update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / rpx.ma

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 70351ad4f0bd7d1eeb8a5f2df770790fdf8dd497..b3c8ba2fd43dec6fe786116bd215b73e09182263 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx.ma
@@ -27,111 +27,111 @@ interpretation
 
 (* Basic properties ***********************************************************)
 
-lemma rpx_atom: â\88\80h,I,G. â¦\83G,â\8b\86â¦\84 â\8a¢ â¬\88[h,â\93ª{I}] ⋆.
+lemma rpx_atom: â\88\80h,I,G. â\9dªG,â\8b\86â\9d« â\8a¢ â¬\88[h,â\93ª[I]] ⋆.
 /2 width=1 by rex_atom/ qed.
 
 lemma rpx_sort: ∀h,I1,I2,G,L1,L2,s.
-                â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,â\8b\86s] L2 â\86\92 â¦\83G,L1.â\93\98{I1}â¦\84 â\8a¢ â¬\88[h,â\8b\86s] L2.â\93\98{I2}.
+                â\9dªG,L1â\9d« â\8a¢ â¬\88[h,â\8b\86s] L2 â\86\92 â\9dªG,L1.â\93\98[I1]â\9d« â\8a¢ â¬\88[h,â\8b\86s] L2.â\93\98[I2].
 /2 width=1 by rex_sort/ qed.
 
 lemma rpx_pair: ∀h,I,G,L1,L2,V1,V2.
-                â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,V1] L2 â\86\92 â¦\83G,L1â¦\84 â\8a¢ V1 â¬\88[h] V2 â\86\92 â¦\83G,L1.â\93\91{I}V1â¦\84 â\8a¢ â¬\88[h,#0] L2.â\93\91{I}V2.
+                â\9dªG,L1â\9d« â\8a¢ â¬\88[h,V1] L2 â\86\92 â\9dªG,L1â\9d« â\8a¢ V1 â¬\88[h] V2 â\86\92 â\9dªG,L1.â\93\91[I]V1â\9d« â\8a¢ â¬\88[h,#0] L2.â\93\91[I]V2.
 /2 width=1 by rex_pair/ qed.
 
 lemma rpx_lref: ∀h,I1,I2,G,L1,L2,i.
-                â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,#i] L2 â\86\92 â¦\83G,L1.â\93\98{I1}â¦\84 â\8a¢ â¬\88[h,#â\86\91i] L2.â\93\98{I2}.
+                â\9dªG,L1â\9d« â\8a¢ â¬\88[h,#i] L2 â\86\92 â\9dªG,L1.â\93\98[I1]â\9d« â\8a¢ â¬\88[h,#â\86\91i] L2.â\93\98[I2].
 /2 width=1 by rex_lref/ qed.
 
 lemma rpx_gref: ∀h,I1,I2,G,L1,L2,l.
-                â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,§l] L2 â\86\92 â¦\83G,L1.â\93\98{I1}â¦\84 â\8a¢ â¬\88[h,§l] L2.â\93\98{I2}.
+                â\9dªG,L1â\9d« â\8a¢ â¬\88[h,§l] L2 â\86\92 â\9dªG,L1.â\93\98[I1]â\9d« â\8a¢ â¬\88[h,§l] L2.â\93\98[I2].
 /2 width=1 by rex_gref/ qed.
 
 lemma rpx_bind_repl_dx: ∀h,I,I1,G,L1,L2,T.
-                        â¦\83G,L1.â\93\98{I}â¦\84 â\8a¢ â¬\88[h,T] L2.â\93\98{I1} →
-                        â\88\80I2. â¦\83G,L1â¦\84 ⊢ I ⬈[h] I2 →
-                        â¦\83G,L1.â\93\98{I}â¦\84 â\8a¢ â¬\88[h,T] L2.â\93\98{I2}.
+                        â\9dªG,L1.â\93\98[I]â\9d« â\8a¢ â¬\88[h,T] L2.â\93\98[I1] →
+                        â\88\80I2. â\9dªG,L1â\9d« ⊢ I ⬈[h] I2 →
+                        â\9dªG,L1.â\93\98[I]â\9d« â\8a¢ â¬\88[h,T] L2.â\93\98[I2].
 /2 width=2 by rex_bind_repl_dx/ qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma rpx_inv_atom_sn: â\88\80h,G,Y2,T. â¦\83G,â\8b\86â¦\84 ⊢ ⬈[h,T] Y2 → Y2 = ⋆.
+lemma rpx_inv_atom_sn: â\88\80h,G,Y2,T. â\9dªG,â\8b\86â\9d« ⊢ ⬈[h,T] Y2 → Y2 = ⋆.
 /2 width=3 by rex_inv_atom_sn/ qed-.
 
