update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / syntax / path_structure.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_structure.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_structure.ma
index 95c728682db4058cc10f4caca52bb357be601634..288575c4e7680630668be3a61108478261a6d0c4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_structure.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_structure.ma
@@ -23,12 +23,11 @@ match p with
 [ list_empty     ⇒ 𝐞
 | list_lcons l q ⇒
    match l with
-   [ label_d k    ⇒ structure q
-   | label_d2 k d ⇒ structure q
-   | label_m      ⇒ structure q
-   | label_L      ⇒ (structure q)◖𝗟
-   | label_A      ⇒ (structure q)◖𝗔
-   | label_S      ⇒ (structure q)◖𝗦
+   [ label_d k ⇒ structure q
+   | label_m   ⇒ structure q
+   | label_L   ⇒ (structure q)◖𝗟
+   | label_A   ⇒ (structure q)◖𝗔
+   | label_S   ⇒ (structure q)◖𝗦
    ]
 ].
 
@@ -46,10 +45,6 @@ lemma structure_d_dx (p) (k):
       ⊗p = ⊗(p◖𝗱k).
 // qed.
 
-lemma structure_d2_dx (p) (k) (d):
-      ⊗p = ⊗(p◖𝗱❨k,d❩).
-// qed.
-
 lemma structure_m_dx (p):
       ⊗p = ⊗(p◖𝗺).
 // qed.
@@ -71,13 +66,13 @@ lemma structure_S_dx (p):
 theorem structure_idem (p):
         ⊗p = ⊗⊗p.
 #p elim p -p //
-* [ #k | #k #d ] #p #IH //
+* [ #k ] #p #IH //
 qed.
 
 theorem structure_append (p) (q):
         ⊗p●⊗q = ⊗(p●q).
 #p #q elim q -q //
-* [ #k | #k #d ] #q #IH //
+* [ #k ] #q #IH //
 <list_append_lcons_sn //
 qed.
 
@@ -88,11 +83,6 @@ lemma structure_d_sn (p) (k):
 #p #k <structure_append //
 qed.
 
-lemma structure_d2_sn (p) (k) (d):
-      ⊗p = ⊗(𝗱❨k,d❩◗p).
-#p #k #d <structure_append //
-qed.
-
 lemma structure_m_sn (p):
       ⊗p = ⊗(𝗺◗p).
 #p <structure_append //
@@ -117,23 +107,9 @@ qed.
 
 lemma eq_inv_d_dx_structure (h) (q) (p):
       q◖𝗱h = ⊗p → ⊥.
-#h #q #p elim p -p [| * [ #k | #k #d ] #p #IH ]
+#h #q #p elim p -p [| * [ #k ] #p #IH ]
 [ <structure_empty #H0 destruct
 | <structure_d_dx #H0 /2 width=1 by/
-| <structure_d2_dx #H0 /2 width=1 by/
-| <structure_m_dx #H0 /2 width=1 by/
-| <structure_L_dx #H0 destruct
-| <structure_A_dx #H0 destruct
-| <structure_S_dx #H0 destruct
-]
-qed-.
-
-lemma eq_inv_d2_dx_structure (d) (h) (q) (p):
-      q◖𝗱❨h,d❩ = ⊗p → ⊥.
-#d #h #q #p elim p -p [| * [ #k | #k #d ] #p #IH ]
-[ <structure_empty #H0 destruct
-| <structure_d_dx #H0 /2 width=1 by/
-| <structure_d2_dx #H0 /2 width=1 by/
 | <structure_m_dx #H0 /2 width=1 by/
 | <structure_L_dx #H0 destruct
 | <structure_A_dx #H0 destruct
@@ -143,10 +119,9 @@ qed-.
 
