X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Frpx.ma;h=c127801613e705d1ec70b7ce80388d9b68591f5f;hp=b3c8ba2fd43dec6fe786116bd215b73e09182263;hb=3c7b4071a9ac096b02334c1d47468776b948e2de;hpb=2f6f2b7c01d47d23f61dd48d767bcb37aecdcfea

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx.ma
index b3c8ba2fd..c12780161 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx.ma
@@ -12,126 +12,140 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predtysn_5.ma".
+include "basic_2/notation/relations/predtysn_4.ma".
 include "static_2/static/rex.ma".
 include "basic_2/rt_transition/cpx_ext.ma".
 
-(* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
+(* EXTENDED PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS **********)
 
-definition rpx (h) (G): relation3 term lenv lenv ≝
-                        rex (cpx h G).
+definition rpx (G): relation3 term lenv lenv ≝
+           rex (cpx G).
 
 interpretation
-   "unbound parallel rt-transition on referred entries (local environment)"
-   'PRedTySn h T G L1 L2 = (rpx h G T L1 L2).
+  "extended parallel rt-transition on referred entries (local environment)"
+  'PRedTySn T G L1 L2 = (rpx G T L1 L2).
 
 (* Basic properties ***********************************************************)
 
-lemma rpx_atom: ∀h,I,G. ❪G,⋆❫ ⊢ ⬈[h,⓪[I]] ⋆.
+lemma rpx_atom (G):
+      ∀I. ❪G,⋆❫ ⊢ ⬈[⓪[I]] ⋆.
 /2 width=1 by rex_atom/ qed.
 
-lemma rpx_sort: ∀h,I1,I2,G,L1,L2,s.
-                ❪G,L1❫ ⊢ ⬈[h,⋆s] L2 → ❪G,L1.ⓘ[I1]❫ ⊢ ⬈[h,⋆s] L2.ⓘ[I2].
+lemma rpx_sort (G):
+      ∀I1,I2,L1,L2,s.
+      ❪G,L1❫ ⊢ ⬈[⋆s] L2 → ❪G,L1.ⓘ[I1]❫ ⊢ ⬈[⋆s] L2.ⓘ[I2].
 /2 width=1 by rex_sort/ qed.
 
-lemma rpx_pair: ∀h,I,G,L1,L2,V1,V2.
-                ❪G,L1❫ ⊢ ⬈[h,V1] L2 → ❪G,L1❫ ⊢ V1 ⬈[h] V2 → ❪G,L1.ⓑ[I]V1❫ ⊢ ⬈[h,#0] L2.ⓑ[I]V2.
+lemma rpx_pair (G):
+      ∀I,L1,L2,V1,V2.
+      ❪G,L1❫ ⊢ ⬈[V1] L2 → ❪G,L1❫ ⊢ V1 ⬈ V2 → ❪G,L1.ⓑ[I]V1❫ ⊢ ⬈[#0] L2.ⓑ[I]V2.
 /2 width=1 by rex_pair/ qed.
 
-lemma rpx_lref: ∀h,I1,I2,G,L1,L2,i.
-                ❪G,L1❫ ⊢ ⬈[h,#i] L2 → ❪G,L1.ⓘ[I1]❫ ⊢ ⬈[h,#↑i] L2.ⓘ[I2].
+lemma rpx_lref (G):
+      ∀I1,I2,L1,L2,i.
+      ❪G,L1❫ ⊢ ⬈[#i] L2 → ❪G,L1.ⓘ[I1]❫ ⊢ ⬈[#↑i] L2.ⓘ[I2].
 /2 width=1 by rex_lref/ qed.
 
-lemma rpx_gref: ∀h,I1,I2,G,L1,L2,l.
-                ❪G,L1❫ ⊢ ⬈[h,§l] L2 → ❪G,L1.ⓘ[I1]❫ ⊢ ⬈[h,§l] L2.ⓘ[I2].
+lemma rpx_gref (G):
+      ∀I1,I2,L1,L2,l.
+      ❪G,L1❫ ⊢ ⬈[§l] L2 → ❪G,L1.ⓘ[I1]❫ ⊢ ⬈[§l] L2.ⓘ[I2].
 /2 width=1 by rex_gref/ qed.
 
-lemma rpx_bind_repl_dx: ∀h,I,I1,G,L1,L2,T.
-                        ❪G,L1.ⓘ[I]❫ ⊢ ⬈[h,T] L2.ⓘ[I1] →
-                        ∀I2. ❪G,L1❫ ⊢ I ⬈[h] I2 →
-                        ❪G,L1.ⓘ[I]❫ ⊢ ⬈[h,T] L2.ⓘ[I2].
+lemma rpx_bind_repl_dx (G):
+      ∀I,I1,L1,L2,T. ❪G,L1.ⓘ[I]❫ ⊢ ⬈[T] L2.ⓘ[I1] →
+      ∀I2. ❪G,L1❫ ⊢ I ⬈ I2 → ❪G,L1.ⓘ[I]❫ ⊢ ⬈[T] L2.ⓘ[I2].
 /2 width=2 by rex_bind_repl_dx/ qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma rpx_inv_atom_sn: ∀h,G,Y2,T. ❪G,⋆❫ ⊢ ⬈[h,T] Y2 → Y2 = ⋆.
+lemma rpx_inv_atom_sn (G):
+      ∀Y2,T. ❪G,⋆❫ ⊢ ⬈[T] Y2 → Y2 = ⋆.
 /2 width=3 by rex_inv_atom_sn/ qed-.
 
-lemma rpx_inv_atom_dx: ∀h,G,Y1,T. ❪G,Y1❫ ⊢ ⬈[h,T] ⋆ → Y1 = ⋆.
+lemma rpx_inv_atom_dx (G):
+      ∀Y1,T. ❪G,Y1❫ ⊢ ⬈[T] ⋆ → Y1 = ⋆.
 /2 width=3 by rex_inv_atom_dx/ qed-.
 
-lemma rpx_inv_sort: ∀h,G,Y1,Y2,s. ❪G,Y1❫ ⊢ ⬈[h,⋆s] Y2 →
-                    ∨∨ Y1 = ⋆ ∧ Y2 = ⋆
-                     | ∃∃I1,I2,L1,L2. ❪G,L1❫ ⊢ ⬈[h,⋆s] L2 &
-                                      Y1 = L1.ⓘ[I1] & Y2 = L2.ⓘ[I2].
+lemma rpx_inv_sort (G):
+      ∀Y1,Y2,s. ❪G,Y1❫ ⊢ ⬈[⋆s] Y2 →
+      ∨∨ ∧∧ Y1 = ⋆ & Y2 = ⋆
+       | ∃∃I1,I2,L1,L2. ❪G,L1❫ ⊢ ⬈[⋆s] L2 & Y1 = L1.ⓘ[I1] & Y2 = L2.ⓘ[I2].
 /2 width=1 by rex_inv_sort/ qed-.
 
-lemma rpx_inv_lref: ∀h,G,Y1,Y2,i. ❪G,Y1❫ ⊢ ⬈[h,#↑i] Y2 →
-                    ∨∨ Y1 = ⋆ ∧ Y2 = ⋆
-                     | ∃∃I1,I2,L1,L2. ❪G,L1❫ ⊢ ⬈[h,#i] L2 &
-                                      Y1 = L1.ⓘ[I1] & Y2 = L2.ⓘ[I2].
+lemma rpx_inv_lref (G):
+      ∀Y1,Y2,i. ❪G,Y1❫ ⊢ ⬈[#↑i] Y2 →
+      ∨∨ ∧∧ Y1 = ⋆ & Y2 = ⋆
+       | ∃∃I1,I2,L1,L2. ❪G,L1❫ ⊢ ⬈[#i] L2 & Y1 = L1.ⓘ[I1] & Y2 = L2.ⓘ[I2].
 /2 width=1 by rex_inv_lref/ qed-.
 
-lemma rpx_inv_gref: ∀h,G,Y1,Y2,l. ❪G,Y1❫ ⊢ ⬈[h,§l] Y2 →
-                    ∨∨ Y1 = ⋆ ∧ Y2 = ⋆
-                     | ∃∃I1,I2,L1,L2. ❪G,L1❫ ⊢ ⬈[h,§l] L2 &
-                                      Y1 = L1.ⓘ[I1] & Y2 = L2.ⓘ[I2].
+lemma rpx_inv_gref (G):
+      ∀Y1,Y2,l. ❪G,Y1❫ ⊢ ⬈[§l] Y2 →
+      ∨∨ ∧∧ Y1 = ⋆ & Y2 = ⋆
+       | ∃∃I1,I2,L1,L2. ❪G,L1❫ ⊢ ⬈[§l] L2 & Y1 = L1.ⓘ[I1] & Y2 = L2.ⓘ[I2].
 /2 width=1 by rex_inv_gref/ qed-.
 
-lemma rpx_inv_bind: ∀h,p,I,G,L1,L2,V,T. ❪G,L1❫ ⊢ ⬈[h,ⓑ[p,I]V.T] L2 →
-                    ∧∧ ❪G,L1❫ ⊢ ⬈[h,V] L2 & ❪G,L1.ⓑ[I]V❫ ⊢ ⬈[h,T] L2.ⓑ[I]V.
+lemma rpx_inv_bind (G):
+      ∀p,I,L1,L2,V,T. ❪G,L1❫ ⊢ ⬈[ⓑ[p,I]V.T] L2 →
+      ∧∧ ❪G,L1❫ ⊢ ⬈[V] L2 & ❪G,L1.ⓑ[I]V❫ ⊢ ⬈[T] L2.ⓑ[I]V.
 /2 width=2 by rex_inv_bind/ qed-.
 