-lemma rpx_inv_atom_dx: â\88\80h,G,Y1,T. â¦\83G,Y1â¦\84 ⊢ ⬈[h,T] ⋆ → Y1 = ⋆.
+lemma rpx_inv_atom_dx: â\88\80h,G,Y1,T. â\9dªG,Y1â\9d« ⊢ ⬈[h,T] ⋆ → Y1 = ⋆.
 /2 width=3 by rex_inv_atom_dx/ qed-.
 
-lemma rpx_inv_sort: â\88\80h,G,Y1,Y2,s. â¦\83G,Y1â¦\84 ⊢ ⬈[h,⋆s] Y2 →
+lemma rpx_inv_sort: â\88\80h,G,Y1,Y2,s. â\9dªG,Y1â\9d« ⊢ ⬈[h,⋆s] Y2 →
                     ∨∨ Y1 = ⋆ ∧ Y2 = ⋆
-                     | â\88\83â\88\83I1,I2,L1,L2. â¦\83G,L1â¦\84 ⊢ ⬈[h,⋆s] L2 &
-                                      Y1 = L1.ⓘ{I1} & Y2 = L2.ⓘ{I2}.
+                     | â\88\83â\88\83I1,I2,L1,L2. â\9dªG,L1â\9d« ⊢ ⬈[h,⋆s] L2 &
+                                      Y1 = L1.ⓘ[I1] & Y2 = L2.ⓘ[I2].
 /2 width=1 by rex_inv_sort/ qed-.
 
-lemma rpx_inv_lref: â\88\80h,G,Y1,Y2,i. â¦\83G,Y1â¦\84 ⊢ ⬈[h,#↑i] Y2 →
+lemma rpx_inv_lref: â\88\80h,G,Y1,Y2,i. â\9dªG,Y1â\9d« ⊢ ⬈[h,#↑i] Y2 →
                     ∨∨ Y1 = ⋆ ∧ Y2 = ⋆
-                     | â\88\83â\88\83I1,I2,L1,L2. â¦\83G,L1â¦\84 ⊢ ⬈[h,#i] L2 &
-                                      Y1 = L1.ⓘ{I1} & Y2 = L2.ⓘ{I2}.
+                     | â\88\83â\88\83I1,I2,L1,L2. â\9dªG,L1â\9d« ⊢ ⬈[h,#i] L2 &
+                                      Y1 = L1.ⓘ[I1] & Y2 = L2.ⓘ[I2].
 /2 width=1 by rex_inv_lref/ qed-.
 
-lemma rpx_inv_gref: â\88\80h,G,Y1,Y2,l. â¦\83G,Y1â¦\84 ⊢ ⬈[h,§l] Y2 →
+lemma rpx_inv_gref: â\88\80h,G,Y1,Y2,l. â\9dªG,Y1â\9d« ⊢ ⬈[h,§l] Y2 →
                     ∨∨ Y1 = ⋆ ∧ Y2 = ⋆
-                     | â\88\83â\88\83I1,I2,L1,L2. â¦\83G,L1â¦\84 ⊢ ⬈[h,§l] L2 &
-                                      Y1 = L1.ⓘ{I1} & Y2 = L2.ⓘ{I2}.
+                     | â\88\83â\88\83I1,I2,L1,L2. â\9dªG,L1â\9d« ⊢ ⬈[h,§l] L2 &
+                                      Y1 = L1.ⓘ[I1] & Y2 = L2.ⓘ[I2].
 /2 width=1 by rex_inv_gref/ qed-.
 
-lemma rpx_inv_bind: â\88\80h,p,I,G,L1,L2,V,T. â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,â\93\91{p,I}V.T] L2 →
-                    â\88§â\88§ â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,V] L2 & â¦\83G,L1.â\93\91{I}Vâ¦\84 â\8a¢ â¬\88[h,T] L2.â\93\91{I}V.
+lemma rpx_inv_bind: â\88\80h,p,I,G,L1,L2,V,T. â\9dªG,L1â\9d« â\8a¢ â¬\88[h,â\93\91[p,I]V.T] L2 →
+                    â\88§â\88§ â\9dªG,L1â\9d« â\8a¢ â¬\88[h,V] L2 & â\9dªG,L1.â\93\91[I]Vâ\9d« â\8a¢ â¬\88[h,T] L2.â\93\91[I]V.
 /2 width=2 by rex_inv_bind/ qed-.
 
