Changeset 908 for src/ASM/AssemblyProof.ma

Timestamp:

Jun 9, 2011, 1:22:15 AM (10 years ago)

Author:

sacerdot

Message:

Next big lemma proved!

File:

• src/ASM/AssemblyProof.ma (modified) (1 diff)

src/ASM/AssemblyProof.ma

@@ -1364 +1364 @@
        sigma program newppc = bitvector_of_nat … (nat_of_bitvector … (sigma program ppc) + len).
 
+axiom bitvector_of_nat_nat_of_bitvector:
+ ∀n,v. bitvector_of_nat n (nat_of_bitvector n v) = v.
+
+lemma fetch_assembly_pseudo2:
+ ∀program,assembled,costs,labels,datalabels.
+  Some … 〈labels,datalabels〉 = build_maps program →
+  Some … 〈assembled,costs〉 = assembly program →
+  let code_memory ≝ load_code_memory assembled in
+  let lookup_labels ≝ λx. lookup ?? x labels (zero ?) in
+  let lookup_datalabels ≝ λx. lookup ?? x datalabels (zero ?) in
+   ∀ppc,instructions.
+    let expansion ≝ jump_expansion_policy program ppc in
+    let 〈pi,newppc〉 ≝ fetch_pseudo_instruction (\snd program) ppc in
+     Some ? instructions = expand_pseudo_instruction lookup_labels lookup_datalabels ppc expansion pi →
+      fetch_many code_memory (sigma program newppc) (sigma program ppc) instructions.
+ #program #assembled #costs #labels #datalabels #BUILD_MAPS #ASSEMBLY #ppc #instructions whd
+ generalize in match (assembly_ok … BUILD_MAPS ASSEMBLY ppc)
+ cases (fetch_pseudo_instruction (\snd program) ppc) #pi #newppc
+ generalize in match (fetch_assembly_pseudo program ppc
+  (λx. lookup ?? x labels (zero ?)) (λx. lookup ?? x datalabels (zero ?)) pi
+  (load_code_memory assembled)) 
+ whd in ⊢ ((∀_.∀_.∀_.∀_.%) → (∀_.∀_.%) → ?)
+ #H1 #H2 whd #EXPAND whd in H1:(∀_.∀_.∀_.∀_.? → ???% → ?) H2:(∀_.∀_.???% → ?);
+ <EXPAND in H1 H2; whd in ⊢ ((∀_.∀_.∀_.∀_.? → ???% → ?) → (∀_.∀_.???% → ?) → ?)
+ #H1 #H2
+ cases (H2 ?? (refl …)) -H2; #K1 #K2 >K2
+ generalize in match (H1 ??? (nat_of_bitvector … (sigma program ppc)) (refl …) (refl …) ?) -H1;
+  [ #K3 >bitvector_of_nat_nat_of_bitvector in K3; #R @R
+  | >bitvector_of_nat_nat_of_bitvector @K1 ]
+qed.
+
 (* OLD?
 definition assembly_specification: