made executable again

[helm.git] / helm / software / matita / contribs / dama / dama / models / q_rebase.ma

diff --git a/helm/software/matita/contribs/dama/dama/models/q_rebase.ma b/helm/software/matita/contribs/dama/dama/models/q_rebase.ma
index 93e0d19e73d47c5dcde8289963e817efc62afe3b..b14f0bd17bd07fd4a115e38c28257f0890c554fc 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/models/q_rebase.ma
+++ b/helm/software/matita/contribs/dama/dama/models/q_rebase.ma
@@ -12,22 +12,122 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "models/q_function.ma".
+include "dama/russell_support.ma".
+include "models/q_copy.ma".
+(*
+definition rebase_spec ≝ 
+ λl1,l2:q_f.λp:q_f × q_f. 
+   And3
+    (same_bases (bars (\fst p)) (bars (\snd p)))
+    (same_values l1 (\fst p)) 
+    (same_values l2 (\snd p)).
+
+inductive rebase_cases : list bar → list bar → (list bar) × (list bar) → Prop ≝
+| rb_fst_full  : ∀b,h1,xs.
+   rebase_cases (〈b,h1〉::xs) [] 〈〈b,h1〉::xs,〈b,〈OQ,OQ〉〉::copy xs〉
+| rb_snd_full  : ∀b,h1,ys.
+   rebase_cases [] (〈b,h1〉::ys) 〈〈b,〈OQ,OQ〉〉::copy ys,〈b,h1〉::ys〉  
+| rb_all_full  : ∀b,h1,h2,h3,h4,xs,ys,r1,r2.
+   \snd(\last ▭ (〈b,h1〉::xs)) = \snd(\last ▭ (〈b,h3〉::r1)) →
+   \snd(\last ▭ (〈b,h2〉::ys)) = \snd(\last ▭ (〈b,h4〉::r2)) →
+   rebase_cases (〈b,h1〉::xs) (〈b,h2〉::ys) 〈〈b,h3〉::r1,〈b,h4〉::r2〉
+| rb_all_full_l  : ∀b1,b2,h1,h2,xs,ys,r1,r2.
+   \snd(\last ▭ (〈b1,h1〉::xs)) = \snd(\last ▭ (〈b1,h1〉::r1)) →
+   \snd(\last ▭ (〈b2,h2〉::ys)) = \snd(\last ▭ (〈b1,h2〉::r2)) →
+   b1 < b2 →
+   rebase_cases (〈b1,h1〉::xs) (〈b2,h2〉::ys) 〈〈b1,h1〉::r1,〈b1,〈OQ,OQ〉〉::r2〉 
+| rb_all_full_r  : ∀b1,b2,h1,h2,xs,ys,r1,r2.
+   \snd(\last ▭ (〈b1,h1〉::xs)) = \snd(\last ▭ (〈b2,h1〉::r1)) →
+   \snd(\last ▭ (〈b2,h2〉::ys)) = \snd(\last ▭ (〈b2,h2〉::r2)) →
+   b2 < b1 →
+   rebase_cases (〈b1,h1〉::xs) (〈b2,h2〉::ys) 〈〈b2,〈OQ,OQ〉〉::r1,〈b2,h2〉::r2〉     
+| rb_all_empty : rebase_cases [] [] 〈[],[]〉.
+
+alias symbol "pi2" = "pair pi2".
+alias symbol "pi1" = "pair pi1".
+alias symbol "leq" = "natural 'less or equal to'".
+inductive rebase_spec_aux_p (l1, l2:list bar) (p:(list bar) × (list bar)) : Prop ≝
+| prove_rebase_spec_aux:
+   rebase_cases l1 l2 p →
+   (sorted q2_lt (\fst p)) →
+   (sorted q2_lt (\snd p)) → 
+   (same_bases (\fst p) (\snd p)) →
+   (same_values_simpl l1 (\fst p)) → 
+   (same_values_simpl l2 (\snd p)) →  
+   rebase_spec_aux_p l1 l2 p.   
+
+lemma aux_preserves_sorting:
+ ∀b,b3,l2,l3,w. rebase_cases l2 l3 w → 
+  sorted q2_lt (b::l2) → sorted q2_lt (b3::l3) → \fst b3 = \fst b →
+  sorted q2_lt (\fst w) → sorted q2_lt (\snd w) → 
+  same_bases (\fst w) (\snd w) → 
+    sorted q2_lt (b :: \fst w).
+intros 6; cases H; simplify; intros; clear H;
+[ apply (sorted_cons q2_lt); [2:assumption] apply (inversion_sorted2 ??? H1);
+| apply (sorted_cons q2_lt); [2:assumption]
+  whd; rewrite < H3; apply (inversion_sorted2 ??? H2);
+| apply (sorted_cons q2_lt); [2:assumption] apply (inversion_sorted2 ??? H3);
+| apply (sorted_cons q2_lt); [2:assumption] apply (inversion_sorted2 ??? H4);
+| apply (sorted_cons q2_lt); [2:assumption] 
+  whd; rewrite < H6; apply (inversion_sorted2 ??? H5);
+| apply (sorted_one q2_lt);]
+qed.   
+
+lemma aux_preserves_sorting2:
+ ∀b,b3,l2,l3,w. rebase_cases l2 l3 w → 
+  sorted q2_lt (b::l2) → sorted q2_lt (b3::l3) → \fst b3 = \fst b →
+  sorted q2_lt (\fst w) → sorted q2_lt (\snd w) → same_bases (\fst w) (\snd w) → 
+  sorted q2_lt (b :: \snd w).
+intros 6; cases H; simplify; intros; clear H;
+[ apply (sorted_cons q2_lt); [2:assumption] apply (inversion_sorted2 ??? H1);   
+| apply (sorted_cons q2_lt); [2:assumption] 
+  whd; rewrite < H3; apply (inversion_sorted2 ??? H2);
+| apply (sorted_cons q2_lt); [2: assumption] apply (inversion_sorted2 ??? H3);
+| apply (sorted_cons q2_lt); [2: assumption] apply (inversion_sorted2 ??? H4);
+| apply (sorted_cons q2_lt); [2: assumption] 
+  whd; rewrite < H6; apply (inversion_sorted2 ??? H5);
+| apply (sorted_one q2_lt);]
+qed.
+*)
+
+
+
+definition rebase_spec_aux ≝ 
+ λl1,l2
+ :list bar.λp:(list bar) × (list bar).
+ sorted q2_lt l1 → (\snd (\last ▭ l1) = 〈OQ,OQ〉) →
+ sorted q2_lt l2 → (\snd (\last ▭ l2) = 〈OQ,OQ〉) → 
+   rebase_spec_aux_p l1 l2 p.
 