-lemma rpx_inv_flat: â\88\80h,I,G,L1,L2,V,T. â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,â\93\95{I}V.T] L2 →
-                    â\88§â\88§ â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,V] L2 & â¦\83G,L1â¦\84 ⊢ ⬈[h,T] L2.
+lemma rpx_inv_flat: â\88\80h,I,G,L1,L2,V,T. â\9dªG,L1â\9d« â\8a¢ â¬\88[h,â\93\95[I]V.T] L2 →
+                    â\88§â\88§ â\9dªG,L1â\9d« â\8a¢ â¬\88[h,V] L2 & â\9dªG,L1â\9d« ⊢ ⬈[h,T] L2.
 /2 width=2 by rex_inv_flat/ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma rpx_inv_sort_bind_sn: â\88\80h,I1,G,Y2,L1,s. â¦\83G,L1.â\93\98{I1}â¦\84 ⊢ ⬈[h,⋆s] Y2 →
-                            â\88\83â\88\83I2,L2. â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,â\8b\86s] L2 & Y2 = L2.â\93\98{I2}.
+lemma rpx_inv_sort_bind_sn: â\88\80h,I1,G,Y2,L1,s. â\9dªG,L1.â\93\98[I1]â\9d« ⊢ ⬈[h,⋆s] Y2 →
+                            â\88\83â\88\83I2,L2. â\9dªG,L1â\9d« â\8a¢ â¬\88[h,â\8b\86s] L2 & Y2 = L2.â\93\98[I2].
 /2 width=2 by rex_inv_sort_bind_sn/ qed-.
 
-lemma rpx_inv_sort_bind_dx: â\88\80h,I2,G,Y1,L2,s. â¦\83G,Y1â¦\84 â\8a¢ â¬\88[h,â\8b\86s] L2.â\93\98{I2} →
-                            â\88\83â\88\83I1,L1. â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,â\8b\86s] L2 & Y1 = L1.â\93\98{I1}.
+lemma rpx_inv_sort_bind_dx: â\88\80h,I2,G,Y1,L2,s. â\9dªG,Y1â\9d« â\8a¢ â¬\88[h,â\8b\86s] L2.â\93\98[I2] →
+                            â\88\83â\88\83I1,L1. â\9dªG,L1â\9d« â\8a¢ â¬\88[h,â\8b\86s] L2 & Y1 = L1.â\93\98[I1].
 /2 width=2 by rex_inv_sort_bind_dx/ qed-.
 
-lemma rpx_inv_zero_pair_sn: â\88\80h,I,G,Y2,L1,V1. â¦\83G,L1.â\93\91{I}V1â¦\84 ⊢ ⬈[h,#0] Y2 →
-                            â\88\83â\88\83L2,V2. â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,V1] L2 & â¦\83G,L1â¦\84 ⊢ V1 ⬈[h] V2 &
-                                     Y2 = L2.ⓑ{I}V2.
+lemma rpx_inv_zero_pair_sn: â\88\80h,I,G,Y2,L1,V1. â\9dªG,L1.â\93\91[I]V1â\9d« ⊢ ⬈[h,#0] Y2 →
+                            â\88\83â\88\83L2,V2. â\9dªG,L1â\9d« â\8a¢ â¬\88[h,V1] L2 & â\9dªG,L1â\9d« ⊢ V1 ⬈[h] V2 &
+                                     Y2 = L2.ⓑ[I]V2.
 /2 width=1 by rex_inv_zero_pair_sn/ qed-.
 
-lemma rpx_inv_zero_pair_dx: â\88\80h,I,G,Y1,L2,V2. â¦\83G,Y1â¦\84 â\8a¢ â¬\88[h,#0] L2.â\93\91{I}V2 →
-                            â\88\83â\88\83L1,V1. â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,V1] L2 & â¦\83G,L1â¦\84 ⊢ V1 ⬈[h] V2 &
-                                     Y1 = L1.ⓑ{I}V1.
+lemma rpx_inv_zero_pair_dx: â\88\80h,I,G,Y1,L2,V2. â\9dªG,Y1â\9d« â\8a¢ â¬\88[h,#0] L2.â\93\91[I]V2 →
+                            â\88\83â\88\83L1,V1. â\9dªG,L1â\9d« â\8a¢ â¬\88[h,V1] L2 & â\9dªG,L1â\9d« ⊢ V1 ⬈[h] V2 &
+                                     Y1 = L1.ⓑ[I]V1.
 /2 width=1 by rex_inv_zero_pair_dx/ qed-.
 
