update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / substitution / fsubst_eq.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_eq.ma
index a6681b59227b68d7a15df0915012b0c13dc86eaa..c3a985716d5427f56434ec93bc6503420a04f7e6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_eq.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_eq.ma
@@ -13,10 +13,21 @@
 (**************************************************************************)
 
 include "delayed_updating/substitution/fsubst.ma".
-include "delayed_updating/syntax/prototerm_equivalence.ma".
+include "delayed_updating/syntax/prototerm_eq.ma".
+
+(* FOCALIZED SUBSTITUTION ***************************************************)
 
 (* Constructions with subset_equivalence ************************************)
 
+lemma fsubst_empty_rc (t) (u):
+      u ⇔ t[⋔𝐞←u].
+#t #u @conj #p
+[ #Hp /3 width=3 by or_introl, ex2_intro/ ]
+* *
+[ #r #Hr #H0 destruct // ]
+#H1p #H2p elim H2p -H2p //
+qed.
+
 lemma subset_inclusion_fsubst_bi (t1) (t2) (u1) (u2) (p):
       t1 ⊆ t2 → u1 ⊆ u2 → t1[⋔p←u1] ⊆ t2[⋔p←u2].
 #t1 #t2 #u1 #u2 #p #Ht #Hu #q * *
@@ -26,8 +37,8 @@ lemma subset_inclusion_fsubst_bi (t1) (t2) (u1) (u2) (p):
 ]
 qed.
 
-lemma fsubst_eq_repl (t1) (t2) (u1) (u2) (p):
-      t1 ⇔ t2 → u1 ⇔ u2 → t1[⋔p←u1] ⇔ t2[⋔p←u2].
-#t1 #t2 #u1 #u2 #p * #H1t #H2t * #H1u #H2u
+lemma fsubst_eq_repl (t1) (t2) (u1) (u2) (p1) (p2):
+      t1 ⇔ t2 → p1 = p2 → u1 ⇔ u2 → t1[⋔p1←u1] ⇔ t2[⋔p2←u2].
+#t1 #t2 #u1 #u2 #p1 #p2 * #H1t #H2t #Hp * #H1u #H2u
 /3 width=5 by conj, subset_inclusion_fsubst_bi/
 qed.