- 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 f6bc891d7af225ef58240b517c592bdf69f83728..6fb68863e758177595807af0401070bc8d233c7f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq.ma
@@ -73,6 +73,7 @@ lemma tdeq_lfdeq_conf_sn: ∀h,o. s_r_confluent1 … (cdeq h o) (lfdeq h o).
 /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/
@@ -81,6 +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.
@@ -93,6 +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.
@@ -125,10 +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-.
@@ -156,32 +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 31: 
-              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_dec 
+              lleq_skip lleq_lref lleq_free
+              lleq_Y lleq_ge_up lleq_ge
+               
 *)