-lemma rpx_inv_lref_bind_sn: â\88\80h,I1,G,Y2,L1,i. â¦\83G,L1.â\93\98{I1}â¦\84 ⊢ ⬈[h,#↑i] Y2 →
-                            â\88\83â\88\83I2,L2. â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,#i] L2 & Y2 = L2.â\93\98{I2}.
+lemma rpx_inv_lref_bind_sn: â\88\80h,I1,G,Y2,L1,i. â\9dªG,L1.â\93\98[I1]â\9d« ⊢ ⬈[h,#↑i] Y2 →
+                            â\88\83â\88\83I2,L2. â\9dªG,L1â\9d« â\8a¢ â¬\88[h,#i] L2 & Y2 = L2.â\93\98[I2].
 /2 width=2 by rex_inv_lref_bind_sn/ qed-.
 
-lemma rpx_inv_lref_bind_dx: â\88\80h,I2,G,Y1,L2,i. â¦\83G,Y1â¦\84 â\8a¢ â¬\88[h,#â\86\91i] L2.â\93\98{I2} →
-                            â\88\83â\88\83I1,L1. â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,#i] L2 & Y1 = L1.â\93\98{I1}.
+lemma rpx_inv_lref_bind_dx: â\88\80h,I2,G,Y1,L2,i. â\9dªG,Y1â\9d« â\8a¢ â¬\88[h,#â\86\91i] L2.â\93\98[I2] →
+                            â\88\83â\88\83I1,L1. â\9dªG,L1â\9d« â\8a¢ â¬\88[h,#i] L2 & Y1 = L1.â\93\98[I1].
 /2 width=2 by rex_inv_lref_bind_dx/ qed-.
 
-lemma rpx_inv_gref_bind_sn: â\88\80h,I1,G,Y2,L1,l. â¦\83G,L1.â\93\98{I1}â¦\84 ⊢ ⬈[h,§l] Y2 →
-                            â\88\83â\88\83I2,L2. â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,§l] L2 & Y2 = L2.â\93\98{I2}.
+lemma rpx_inv_gref_bind_sn: â\88\80h,I1,G,Y2,L1,l. â\9dªG,L1.â\93\98[I1]â\9d« ⊢ ⬈[h,§l] Y2 →
+                            â\88\83â\88\83I2,L2. â\9dªG,L1â\9d« â\8a¢ â¬\88[h,§l] L2 & Y2 = L2.â\93\98[I2].
 /2 width=2 by rex_inv_gref_bind_sn/ qed-.
 
-lemma rpx_inv_gref_bind_dx: â\88\80h,I2,G,Y1,L2,l. â¦\83G,Y1â¦\84 â\8a¢ â¬\88[h,§l] L2.â\93\98{I2} →
-                            â\88\83â\88\83I1,L1. â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,§l] L2 & Y1 = L1.â\93\98{I1}.
+lemma rpx_inv_gref_bind_dx: â\88\80h,I2,G,Y1,L2,l. â\9dªG,Y1â\9d« â\8a¢ â¬\88[h,§l] L2.â\93\98[I2] →
+                            â\88\83â\88\83I1,L1. â\9dªG,L1â\9d« â\8a¢ â¬\88[h,§l] L2 & Y1 = L1.â\93\98[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.
-                       â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,â\91¡{I}V.T] L2 â\86\92 â¦\83G,L1â¦\84 ⊢ ⬈[h,V] L2.
+                       â\9dªG,L1â\9d« â\8a¢ â¬\88[h,â\91¡[I]V.T] L2 â\86\92 â\9dªG,L1â\9d« ⊢ ⬈[h,V] L2.
 /2 width=3 by rex_fwd_pair_sn/ qed-.
 
 lemma rpx_fwd_bind_dx: ∀h,p,I,G,L1,L2,V,T.
-                       â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,â\93\91{p,I}V.T] L2 â\86\92 â¦\83G,L1.â\93\91{I}Vâ¦\84 â\8a¢ â¬\88[h,T] L2.â\93\91{I}V.
+                       â\9dªG,L1â\9d« â\8a¢ â¬\88[h,â\93\91[p,I]V.T] L2 â\86\92 â\9dªG,L1.â\93\91[I]Vâ\9d« â\8a¢ â¬\88[h,T] L2.â\93\91[I]V.
 /2 width=2 by rex_fwd_bind_dx/ qed-.
 
 lemma rpx_fwd_flat_dx: ∀h,I,G,L1,L2,V,T.
-                       â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,â\93\95{I}V.T] L2 â\86\92 â¦\83G,L1â¦\84 ⊢ ⬈[h,T] L2.
+                       â\9dªG,L1â\9d« â\8a¢ â¬\88[h,â\93\95[I]V.T] L2 â\86\92 â\9dªG,L1â\9d« ⊢ ⬈[h,T] L2.
 /2 width=3 by rex_fwd_flat_dx/ qed-.