X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Flfxs.ma;h=367b19d32635e5379dfba65f018effe0eada6f70;hb=58ea181757dce19b875b2f5a224fe193b2263004;hp=92888ef469eac6ddc990da415c4aa0d02071d441;hpb=09b4420070d6a71990e16211e499b51dbb0742cb;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs.ma
index 92888ef46..367b19d32 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs.ma
@@ -43,12 +43,13 @@ definition R_confluent2_lfxs: relation4 (relation3 lenv term term)
                               ∀L1. L0 ⦻*[RP1, T0] L1 → ∀L2. L0 ⦻*[RP2, T0] L2 →
                               ∃∃T. R2 L1 T1 T & R1 L2 T2 T.
 
-(* Basic properties ***********************************************************)
+(* Basic properties *********************************************************)
 
 lemma lfxs_atom: ∀R,I. ⋆ ⦻*[R, ⓪{I}] ⋆.
 /3 width=3 by lexs_atom, frees_atom, ex2_intro/
 qed.
 
+(* Basic_2A1: uses: llpx_sn_sort *)
 lemma lfxs_sort: ∀R,I,L1,L2,V1,V2,s.
                  L1 ⦻*[R, ⋆s] L2 → L1.ⓑ{I}V1 ⦻*[R, ⋆s] L2.ⓑ{I}V2.
 #R #I #L1 #L2 #V1 #V2 #s * /3 width=3 by lexs_push, frees_sort, ex2_intro/
@@ -64,6 +65,7 @@ lemma lfxs_lref: ∀R,I,L1,L2,V1,V2,i.
 #R #I #L1 #L2 #V1 #V2 #i * /3 width=3 by lexs_push, frees_lref, ex2_intro/
 qed.
 
+(* Basic_2A1: uses: llpx_sn_gref *)
 lemma lfxs_gref: ∀R,I,L1,L2,V1,V2,l.
                  L1 ⦻*[R, §l] L2 → L1.ⓑ{I}V1 ⦻*[R, §l] L2.ⓑ{I}V2.
 #R #I #L1 #L2 #V1 #V2 #l * /3 width=3 by lexs_push, frees_gref, ex2_intro/
@@ -77,23 +79,39 @@ lemma lfxs_pair_repl_dx: ∀R,I,L1,L2,T,V,V1.
 /3 width=5 by lexs_pair_repl, ex2_intro/
 qed-.
 
+lemma lfxs_sym: ∀R. lexs_frees_confluent R cfull →
+                (∀L1,L2,T1,T2. R L1 T1 T2 → R L2 T2 T1) →
+                ∀T. symmetric … (lfxs R T).
+#R #H1R #H2R #T #L1 #L2 * #f1 #Hf1 #HL12 elim (H1R … Hf1 … HL12) -Hf1
+/4 width=5 by sle_lexs_trans, lexs_sym, ex2_intro/
+qed-.
+
+(* Basic_2A1: uses: llpx_sn_co *)
 lemma lfxs_co: ∀R1,R2. (∀L,T1,T2. R1 L T1 T2 → R2 L T1 T2) →
                ∀L1,L2,T. L1 ⦻*[R1, T] L2 → L1 ⦻*[R2, T] L2.
 #R1 #R2 #HR #L1 #L2 #T * /4 width=7 by lexs_co, ex2_intro/
 qed-.
 
+lemma lfxs_isid: ∀R1,R2,L1,L2,T1,T2.
+                 (∀f. L1 ⊢ 𝐅*⦃T1⦄ ≡ f → 𝐈⦃f⦄) → 
+                 (∀f. 𝐈⦃f⦄ → L1 ⊢ 𝐅*⦃T2⦄ ≡ f) → 
+                 L1 ⦻*[R1, T1] L2 → L1 ⦻*[R2, T2] L2.
+#R1 #R2 #L1 #L2 #T1 #T2 #H1 #H2 *
+/4 width=7 by lexs_co_isid, ex2_intro/
+qed-.
+
 (* Basic inversion lemmas ***************************************************)
 
-lemma lfxs_inv_atom_sn: ∀R,I,Y2. ⋆ ⦻*[R, ⓪{I}] Y2 → Y2 = ⋆.
-#R #I #Y2 * /2 width=4 by lexs_inv_atom1/
+lemma lfxs_inv_atom_sn: ∀R,Y2,T. ⋆ ⦻*[R, T] Y2 → Y2 = ⋆.
+#R #Y2 #T * /2 width=4 by lexs_inv_atom1/
 qed-.
 
