- lfpxs based on tc_lfxs

[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 21c37f3b3bf30c1b8a14d590156c2dec2b46f53c..172f88ed52e57a5cd9b8b6321365018eeff34d98 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx.ma
@@ -46,27 +46,47 @@ lemma lfpx_gref: ∀h,I,G,L1,L2,V1,V2,l.
                  ⦃G, L1⦄ ⊢ ⬈[h, §l] L2 → ⦃G, L1.ⓑ{I}V1⦄ ⊢ ⬈[h, §l] L2.ⓑ{I}V2.
 /2 width=1 by lfxs_gref/ qed.
 
+lemma lfpx_pair_repl_dx: ∀h,I,G,L1,L2,T,V,V1.
+                         ⦃G, L1.ⓑ{I}V⦄ ⊢ ⬈[h, T] L2.ⓑ{I}V1 →
+                         ∀V2. ⦃G, L1⦄ ⊢ V ⬈[h] V2 →
+                         ⦃G, L1.ⓑ{I}V⦄ ⊢ ⬈[h, T] L2.ⓑ{I}V2.
+/2 width=2 by lfxs_pair_repl_dx/ qed-.
+
 (* Basic inversion lemmas ***************************************************)
 
-lemma lfpx_inv_atom_sn: ∀h,I,G,Y2. ⦃G, ⋆⦄ ⊢ ⬈[h, ⓪{I}] Y2 → Y2 = ⋆.
+(* 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-.
 
-lemma lfpx_inv_atom_dx: ∀h,I,G,Y1. ⦃G, Y1⦄ ⊢ ⬈[h, ⓪{I}] ⋆ → Y1 = ⋆.
+(* 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-.
 
+lemma lfpx_inv_sort: ∀h,G,Y1,Y2,s. ⦃G, Y1⦄ ⊢ ⬈[h, ⋆s] Y2 →
+                     (Y1 = ⋆ ∧ Y2 = ⋆) ∨
+                     ∃∃I,L1,L2,V1,V2. ⦃G, L1⦄ ⊢ ⬈[h, ⋆s] L2 &
+                                      Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2.
+/2 width=1 by lfxs_inv_sort/ qed-.
+
 lemma lfpx_inv_zero: ∀h,G,Y1,Y2. ⦃G, Y1⦄ ⊢ ⬈[h, #0] Y2 →
-                     (Y1 = ⋆ ∧ 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 →
-                     (Y1 = ⋆ ∧ Y2 = ⋆) ∨ 
+                     (Y1 = ⋆ ∧ Y2 = ⋆) ∨
                      ∃∃I,L1,L2,V1,V2. ⦃G, L1⦄ ⊢ ⬈[h, #i] L2 &
                                       Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2.
 /2 width=1 by lfxs_inv_lref/ qed-.
 
+lemma lfpx_inv_gref: ∀h,G,Y1,Y2,l. ⦃G, Y1⦄ ⊢ ⬈[h, §l] Y2 →
+                     (Y1 = ⋆ ∧ Y2 = ⋆) ∨
+                     ∃∃I,L1,L2,V1,V2. ⦃G, L1⦄ ⊢ ⬈[h, §l] L2 &
+                                      Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2.
+/2 width=1 by lfxs_inv_gref/ qed-.
+
 lemma lfpx_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.
 /2 width=2 by lfxs_inv_bind/ qed-.
@@ -77,6 +97,14 @@ lemma lfpx_inv_flat: ∀h,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈[h, ⓕ{I}V.T] L2 
 
 (* Advanced inversion lemmas ************************************************)
 