-lemma rpx_inv_flat: ∀h,I,G,L1,L2,V,T. ❪G,L1❫ ⊢ ⬈[h,ⓕ[I]V.T] L2 →
-                    ∧∧ ❪G,L1❫ ⊢ ⬈[h,V] L2 & ❪G,L1❫ ⊢ ⬈[h,T] L2.
+lemma rpx_inv_flat (G):
+      ∀I,L1,L2,V,T. ❪G,L1❫ ⊢ ⬈[ⓕ[I]V.T] L2 →
+      ∧∧ ❪G,L1❫ ⊢ ⬈[V] L2 & ❪G,L1❫ ⊢ ⬈[T] L2.
 /2 width=2 by rex_inv_flat/ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma rpx_inv_sort_bind_sn: ∀h,I1,G,Y2,L1,s. ❪G,L1.ⓘ[I1]❫ ⊢ ⬈[h,⋆s] Y2 →
-                            ∃∃I2,L2. ❪G,L1❫ ⊢ ⬈[h,⋆s] L2 & Y2 = L2.ⓘ[I2].
+lemma rpx_inv_sort_bind_sn (G):
+      ∀I1,Y2,L1,s. ❪G,L1.ⓘ[I1]❫ ⊢ ⬈[⋆s] Y2 →
+      ∃∃I2,L2. ❪G,L1❫ ⊢ ⬈[⋆s] L2 & Y2 = L2.ⓘ[I2].
 /2 width=2 by rex_inv_sort_bind_sn/ qed-.
 
-lemma rpx_inv_sort_bind_dx: ∀h,I2,G,Y1,L2,s. ❪G,Y1❫ ⊢ ⬈[h,⋆s] L2.ⓘ[I2] →
-                            ∃∃I1,L1. ❪G,L1❫ ⊢ ⬈[h,⋆s] L2 & Y1 = L1.ⓘ[I1].
+lemma rpx_inv_sort_bind_dx (G):
+      ∀I2,Y1,L2,s. ❪G,Y1❫ ⊢ ⬈[⋆s] L2.ⓘ[I2] →
+      ∃∃I1,L1. ❪G,L1❫ ⊢ ⬈[⋆s] L2 & Y1 = L1.ⓘ[I1].
 /2 width=2 by rex_inv_sort_bind_dx/ qed-.
 
-lemma rpx_inv_zero_pair_sn: ∀h,I,G,Y2,L1,V1. ❪G,L1.ⓑ[I]V1❫ ⊢ ⬈[h,#0] Y2 →
-                            ∃∃L2,V2. ❪G,L1❫ ⊢ ⬈[h,V1] L2 & ❪G,L1❫ ⊢ V1 ⬈[h] V2 &
-                                     Y2 = L2.ⓑ[I]V2.
+lemma rpx_inv_zero_pair_sn (G):
+      ∀I,Y2,L1,V1. ❪G,L1.ⓑ[I]V1❫ ⊢ ⬈[#0] Y2 →
+      ∃∃L2,V2. ❪G,L1❫ ⊢ ⬈[V1] L2 & ❪G,L1❫ ⊢ V1 ⬈ V2 & Y2 = L2.ⓑ[I]V2.
 /2 width=1 by rex_inv_zero_pair_sn/ qed-.
 
-lemma rpx_inv_zero_pair_dx: ∀h,I,G,Y1,L2,V2. ❪G,Y1❫ ⊢ ⬈[h,#0] L2.ⓑ[I]V2 →
-                            ∃∃L1,V1. ❪G,L1❫ ⊢ ⬈[h,V1] L2 & ❪G,L1❫ ⊢ V1 ⬈[h] V2 &
-                                     Y1 = L1.ⓑ[I]V1.
+lemma rpx_inv_zero_pair_dx (G):
+      ∀I,Y1,L2,V2. ❪G,Y1❫ ⊢ ⬈[#0] L2.ⓑ[I]V2 →
+      ∃∃L1,V1. ❪G,L1❫ ⊢ ⬈[V1] L2 & ❪G,L1❫ ⊢ V1 ⬈ V2 & Y1 = L1.ⓑ[I]V1.
 /2 width=1 by rex_inv_zero_pair_dx/ qed-.
 