-lemma lfxs_inv_atom_dx: ∀R,I,Y1. Y1 ⦻*[R, ⓪{I}] ⋆ → Y1 = ⋆.
+lemma lfxs_inv_atom_dx: ∀R,Y1,T. Y1 ⦻*[R, T] ⋆ → Y1 = ⋆.
 #R #I #Y1 * /2 width=4 by lexs_inv_atom2/
 qed-.
 
 lemma lfxs_inv_sort: ∀R,Y1,Y2,s. Y1 ⦻*[R, ⋆s] Y2 →
-                     (Y1 = ⋆ ∧ Y2 = ⋆) ∨ 
+                     (Y1 = ⋆ ∧ Y2 = ⋆) ∨
                      ∃∃I,L1,L2,V1,V2. L1 ⦻*[R, ⋆s] L2 &
                                       Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2.
 #R * [ | #Y1 #I #V1 ] #Y2 #s * #f #H1 #H2
@@ -106,7 +124,7 @@ lemma lfxs_inv_sort: ∀R,Y1,Y2,s. Y1 ⦻*[R, ⋆s] Y2 →
 qed-.
 
 lemma lfxs_inv_zero: ∀R,Y1,Y2. Y1 ⦻*[R, #0] Y2 →
-                     (Y1 = ⋆ ∧ Y2 = ⋆) ∨ 
+                     (Y1 = ⋆ ∧ Y2 = ⋆) ∨
                      ∃∃I,L1,L2,V1,V2. L1 ⦻*[R, V1] L2 & R L1 V1 V2 &
                                       Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2.
 #R #Y1 #Y2 * #f #H1 #H2 elim (frees_inv_zero … H1) -H1 *
@@ -117,7 +135,7 @@ lemma lfxs_inv_zero: ∀R,Y1,Y2. Y1 ⦻*[R, #0] Y2 →
 qed-.
 
 lemma lfxs_inv_lref: ∀R,Y1,Y2,i. Y1 ⦻*[R, #⫯i] Y2 →
-                     (Y1 = ⋆ ∧ Y2 = ⋆) ∨ 
+                     (Y1 = ⋆ ∧ Y2 = ⋆) ∨
                      ∃∃I,L1,L2,V1,V2. L1 ⦻*[R, #i] L2 &
                                       Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2.
 #R #Y1 #Y2 #i * #f #H1 #H2 elim (frees_inv_lref … H1) -H1 *
@@ -140,12 +158,14 @@ lemma lfxs_inv_gref: ∀R,Y1,Y2,l. Y1 ⦻*[R, §l] Y2 →
 ]
 qed-.
 
+(* Basic_2A1: uses: llpx_sn_inv_bind llpx_sn_inv_bind_O *)
 lemma lfxs_inv_bind: ∀R,p,I,L1,L2,V1,V2,T. L1 ⦻*[R, ⓑ{p,I}V1.T] L2 → R L1 V1 V2 →
                      L1 ⦻*[R, V1] L2 ∧ L1.ⓑ{I}V1 ⦻*[R, T] L2.ⓑ{I}V2.
 #R #p #I #L1 #L2 #V1 #V2 #T * #f #Hf #HL #HV elim (frees_inv_bind … Hf) -Hf
 /6 width=6 by sle_lexs_trans, lexs_inv_tl, sor_inv_sle_dx, sor_inv_sle_sn, ex2_intro, conj/
 qed-.
 
