component rt_transition completed!

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr.ma
index a38aff49da8083feb56e641e9e95e34fcfd0db98..61fc781b245d0eb0808743edaf7252470b1959b4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr.ma
@@ -34,8 +34,8 @@ lemma lfpr_sort: ∀h,I,G,L1,L2,V1,V2,s.
                  ⦃G, L1⦄ ⊢ ➡[h, ⋆s] L2 → ⦃G, L1.ⓑ{I}V1⦄ ⊢ ➡[h, ⋆s] L2.ⓑ{I}V2.
 /2 width=1 by lfxs_sort/ qed.
 
-lemma lfpr_zero: ∀h,I,G,L1,L2,V.
-                 ⦃G, L1⦄ ⊢ ➡[h, V] L2 → ⦃G, L1.ⓑ{I}V⦄ ⊢ ➡[h, #0] L2.ⓑ{I}V.
+lemma lfpr_zero: ∀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.
 /2 width=1 by lfxs_zero/ qed.
 
 lemma lfpr_lref: ∀h,I,G,L1,L2,V1,V2,i.
@@ -46,6 +46,12 @@ lemma lfpr_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 lfpr_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 lfpr_inv_atom_sn: ∀h,I,G,Y2. ⦃G, ⋆⦄ ⊢ ➡[h, ⓪{I}] Y2 → Y2 = ⋆.
@@ -54,6 +60,12 @@ lemma lfpr_inv_atom_sn: ∀h,I,G,Y2. ⦃G, ⋆⦄ ⊢ ➡[h, ⓪{I}] Y2 → Y2 =
 lemma lfpr_inv_atom_dx: ∀h,I,G,Y1. ⦃G, Y1⦄ ⊢ ➡[h, ⓪{I}] ⋆ → Y1 = ⋆.
 /2 width=3 by lfxs_inv_atom_dx/ qed-.
 
+lemma lfpr_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 lfpr_inv_zero: ∀h,G,Y1,Y2. ⦃G, Y1⦄ ⊢ ➡[h, #0] Y2 →
                      (Y1 = ⋆ ∧ Y2 = ⋆) ∨
                      ∃∃I,L1,L2,V1,V2. ⦃G, L1⦄ ⊢ ➡[h, V1] L2 &
@@ -67,6 +79,12 @@ lemma lfpr_inv_lref: ∀h,G,Y1,Y2,i. ⦃G, Y1⦄ ⊢ ➡[h, #⫯i] Y2 →
                                       Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2.
 /2 width=1 by lfxs_inv_lref/ qed-.
 
+lemma lfpr_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 lfpr_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 +95,14 @@ lemma lfpr_inv_flat: ∀h,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ➡[h, ⓕ{I}V.T] L2 
 
 (* Advanced inversion lemmas ************************************************)
 
+lemma lfpr_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 lfpr_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 lfpr_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.
@@ -95,6 +121,14 @@ lemma lfpr_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 lfpr_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 lfpr_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 lfpr_fwd_bind_sn: ∀h,p,I,G,L1,L2,V,T.
@@ -117,14 +151,17 @@ lemma lfpr_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 11:
+(* Basic_2A1: removed theorems 16:
               lpr_inv_atom1 lpr_inv_pair1 lpr_inv_atom2 lpr_inv_pair2
               lpr_refl lpr_pair
               lpr_fwd_length lpr_lpx
               lpr_drop_conf drop_lpr_trans lpr_drop_trans_O1
+              cpr_conf_lpr lpr_cpr_conf_dx lpr_cpr_conf_sn
+              fqu_lpr_trans fquq_lpr_trans
 *)
-(* Basic_1: removed theorems 7: wcpr0_gen_sort wcpr0_gen_head
-                                wcpr0_getl wcpr0_getl_back
-                                pr0_subst1_back
-                                wcpr0_drop wcpr0_drop_back
+(* Basic_1: removed theorems 7:
+            wcpr0_gen_sort wcpr0_gen_head
+            wcpr0_getl wcpr0_getl_back
+            pr0_subst1_back
+            wcpr0_drop wcpr0_drop_back
 *)