 alias symbol "lt" = "Q less than".
 alias symbol "Q" = "Rationals".
 axiom q_unlimited: ∀x:ℚ.∃y:ratio.x<Qpos y.                
 axiom q_halving: ∀x,y:ℚ.∃z:ℚ.x<z ∧ z<y.
+alias symbol "not" = "logical not".
+axiom q_not_OQ_lt_Qneg: ∀r. ¬ (OQ < Qneg r).
 lemma same_values_unit_OQ: 
-  ∀b1,b2,h1,l. b2 < b1 → sorted q2_lt (〈b1,h1〉::l) →
+  ∀b1,b2,h1,l. OQ < b2 → b2 < b1 → sorted q2_lt (〈b1,h1〉::l) →
     sorted q2_lt  [〈b2,〈OQ,OQ〉〉] → 
     same_values_simpl (〈b1,h1〉::l) [〈b2,〈OQ,OQ〉〉]  → h1 = 〈OQ,OQ〉.
-intros 4; cases l;
+intros 5 (b1 b2 h1 l POS); cases l;
 [1: intros; cases (q_unlimited b1); cut (b2 < Qpos w); [2:apply (q_lt_trans ??? H H4);] 
     lapply (H3 H1 ? H2 ? w H4 Hcut) as K; simplify; [1,2: autobatch]
     rewrite > (value_unit 〈b1,h1〉) in K;
     rewrite > (value_unit 〈b2,〈OQ,OQ〉〉) in K; assumption;
-|2: intros; (* MANCA che le basi sono positive, 
+|2: intros; unfold in H3; lapply depth=0 (H3 H1 ? H2 ?) as K; [1,2:simplify; autobatch]
+    clear H3; cases (q_halving b1 (b1 + \fst p)) (w Pw); cases w in Pw; intros;
+    [cases (q_lt_le_incompat ?? POS); apply q_lt_to_le; cases H3;
+     apply (q_lt_trans ???? H4); assumption;
+    |3: elim H3; lapply (q_lt_trans ??? H H4); lapply (q_lt_trans ??? POS Hletin);
+        cases (q_not_OQ_lt_Qneg ? Hletin1);
+    | cases H3; lapply (K r);
+      [2: simplify; assumption
+      |3: simplify; apply (q_lt_trans ???? H4); assumption;
+      |rewrite > (value_head b1,h1 .. q) in Hletin;
+        
+
+
+ (* MANCA che le basi sono positive, 
                poi con halving prendi tra b1 e \fst p e hai h1=OQ,OQ*)