X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fdama%2Fdama%2Fmodels%2Fq_function.ma;h=e2187b51014799aed94ac412bef1ac57f24056d9;hb=d03c932e859d59c0ae381f941b4003d744b6b106;hp=624755ed77a4c3e6e48f9795e88bc5b20ab48124;hpb=f8f3f0bf31de02f543b9bb5e944ea01fd706d3a0;p=helm.git

diff --git a/helm/software/matita/contribs/dama/dama/models/q_function.ma b/helm/software/matita/contribs/dama/dama/models/q_function.ma
index 624755ed7..e2187b510 100644
--- a/helm/software/matita/contribs/dama/dama/models/q_function.ma
+++ b/helm/software/matita/contribs/dama/dama/models/q_function.ma
@@ -12,68 +12,9 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "models/q_bars.ma".
+include "nat_ordered_set.ma".
+include "models/q_shift.ma".
 
-lemma initial_shift_same_values:
-  ∀l1:q_f.∀init.init < start l1 →
-   same_values l1 
-     (mk_q_f init (〈\fst (unpos (start l1 - init) ?),OQ〉:: bars l1)).  
-[apply hide; apply q_lt_minus; rewrite > q_plus_sym; rewrite > q_plus_OQ; assumption]
-intros; generalize in ⊢ (? ? (? ? (? ? (? ? ? (? ? ? (? ? %)) ?) ?))); intro;
-cases (unpos (start l1-init) H1); intro input;
-simplify in ⊢ (? ? ? (? ? ? (? ? ? (? (? ? (? ? (? ? ? % ?) ?)) ?))));
-cases (value (mk_q_f init (〈w,OQ〉::bars l1)) input);
-simplify in ⊢ (? ? ? (? ? ? %));
-cases (q_cmp input (start (mk_q_f init (〈w,OQ〉::bars l1)))) in H3;
-whd in ⊢ (% → ?); simplify in H3;
-[1: intro; cases H4; clear H4; rewrite > H3;
-    cases (value l1 init); simplify; cases (q_cmp init (start l1)) in H4;
-    [1: cases (?:False); apply (q_lt_corefl init); rewrite > H4 in ⊢ (?? %); apply H;
-    |3: cases (?:False); apply (q_lt_antisym init (start l1)); assumption;
-    |2: whd in ⊢ (% → ?); intro; rewrite > H8; clear H8 H4;
-        rewrite > H7; clear H7; rewrite > (?:\fst w1 = O); [reflexivity]
-        symmetry; apply le_n_O_to_eq;
-        rewrite > (sum_bases_O (mk_q_f init (〈w,OQ〉::bars l1)) (\fst w1)); [apply le_n]   
-        clear H6 w2; simplify in H5:(? ? (? ? %));  
-        destruct H3; rewrite > q_d_x_x in H5; assumption;]
-|2: intros; cases (value l1 input); simplify in ⊢ (? ? (? ? ? %) ?);
-    cases (q_cmp input (start l1)) in H5; whd in ⊢ (% → ?);
-    [1: cases (?:False); clear w2 H4 w1 H2 w H1; 
-        apply (q_lt_antisym init (start l1)); [assumption] rewrite < H5; assumption
-    |2: intros; rewrite > H6; clear H6; rewrite > H4; reflexivity;
-    |3: cases (?:False); apply (q_lt_antisym input (start l1)); [2: assumption]
-        apply (q_lt_trans ??? H3 H);]
-|3: intro; cases H4; clear H4;   
-    cases (value l1 input); simplify; cases (q_cmp input (start l1)) in H4; whd in ⊢ (% → ?);
-    [1: intro; cases H8; clear H8; rewrite > H11; rewrite > H7; clear H11 H7;
-        simplify in ⊢ (? ? ? (? ? ? (? ? % ? ?)));
-        cut (\fst w1 = S (\fst w2)) as Key; [rewrite > Key; reflexivity;]
-        cut (\fst w2 = O); [2: clear H10;
-          symmetry; apply le_n_O_to_eq; rewrite > (sum_bases_O l1 (\fst w2)); [apply le_n]
-          apply (q_le_trans ??? H9); rewrite < H4; rewrite > q_d_x_x; 
-          left; reflexivity;]
-        rewrite > Hcut; clear Hcut H10 H9; simplify in H5 H6;
-        cut (ⅆ[input,init] = Qpos w) as E; [2:
-          rewrite > H2; rewrite < H4; rewrite > q_d_sym; 
-          rewrite > q_d_noabs; [reflexivity] right; assumption;]
-        cases (\fst w1) in H5 H6; intros;
-        [1: cases (?:False); clear H5; simplify in H6;
-            apply (q_lt_corefl ⅆ[input,init]);
-            rewrite > E in ⊢ (??%); rewrite < q_plus_OQ in ⊢ (??%);
-            rewrite > q_plus_sym; assumption;
-        |2: cases n in H5 H6; [intros; reflexivity] intros;
-            cases (?:False); clear H6; cases (bars l1) in H5; simplify; intros;
-            [apply (q_pos_OQ one);|apply (q_pos_OQ (\fst b));] 
-            apply (q_le_S ??? (sum_bases_ge_OQ (mk_q_f init ?) n1));[apply [];|3:apply l]
-            simplify in ⊢ (? (? (? % ?) ?) ?); rewrite < (q_plus_minus w);
-            apply q_le_minus_r; rewrite < q_minus_r; 
-            rewrite < E in ⊢ (??%); assumption;]
-    |2: intros; rewrite > H8; rewrite > H7; clear H8 H7;
-        simplify in H5 H6 ⊢ %;
-        simplify in H5:(? ? (? ? %));
-        
-            
-        
 alias symbol "pi2" = "pair pi2".