+lemma lfpx_inv_sort_pair_sn: ∀h,I,G,Y2,L1,V1,s. ⦃G, L1.ⓑ{I}V1⦄ ⊢ ⬈[h, ⋆s] Y2 →
+                             ∃∃L2,V2. ⦃G, L1⦄ ⊢ ⬈[h, ⋆s] L2 & Y2 = L2.ⓑ{I}V2.
+/2 width=2 by lfxs_inv_sort_pair_sn/ qed-.
+
+lemma lfpx_inv_sort_pair_dx: ∀h,I,G,Y1,L2,V2,s. ⦃G, Y1⦄ ⊢ ⬈[h, ⋆s] L2.ⓑ{I}V2 →
+                             ∃∃L1,V1. ⦃G, L1⦄ ⊢ ⬈[h, ⋆s] L2 & Y1 = L1.ⓑ{I}V1.
+/2 width=2 by lfxs_inv_sort_pair_dx/ qed-.
+
 lemma lfpx_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.
@@ -95,31 +123,28 @@ lemma lfpx_inv_lref_pair_dx: ∀h,I,G,Y1,L2,V2,i. ⦃G, Y1⦄ ⊢ ⬈[h, #⫯i]
                              ∃∃L1,V1. ⦃G, L1⦄ ⊢ ⬈[h, #i] L2 & Y1 = L1.ⓑ{I}V1.
 /2 width=2 by lfxs_inv_lref_pair_dx/ qed-.
 
+lemma lfpx_inv_gref_pair_sn: ∀h,I,G,Y2,L1,V1,l. ⦃G, L1.ⓑ{I}V1⦄ ⊢ ⬈[h, §l] Y2 →
+                             ∃∃L2,V2. ⦃G, L1⦄ ⊢ ⬈[h, §l] L2 & Y2 = L2.ⓑ{I}V2.
+/2 width=2 by lfxs_inv_gref_pair_sn/ qed-.
+
+lemma lfpx_inv_gref_pair_dx: ∀h,I,G,Y1,L2,V2,l. ⦃G, Y1⦄ ⊢ ⬈[h, §l] L2.ⓑ{I}V2 →
+                             ∃∃L1,V1. ⦃G, L1⦄ ⊢ ⬈[h, §l] L2 & Y1 = L1.ⓑ{I}V1.
+/2 width=2 by lfxs_inv_gref_pair_dx/ qed-.
+
 (* Basic forward lemmas *****************************************************)
 
-lemma lfpx_fwd_bind_sn: ∀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 → ⦃G, L1⦄ ⊢ ⬈[h, V] L2.
-/2 width=4 by lfxs_fwd_bind_sn/ qed-.
+lemma lfpx_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 → ⦃G, L1⦄ ⊢ ⬈[h, V] L2.
+/2 width=3 by lfxs_fwd_pair_sn/ qed-.
 
 lemma lfpx_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.
 /2 width=2 by lfxs_fwd_bind_dx/ qed-.
 
-lemma lfpx_fwd_flat_sn: ∀h,I,G,L1,L2,V,T.
-                        ⦃G, L1⦄ ⊢ ⬈[h, ⓕ{I}V.T] L2 → ⦃G, L1⦄ ⊢ ⬈[h, V] L2.
-/2 width=3 by lfxs_fwd_flat_sn/ qed-.
-
 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-.
 
-lemma lfpx_fwd_pair_sn: ∀h,I,G,L1,L2,V,T.
-                        ⦃G, L1⦄ ⊢ ⬈[h, ②{I}V.T] L2 → ⦃G, L1⦄ ⊢ ⬈[h, V] L2.
-/2 width=3 by lfxs_fwd_pair_sn/ qed-.
-
-(* Basic_2A1: removed theorems 14:
-              lpx_refl lpx_pair lpx_fwd_length
-              lpx_inv_atom1 lpx_inv_pair1 lpx_inv_atom2 lpx_inv_pair2 lpx_inv_pair
-              lpx_drop_conf drop_lpx_trans lpx_drop_trans_O1
-              lpx_cpx_frees_trans cpx_frees_trans lpx_frees_trans
+(* Basic_2A1: removed theorems 3:
+              lpx_inv_pair1 lpx_inv_pair2 lpx_inv_pair
 *)