+(* Basic_2A1: uses: llpx_sn_inv_flat *)
 lemma lfxs_inv_flat: ∀R,I,L1,L2,V,T. L1 ⦻*[R, ⓕ{I}V.T] L2 →
                      L1 ⦻*[R, V] L2 ∧ L1 ⦻*[R, T] L2.
 #R #I #L1 #L2 #V #T * #f #Hf #HL elim (frees_inv_flat … Hf) -Hf
@@ -224,34 +244,34 @@ qed-.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma lfxs_fwd_bind_sn: ∀R,p,I,L1,L2,V,T. L1 ⦻*[R, ⓑ{p,I}V.T] L2 → L1 ⦻*[R, V] L2.
-#R #p #I #L1 #L2 #V #T * #f #Hf #HL elim (frees_inv_bind … Hf) -Hf
+(* Basic_2A1: uses: llpx_sn_fwd_pair_sn llpx_sn_fwd_bind_sn llpx_sn_fwd_flat_sn *)
+lemma lfxs_fwd_pair_sn: ∀R,I,L1,L2,V,T. L1 ⦻*[R, ②{I}V.T] L2 → L1 ⦻*[R, V] L2.
+#R * [ #p ] #I #L1 #L2 #V #T * #f #Hf #HL
+[ elim (frees_inv_bind … Hf) | elim (frees_inv_flat … Hf) ] -Hf
 /4 width=6 by sle_lexs_trans, sor_inv_sle_sn, ex2_intro/
 qed-.
 
+(* Basic_2A1: uses: llpx_sn_fwd_bind_dx llpx_sn_fwd_bind_O_dx *)
 lemma lfxs_fwd_bind_dx: ∀R,p,I,L1,L2,V1,V2,T. L1 ⦻*[R, ⓑ{p,I}V1.T] L2 →
                         R L1 V1 V2 → L1.ⓑ{I}V1 ⦻*[R, T] L2.ⓑ{I}V2.
 #R #p #I #L1 #L2 #V1 #V2 #T #H #HV elim (lfxs_inv_bind … H HV) -H -HV //
 qed-.
 
-lemma lfxs_fwd_flat_sn: ∀R,I,L1,L2,V,T. L1 ⦻*[R, ⓕ{I}V.T] L2 → L1 ⦻*[R, V] L2.
-#R #I #L1 #L2 #V #T #H elim (lfxs_inv_flat … H) -H //
-qed-.
-
+(* Basic_2A1: uses: llpx_sn_fwd_flat_dx *)
 lemma lfxs_fwd_flat_dx: ∀R,I,L1,L2,V,T. L1 ⦻*[R, ⓕ{I}V.T] L2 → L1 ⦻*[R, T] L2.
 #R #I #L1 #L2 #V #T #H elim (lfxs_inv_flat … H) -H //
 qed-.
 
-lemma lfxs_fwd_pair_sn: ∀R,I,L1,L2,V,T. L1 ⦻*[R, ②{I}V.T] L2 → L1 ⦻*[R, V] L2.
-#R * /2 width=4 by lfxs_fwd_flat_sn, lfxs_fwd_bind_sn/
+lemma lfxs_fwd_dx: ∀R,I,L1,K2,T,V2. L1 ⦻*[R, T] K2.ⓑ{I}V2 →
+                   ∃∃K1,V1. L1 = K1.ⓑ{I}V1.
+#R #I #L1 #K2 #T #V2 * #f elim (pn_split f) * #g #Hg #_ #Hf destruct
+[ elim (lexs_inv_push2 … Hf) | elim (lexs_inv_next2 … Hf) ] -Hf #K1 #V1 #_ #_ #H destruct
+/2 width=3 by ex1_2_intro/
 qed-.
 
-(* Basic_2A1: removed theorems 24:
-              llpx_sn_sort llpx_sn_skip llpx_sn_lref llpx_sn_free llpx_sn_gref
-              llpx_sn_bind llpx_sn_flat
-              llpx_sn_inv_bind llpx_sn_inv_flat
-              llpx_sn_fwd_lref llpx_sn_fwd_pair_sn llpx_sn_fwd_length
-              llpx_sn_fwd_bind_sn llpx_sn_fwd_bind_dx llpx_sn_fwd_flat_sn llpx_sn_fwd_flat_dx
-              llpx_sn_refl llpx_sn_Y llpx_sn_bind_O llpx_sn_ge_up llpx_sn_ge llpx_sn_co
-              llpx_sn_fwd_drop_sn llpx_sn_fwd_drop_dx              
+(* Basic_2A1: removed theorems 9:
+              llpx_sn_skip llpx_sn_lref llpx_sn_free 
+              llpx_sn_fwd_lref
+              llpx_sn_Y llpx_sn_ge_up llpx_sn_ge 
+              llpx_sn_fwd_drop_sn llpx_sn_fwd_drop_dx      
 *)