 lemma eq_inv_m_dx_structure (q) (p):
       q◖𝗺 = ⊗p → ⊥.
-#q #p elim p -p [| * [ #k | #k #d ] #p #IH ]
+#q #p elim p -p [| * [ #k ] #p #IH ]
 [ <structure_empty #H0 destruct
 | <structure_d_dx #H0 /2 width=1 by/
-| <structure_d2_dx #H0 /2 width=1 by/
 | <structure_m_dx #H0 /2 width=1 by/
 | <structure_L_dx #H0 destruct
 | <structure_A_dx #H0 destruct
@@ -157,14 +132,11 @@ qed-.
 lemma eq_inv_L_dx_structure (q) (p):
       q◖𝗟 = ⊗p →
       ∃∃r1,r2. q = ⊗r1 & 𝐞 = ⊗r2 & r1●𝗟◗r2 = p.
-#q #p elim p -p [| * [ #k | #k #d ] #p #IH ]
+#q #p elim p -p [| * [ #k ] #p #IH ]
 [ <structure_empty #H0 destruct
 | <structure_d_dx #H0
   elim IH -IH // -H0 #r1 #r2 #H1 #H0 #H2 destruct
   /2 width=5 by ex3_2_intro/
-| <structure_d2_dx #H0
-  elim IH -IH // -H0 #r1 #r2 #H1 #H0 #H2 destruct
-  /2 width=5 by ex3_2_intro/
 | <structure_m_dx #H0
   elim IH -IH // -H0 #r1 #r2 #H1 #H0 #H2 destruct
   /2 width=5 by ex3_2_intro/
@@ -178,14 +150,11 @@ qed-.
 lemma eq_inv_A_dx_structure (q) (p):
       q◖𝗔 = ⊗p →
       ∃∃r1,r2. q = ⊗r1 & 𝐞 = ⊗r2 & r1●𝗔◗r2 = p.
-#q #p elim p -p [| * [ #k | #k #d ] #p #IH ]
+#q #p elim p -p [| * [ #k ] #p #IH ]
 [ <structure_empty #H0 destruct
 | <structure_d_dx #H0
   elim IH -IH // -H0 #r1 #r2 #H1 #H0 #H2 destruct
   /2 width=5 by ex3_2_intro/
-| <structure_d2_dx #H0
-  elim IH -IH // -H0 #r1 #r2 #H1 #H0 #H2 destruct
-  /2 width=5 by ex3_2_intro/
 | <structure_m_dx #H0
   elim IH -IH // -H0 #r1 #r2 #H1 #H0 #H2 destruct
   /2 width=5 by ex3_2_intro/
@@ -199,14 +168,11 @@ qed-.
 lemma eq_inv_S_dx_structure (q) (p):
       q◖𝗦 = ⊗p →
       ∃∃r1,r2. q = ⊗r1 & 𝐞 = ⊗r2 & r1●𝗦◗r2 = p.
-#q #p elim p -p [| * [ #k | #k #d ] #p #IH ]
+#q #p elim p -p [| * [ #k ] #p #IH ]
 [ <structure_empty #H0 destruct
 | <structure_d_dx #H0
   elim IH -IH // -H0 #r1 #r2 #H1 #H0 #H2 destruct
   /2 width=5 by ex3_2_intro/
-| <structure_d2_dx #H0
-  elim IH -IH // -H0 #r1 #r2 #H1 #H0 #H2 destruct
-  /2 width=5 by ex3_2_intro/
 | <structure_m_dx #H0
   elim IH -IH // -H0 #r1 #r2 #H1 #H0 #H2 destruct
   /2 width=5 by ex3_2_intro/
@@ -222,11 +188,10 @@ qed-.
 theorem eq_inv_append_structure (p) (q) (r):
         p●q = ⊗r →
         ∃∃r1,r2.p = ⊗r1 & q = ⊗r2 & r1●r2 = r.
-#p #q elim q -q [| * [ #k | #k #d ] #q #IH ] #r
+#p #q elim q -q [| * [ #k ] #q #IH ] #r
 [ <list_append_empty_sn #H0 destruct
   /2 width=5 by ex3_2_intro/
 | #H0 elim (eq_inv_d_dx_structure … H0)
-| #H0 elim (eq_inv_d2_dx_structure … H0)
 | #H0 elim (eq_inv_m_dx_structure … H0)
 | #H0 elim (eq_inv_L_dx_structure … H0) -H0 #r1 #r2 #Hr1 #Hr2 #H0 destruct
   elim (IH … Hr1) -IH -Hr1 #s1 #s2 #H1 #H2 #H3 destruct
@@ -253,14 +218,6 @@ elim (eq_inv_append_structure … H0) -H0 #r1 #r2
 elim (eq_inv_d_dx_structure … H0)
 qed-.
 
-lemma eq_inv_d2_sn_structure (d) (h) (q) (p):
-      (𝗱❨h,d❩◗q) = ⊗p → ⊥.
-#d #h #q #p >list_cons_comm #H0
-elim (eq_inv_append_structure … H0) -H0 #r1 #r2
-<list_cons_comm #H0 #H1 #H2 destruct
-elim (eq_inv_d2_dx_structure … H0)
-qed-.
-
 lemma eq_inv_m_sn_structure (q) (p):
       (𝗺 ◗q) = ⊗p → ⊥.
 #q #p >list_cons_comm #H0