cpxs_lfpx completed

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs.ma
index 92888ef469eac6ddc990da415c4aa0d02071d441..a1d50e69f243bd9c9ea175138630e9d3008e16df 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs.ma
@@ -43,7 +43,7 @@ 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/
@@ -77,6 +77,13 @@ 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-.
+
 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/
@@ -93,7 +100,7 @@ lemma lfxs_inv_atom_dx: ∀R,I,Y1. Y1 ⦻*[R, ⓪{I}] ⋆ → Y1 = ⋆.
 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 +113,7 @@ 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 +124,7 @@ 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 *