- lfpxs based on tc_lfxs

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lfdeq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq.ma
index e75c4e734c628216bcff2dc05c788f7b38bf5ec5..6fb68863e758177595807af0401070bc8d233c7f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq.ma
@@ -61,6 +61,19 @@ lemma frees_tdeq_conf_lexs: ∀h,o,f,L1,T1. L1 ⊢ 𝐅*⦃T1⦄ ≡ f → ∀T2
 ]
 qed-.
 
+lemma frees_tdeq_conf: ∀h,o,f,L,T1. L ⊢ 𝐅*⦃T1⦄ ≡ f →
+                       ∀T2. T1 ≡[h, o] T2 → L ⊢ 𝐅*⦃T2⦄ ≡ f.
+/3 width=7 by frees_tdeq_conf_lexs, lexs_refl/ qed-.
+
+lemma frees_lfdeq_conf_lexs: ∀h,o. lexs_frees_confluent (cdeq h o) cfull.
+/3 width=7 by frees_tdeq_conf_lexs, ex2_intro/ qed-.
+
+lemma tdeq_lfdeq_conf_sn: ∀h,o. s_r_confluent1 … (cdeq h o) (lfdeq h o).
+#h #o #L1 #T1 #T2 #HT12 #L2 *
+/3 width=5 by frees_tdeq_conf, ex2_intro/
+qed-.
+
+(* Basic_2A1: uses: lleq_sym *)
 lemma lfdeq_sym: ∀h,o,T. symmetric … (lfdeq h o T).
 #h #o #T #L1 #L2 *
 /4 width=7 by frees_tdeq_conf_lexs, lfxs_sym, tdeq_sym, ex2_intro/
@@ -69,6 +82,7 @@ qed-.
 lemma lfdeq_atom: ∀h,o,I. ⋆ ≡[h, o, ⓪{I}] ⋆.
 /2 width=1 by lfxs_atom/ qed.
 
+(* Basic_2A1: uses: lleq_sort *)
 lemma lfdeq_sort: ∀h,o,I,L1,L2,V1,V2,s.
                   L1 ≡[h, o, ⋆s] L2 → L1.ⓑ{I}V1 ≡[h, o, ⋆s] L2.ⓑ{I}V2.
 /2 width=1 by lfxs_sort/ qed.
@@ -81,6 +95,7 @@ lemma lfdeq_lref: ∀h,o,I,L1,L2,V1,V2,i.
                   L1 ≡[h, o, #i] L2 → L1.ⓑ{I}V1 ≡[h, o, #⫯i] L2.ⓑ{I}V2.
 /2 width=1 by lfxs_lref/ qed.
 
+(* Basic_2A1: uses: lleq_gref *)
 lemma lfdeq_gref: ∀h,o,I,L1,L2,V1,V2,l.
                   L1 ≡[h, o, §l] L2 → L1.ⓑ{I}V1 ≡[h, o, §l] L2.ⓑ{I}V2.
 /2 width=1 by lfxs_gref/ qed.
@@ -93,10 +108,10 @@ lemma lfdeq_pair_repl_dx: ∀h,o,I,L1,L2.∀T:term.∀V,V1.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma lfdeq_inv_atom_sn: ∀h,o,I,Y2. ⋆ ≡[h, o, ⓪{I}] Y2 → Y2 = ⋆.
+lemma lfdeq_inv_atom_sn: ∀h,o,Y2. ∀T:term. ⋆ ≡[h, o, T] Y2 → Y2 = ⋆.
 /2 width=3 by lfxs_inv_atom_sn/ qed-.
 
-lemma lfdeq_inv_atom_dx: ∀h,o,I,Y1. Y1 ≡[h, o, ⓪{I}] ⋆ → Y1 = ⋆.
+lemma lfdeq_inv_atom_dx: ∀h,o,Y1. ∀T:term. Y1 ≡[h, o, T] ⋆ → Y1 = ⋆.
 /2 width=3 by lfxs_inv_atom_dx/ qed-.
 
 lemma lfdeq_inv_zero: ∀h,o,Y1,Y2. Y1 ≡[h, o, #0] Y2 →
@@ -113,10 +128,12 @@ lemma lfdeq_inv_lref: ∀h,o,Y1,Y2,i. Y1 ≡[h, o, #⫯i] Y2 →
                                        Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2.
 /2 width=1 by lfxs_inv_lref/ qed-.
 