 alias symbol "pi1" = "pair pi1".
 definition rebase_spec ≝ 
@@ -155,23 +96,40 @@ in aux : ∀l1,l2,m.∃z.∀s.spec s l1 l2 m z); unfold spec;
         [1: reflexivity
         |2: assumption;
         |3: assumption;
-        |4: intro; rewrite < (H4 input); clear H3 H4 H2 w;
-            cases (value (mk_q_f s1 l2') input);
-            cases (q_cmp input (start (mk_q_f s1 l2'))) in H1;
-            whd in ⊢ (% → ?);
-            [1: intros; cases H2; clear H2; whd in ⊢ (??? %);
-                cases (value (mk_q_f s2 l2) input);
-                cases (q_cmp input (start (mk_q_f s2 l2))) in H2;
-                whd in ⊢ (% → ?);
-                [1: intros; cases H6; clear H6; change with (w1 = w);
-                          
-            (* TODO *) ]]    
+        |4: intro; rewrite > (initial_shift_same_values (mk_q_f s2 l2) s1 H input);
+            rewrite < (H4 input); reflexivity;]
+    |3: letin l1' ≝ (〈\fst (unpos (s1-s2) ?),OQ〉::l1);[
+          apply q_lt_minus; rewrite > q_plus_sym; rewrite > q_plus_OQ;
+          assumption]
+        cases (aux l1' l2 (S (len l1' + len l2)));
+        cases (H1 s2 (le_n ?)); clear H1 aux;
+        exists [apply 〈mk_q_f s2 (\fst w), mk_q_f s2 (\snd w)〉] split;
+        [1: reflexivity
+        |2: assumption;
+        |4: assumption;
+        |3: intro; rewrite > (initial_shift_same_values (mk_q_f s1 l1) s2 H input);
+            rewrite < (H3 input); reflexivity;]]
 |1,2: unfold rest; apply q_lt_minus; rewrite > q_plus_sym; rewrite > q_plus_OQ;
       assumption;        
-|3:(* TODO *)
-|4:(* TODO *)
-|5:(* TODO *)
-|6:(* TODO *)
-|7:(* TODO *)
-|8: intros; cases (?:False); apply (not_le_Sn_O ? H1);]
+|8: intros; cases (?:False); apply (not_le_Sn_O ? H1);
+|3: intros; generalize in match (unpos ??); intro X; cases X; clear X;
+    simplify in ⊢ (???? (??? (??? (??? (?? (? (?? (??? % ?) ?) ??)))) ?));
+    simplify in ⊢ (???? (???? (??? (??? (?? (? (?? (??? % ?) ?) ??)))))); 
+    clear H4; cases (aux (〈w,\snd b〉::l4) l5 n1); clear aux;
+    cut (len (〈w,\snd b〉::l4) + len l5 < n1) as K;[2:
+      simplify in H5; simplify; rewrite > sym_plus in H5; simplify in H5;
+      rewrite > sym_plus in H5; apply le_S_S_to_le; apply H5;] 
+    split;
+    [1: simplify in ⊢ (? % ?); simplify in ⊢ (? ? %); 
+        cases (H4 s K); clear K H4; intro input; cases input; [reflexivity]
+        simplify; apply H7; 
+    |2: simplify in ⊢ (? ? %); cases (H4 s K); clear H4 K H5 spec;
+        intro; 
+        (* input < s + b1 || input >= s + b1 *)
+    |3: simplify in ⊢ (? ? %);]   
+|4: intros; generalize in match (unpos ??); intro X; cases X; clear X;
+    (* duale del 3 *)
+|5: intros; (* triviale, caso in cui non fa nulla *)
+|6,7: (* casi base in cui allunga la lista più corta *) 
+]
 qed.