-lemma rpx_inv_lref_bind_sn: ∀h,I1,G,Y2,L1,i. ❪G,L1.ⓘ[I1]❫ ⊢ ⬈[h,#↑i] Y2 →
-                            ∃∃I2,L2. ❪G,L1❫ ⊢ ⬈[h,#i] L2 & Y2 = L2.ⓘ[I2].
+lemma rpx_inv_lref_bind_sn (G):
+      ∀I1,Y2,L1,i. ❪G,L1.ⓘ[I1]❫ ⊢ ⬈[#↑i] Y2 →
+      ∃∃I2,L2. ❪G,L1❫ ⊢ ⬈[#i] L2 & Y2 = L2.ⓘ[I2].
 /2 width=2 by rex_inv_lref_bind_sn/ qed-.
 
-lemma rpx_inv_lref_bind_dx: ∀h,I2,G,Y1,L2,i. ❪G,Y1❫ ⊢ ⬈[h,#↑i] L2.ⓘ[I2] →
-                            ∃∃I1,L1. ❪G,L1❫ ⊢ ⬈[h,#i] L2 & Y1 = L1.ⓘ[I1].
+lemma rpx_inv_lref_bind_dx (G):
+      ∀I2,Y1,L2,i. ❪G,Y1❫ ⊢ ⬈[#↑i] L2.ⓘ[I2] →
+      ∃∃I1,L1. ❪G,L1❫ ⊢ ⬈[#i] L2 & Y1 = L1.ⓘ[I1].
 /2 width=2 by rex_inv_lref_bind_dx/ qed-.
 
-lemma rpx_inv_gref_bind_sn: ∀h,I1,G,Y2,L1,l. ❪G,L1.ⓘ[I1]❫ ⊢ ⬈[h,§l] Y2 →
-                            ∃∃I2,L2. ❪G,L1❫ ⊢ ⬈[h,§l] L2 & Y2 = L2.ⓘ[I2].
+lemma rpx_inv_gref_bind_sn (G):
+      ∀I1,Y2,L1,l. ❪G,L1.ⓘ[I1]❫ ⊢ ⬈[§l] Y2 →
+      ∃∃I2,L2. ❪G,L1❫ ⊢ ⬈[§l] L2 & Y2 = L2.ⓘ[I2].
 /2 width=2 by rex_inv_gref_bind_sn/ qed-.
 
-lemma rpx_inv_gref_bind_dx: ∀h,I2,G,Y1,L2,l. ❪G,Y1❫ ⊢ ⬈[h,§l] L2.ⓘ[I2] →
-                            ∃∃I1,L1. ❪G,L1❫ ⊢ ⬈[h,§l] L2 & Y1 = L1.ⓘ[I1].
+lemma rpx_inv_gref_bind_dx (G):
+      ∀I2,Y1,L2,l. ❪G,Y1❫ ⊢ ⬈[§l] L2.ⓘ[I2] →
+      ∃∃I1,L1. ❪G,L1❫ ⊢ ⬈[§l] L2 & Y1 = L1.ⓘ[I1].
 /2 width=2 by rex_inv_gref_bind_dx/ qed-.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma rpx_fwd_pair_sn: ∀h,I,G,L1,L2,V,T.
-                       ❪G,L1❫ ⊢ ⬈[h,②[I]V.T] L2 → ❪G,L1❫ ⊢ ⬈[h,V] L2.
+lemma rpx_fwd_pair_sn (G):
+      ∀I,L1,L2,V,T. ❪G,L1❫ ⊢ ⬈[②[I]V.T] L2 → ❪G,L1❫ ⊢ ⬈[V] L2.
 /2 width=3 by rex_fwd_pair_sn/ qed-.
 
-lemma rpx_fwd_bind_dx: ∀h,p,I,G,L1,L2,V,T.
-                       ❪G,L1❫ ⊢ ⬈[h,ⓑ[p,I]V.T] L2 → ❪G,L1.ⓑ[I]V❫ ⊢ ⬈[h,T] L2.ⓑ[I]V.
+lemma rpx_fwd_bind_dx (G):
+      ∀p,I,L1,L2,V,T. ❪G,L1❫ ⊢ ⬈[ⓑ[p,I]V.T] L2 → ❪G,L1.ⓑ[I]V❫ ⊢ ⬈[T] L2.ⓑ[I]V.
 /2 width=2 by rex_fwd_bind_dx/ qed-.
 
-lemma rpx_fwd_flat_dx: ∀h,I,G,L1,L2,V,T.
-                       ❪G,L1❫ ⊢ ⬈[h,ⓕ[I]V.T] L2 → ❪G,L1❫ ⊢ ⬈[h,T] L2.
+lemma rpx_fwd_flat_dx (G):
+      ∀I,L1,L2,V,T. ❪G,L1❫ ⊢ ⬈[ⓕ[I]V.T] L2 → ❪G,L1❫ ⊢ ⬈[T] L2.
 /2 width=3 by rex_fwd_flat_dx/ qed-.