renaming

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx.ma
index 537bb8bc87ecdffae0556804809fe88ff874a9c2..4067962d8fe89682653be2bd9b381f5e51b768b2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx.ma
@@ -16,13 +16,13 @@ include "basic_2/notation/relations/predtysn_5.ma".
 include "basic_2/static/lfxs.ma".
 include "basic_2/rt_transition/cpx_ext.ma".
 
-(* UNCOUNTED PARALLEL RT-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES *****)
+(* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
 
-definition lfpx: sh → genv → relation3 term lenv lenv ≝
-                 λh,G. lfxs (cpx h G).
+definition lfpx (h) (G): relation3 term lenv lenv ≝
+                         lfxs (cpx h G).
 
 interpretation
-   "uncounted parallel rt-transition on referred entries (local environment)"
+   "unbound parallel rt-transition on referred entries (local environment)"
    'PRedTySn h T G L1 L2 = (lfpx h G T L1 L2).
 
 (* Basic properties ***********************************************************)
@@ -39,7 +39,7 @@ lemma lfpx_pair: ∀h,I,G,L1,L2,V1,V2.
 /2 width=1 by lfxs_pair/ qed.
 
 lemma lfpx_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, #⫯i] L2.ⓘ{I2}.
+                 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.ⓘ{I2}.
 /2 width=1 by lfxs_lref/ qed.
 
 lemma lfpx_gref: ∀h,I1,I2,G,L1,L2,l.
@@ -54,11 +54,9 @@ lemma lfpx_bind_repl_dx: ∀h,I,I1,G,L1,L2,T.
 
 (* Basic inversion lemmas ***************************************************)
 
-(* Basic_2A1: uses: lpx_inv_atom1 *)
 lemma lfpx_inv_atom_sn: ∀h,G,Y2,T. ⦃G, ⋆⦄ ⊢ ⬈[h, T] Y2 → Y2 = ⋆.
 /2 width=3 by lfxs_inv_atom_sn/ qed-.
 
-(* Basic_2A1: uses: lpx_inv_atom2 *)
 lemma lfpx_inv_atom_dx: ∀h,G,Y1,T. ⦃G, Y1⦄ ⊢ ⬈[h, T] ⋆ → Y1 = ⋆.
 /2 width=3 by lfxs_inv_atom_dx/ qed-.
 
@@ -67,15 +65,8 @@ lemma lfpx_inv_sort: ∀h,G,Y1,Y2,s. ⦃G, Y1⦄ ⊢ ⬈[h, ⋆s] Y2 →
                       | ∃∃I1,I2,L1,L2. ⦃G, L1⦄ ⊢ ⬈[h, ⋆s] L2 &
                                        Y1 = L1.ⓘ{I1} & Y2 = L2.ⓘ{I2}.
 /2 width=1 by lfxs_inv_sort/ qed-.
-(*
-lemma lfpx_inv_zero: ∀h,G,Y1,Y2. ⦃G, Y1⦄ ⊢ ⬈[h, #0] Y2 →
-                     (Y1 = ⋆ ∧ Y2 = ⋆) ∨
-                     ∃∃I,L1,L2,V1,V2. ⦃G, L1⦄ ⊢ ⬈[h, V1] L2 &
-                                      ⦃G, L1⦄ ⊢ V1 ⬈[h] V2 &
-                                      Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2.
-/2 width=1 by lfxs_inv_zero/ qed-.
-*)
-lemma lfpx_inv_lref: ∀h,G,Y1,Y2,i. ⦃G, Y1⦄ ⊢ ⬈[h, #⫯i] Y2 →
+
+lemma lfpx_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}.
@@ -115,11 +106,11 @@ lemma lfpx_inv_zero_pair_dx: ∀h,I,G,Y1,L2,V2. ⦃G, Y1⦄ ⊢ ⬈[h, #0] L2.
                                       Y1 = L1.ⓑ{I}V1.
 /2 width=1 by lfxs_inv_zero_pair_dx/ qed-.
 
-lemma lfpx_inv_lref_bind_sn: â\88\80h,I1,G,Y2,L1,i. â¦\83G, L1.â\93\98{I1}â¦\84 â\8a¢ â¬\88[h, #⫯i] Y2 →
+lemma lfpx_inv_lref_bind_sn: â\88\80h,I1,G,Y2,L1,i. â¦\83G, L1.â\93\98{I1}â¦\84 â\8a¢ â¬\88[h, #â\86\91i] Y2 →
                              ∃∃I2,L2. ⦃G, L1⦄ ⊢ ⬈[h, #i] L2 & Y2 = L2.ⓘ{I2}.
 /2 width=2 by lfxs_inv_lref_bind_sn/ qed-.
 
-lemma lfpx_inv_lref_bind_dx: â\88\80h,I2,G,Y1,L2,i. â¦\83G, Y1â¦\84 â\8a¢ â¬\88[h, #⫯i] L2.ⓘ{I2} →
+lemma lfpx_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.ⓘ{I2} →
                              ∃∃I1,L1. ⦃G, L1⦄ ⊢ ⬈[h, #i] L2 & Y1 = L1.ⓘ{I1}.
 /2 width=2 by lfxs_inv_lref_bind_dx/ qed-.
 
@@ -144,7 +135,3 @@ lemma lfpx_fwd_bind_dx: ∀h,p,I,G,L1,L2,V,T.
 lemma lfpx_fwd_flat_dx: ∀h,I,G,L1,L2,V,T.
                         ⦃G, L1⦄ ⊢ ⬈[h, ⓕ{I}V.T] L2 → ⦃G, L1⦄ ⊢ ⬈[h, T] L2.
 /2 width=3 by lfxs_fwd_flat_dx/ qed-.
-
-(* Basic_2A1: removed theorems 3:
-              lpx_inv_pair1 lpx_inv_pair2 lpx_inv_pair
-*)