+(* Basic_2A1: uses: lleq_inv_bind lleq_inv_bind_O *)
 lemma lfdeq_inv_bind: ∀h,o,p,I,L1,L2,V,T. L1 ≡[h, o, ⓑ{p,I}V.T] L2 →
                       L1 ≡[h, o, V] L2 ∧ L1.ⓑ{I}V ≡[h, o, T] L2.ⓑ{I}V.
 /2 width=2 by lfxs_inv_bind/ qed-.
 
+(* Basic_2A1: uses: lleq_inv_flat *)
 lemma lfdeq_inv_flat: ∀h,o,I,L1,L2,V,T. L1 ≡[h, o, ⓕ{I}V.T] L2 →
                       L1 ≡[h, o, V] L2 ∧ L1 ≡[h, o, T] L2.
 /2 width=2 by lfxs_inv_flat/ qed-.
@@ -144,27 +161,27 @@ lemma lfdeq_inv_lref_pair_dx: ∀h,o,I,Y1,L2,V2,i. Y1 ≡[h, o, #⫯i] L2.ⓑ{I}
 
 (* Basic forward lemmas *****************************************************)
 
-lemma lfdeq_fwd_bind_sn: ∀h,o,p,I,L1,L2,V,T. L1 ≡[h, o, ⓑ{p,I}V.T] L2 → L1 ≡[h, o, V] L2.
-/2 width=4 by lfxs_fwd_bind_sn/ qed-.
+(* Basic_2A1: uses: lleq_fwd_bind_sn lleq_fwd_flat_sn *)
+lemma lfdeq_fwd_pair_sn: ∀h,o,I,L1,L2,V,T. L1 ≡[h, o, ②{I}V.T] L2 → L1 ≡[h, o, V] L2.
+/2 width=3 by lfxs_fwd_pair_sn/ qed-.
 
+(* Basic_2A1: uses: lleq_fwd_bind_dx lleq_fwd_bind_O_dx *)
 lemma lfdeq_fwd_bind_dx: ∀h,o,p,I,L1,L2,V,T.
                          L1 ≡[h, o, ⓑ{p,I}V.T] L2 → L1.ⓑ{I}V ≡[h, o, T] L2.ⓑ{I}V.
 /2 width=2 by lfxs_fwd_bind_dx/ qed-.
 
-lemma lfdeq_fwd_flat_sn: ∀h,o,I,L1,L2,V,T. L1 ≡[h, o, ⓕ{I}V.T] L2 → L1 ≡[h, o, V] L2.
-/2 width=3 by lfxs_fwd_flat_sn/ qed-.
-
+(* Basic_2A1: uses: lleq_fwd_flat_dx *)
 lemma lfdeq_fwd_flat_dx: ∀h,o,I,L1,L2,V,T. L1 ≡[h, o, ⓕ{I}V.T] L2 → L1 ≡[h, o, T] L2.
 /2 width=3 by lfxs_fwd_flat_dx/ qed-.
 
-lemma lfdeq_fwd_pair_sn: ∀h,o,I,L1,L2,V,T. L1 ≡[h, o, ②{I}V.T] L2 → L1 ≡[h, o, V] L2.
-/2 width=3 by lfxs_fwd_pair_sn/ qed-.
+lemma lfdeq_fwd_dx: ∀h,o,I,L1,K2,V2. ∀T:term. L1 ≡[h, o, T] K2.ⓑ{I}V2 →
+                    ∃∃K1,V1. L1 = K1.ⓑ{I}V1.
+/2 width=5 by lfxs_fwd_dx/ qed-.
 
-(* Basic_2A1: removed theorems 30: 
-              lleq_ind lleq_inv_bind lleq_inv_flat lleq_fwd_length lleq_fwd_lref
+(* Basic_2A1: removed theorems 10:
+              lleq_ind lleq_fwd_lref
               lleq_fwd_drop_sn lleq_fwd_drop_dx
-              lleq_fwd_bind_sn lleq_fwd_bind_dx lleq_fwd_flat_sn lleq_fwd_flat_dx
-              lleq_sort lleq_skip lleq_lref lleq_free lleq_gref lleq_bind lleq_flat
-              lleq_refl lleq_Y lleq_sym lleq_ge_up lleq_ge lleq_bind_O llpx_sn_lrefl
-              lleq_trans lleq_canc_sn lleq_canc_dx lleq_nlleq_trans nlleq_lleq_div
+              lleq_skip lleq_lref lleq_free
+              lleq_Y lleq_ge_up lleq_ge
+               
 *)