 ⬆*[1] V2 ≘ W2 → Q G (K.ⓑ{I}V1) (#0) W2
+                 ⇧*[1] V2 ≘ W2 → Q G (K.ⓑ{I}V1) (#0) W2
                ) → (∀I,G,K,T,U,i. ⦃G,K⦄ ⊢ #i ⬈[h] T → Q G K (#i) T →
-                 ⬆*[1] T ≘ U → Q G (K.ⓘ{I}) (#↑i) (U)
+                 ⇧*[1] T ≘ U → Q G (K.ⓘ{I}) (#↑i) (U)
                ) → (∀p,I,G,L,V1,V2,T1,T2. ⦃G,L⦄ ⊢ V1 ⬈[h] V2 → ⦃G,L.ⓑ{I}V1⦄ ⊢ T1 ⬈[h] T2 →
                   Q G L V1 V2 → Q G (L.ⓑ{I}V1) T1 T2 → Q G L (ⓑ{p,I}V1.T1) (ⓑ{p,I}V2.T2)
                ) → (∀I,G,L,V1,V2,T1,T2. ⦃G,L⦄ ⊢ V1 ⬈[h] V2 → ⦃G,L⦄ ⊢ T1 ⬈[h] T2 →
                   Q G L V1 V2 → Q G L T1 T2 → Q G L (ⓕ{I}V1.T1) (ⓕ{I}V2.T2)
-               ) → (∀G,L,V,T1,T,T2. ⬆*[1] T ≘ T1 → ⦃G,L⦄ ⊢ T ⬈[h] T2 → Q G L T T2 →
+               ) → (∀G,L,V,T1,T,T2. ⇧*[1] T ≘ T1 → ⦃G,L⦄ ⊢ T ⬈[h] T2 → Q G L T T2 →
                   Q G L (+ⓓV.T1) T2
                ) → (∀G,L,V,T1,T2. ⦃G,L⦄ ⊢ T1 ⬈[h] T2 → Q G L T1 T2 →
                   Q G L (ⓝV.T1) T2
@@ -260,7 +267,7 @@ lemma cpx_ind: ∀h. ∀Q:relation4 genv lenv term term.
                   Q G L (ⓐV1.ⓛ{p}W1.T1) (ⓓ{p}ⓝW2.V2.T2)
                ) → (∀p,G,L,V1,V,V2,W1,W2,T1,T2. ⦃G,L⦄ ⊢ V1 ⬈[h] V → ⦃G,L⦄ ⊢ W1 ⬈[h] W2 → ⦃G,L.ⓓW1⦄ ⊢ T1 ⬈[h] T2 →
                   Q G L V1 V → Q G L W1 W2 → Q G (L.ⓓW1) T1 T2 →
-                  ⬆*[1] V ≘ V2 → Q G L (ⓐV1.ⓓ{p}W1.T1) (ⓓ{p}W2.ⓐV2.T2)
+                  ⇧*[1] V ≘ V2 → Q G L (ⓐV1.ⓓ{p}W1.T1) (ⓓ{p}W2.ⓐV2.T2)
                ) →
                ∀G,L,T1,T2. ⦃G,L⦄ ⊢ T1 ⬈[h] T2 → Q G L T1 T2.
 #h #Q #IH1 #IH2 #IH3 #IH4 #IH5 #IH6 #IH7 #IH8 #IH9 #IH10 #IH11 #G #L #T1 #T2