X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Flib%2Fturing%2Fif_machine.ma;h=3d6675d02b5dd4087affdaaf58901935d28c3ceb;hb=45ab745cdc286db123f9811adef343c9178c28de;hp=28983b11eb86b4a54bc5e7efbf8f4e2cd77ea4c1;hpb=28c261aad4d710c9f218fbbbaf1ed3b45c1caf72;p=helm.git

diff --git a/matita/matita/lib/turing/if_machine.ma b/matita/matita/lib/turing/if_machine.ma
index 28983b11e..3d6675d02 100644
--- a/matita/matita/lib/turing/if_machine.ma
+++ b/matita/matita/lib/turing/if_machine.ma
@@ -58,6 +58,46 @@ axiom tdaemon : ∀X:Type[0].X.
 axiom sem_if: ∀sig,M1,M2,M3,Rtrue,Rfalse,R2,R3,acc.
   accRealize sig M1 acc Rtrue Rfalse → Realize sig M2 R2 → Realize sig M3 R3 → 
     Realize sig (ifTM sig M1 M2 M3 acc) (λt1,t2. (Rtrue ∘ R2) t1 t2 ∨ (Rfalse ∘ R3) t1 t2).
+    
+lemma sem_if_app: ∀sig,M1,M2,M3,Rtrue,Rfalse,R2,R3,R4,acc.
+  accRealize sig M1 acc Rtrue Rfalse → Realize sig M2 R2 → Realize sig M3 R3 → 
+    (∀t1,t2,t3. (Rtrue t1 t3 ∧ R2 t3 t2) ∨ (Rfalse t1 t3 ∧ R3 t3 t2) → R4 t1 t2) →  
+    Realize sig 
+     (ifTM sig M1 M2 M3 acc) R4.
+#sig #M1 #M2 #M3 #Rtrue #Rfalse #R2 #R3 #R4 #acc
+#HRacc #HRtrue #HRfalse #Hsub
+#t cases (sem_if … HRacc HRtrue HRfalse t)
+#k * #outc * #Hloop #Houtc @(ex_intro … k) @(ex_intro … outc)
+% [@Hloop] cases Houtc
+  [* #t3 * #Hleft #Hright @(Hsub … t3) %1 /2/
+  |* #t3 * #Hleft #Hright @(Hsub … t3) %2 /2/ ]
+qed.
+
+axiom acc_sem_if: ∀sig,M1,M2,M3,Rtrue,Rfalse,R2,R3,acc.
+  accRealize sig M1 acc Rtrue Rfalse → Realize sig M2 R2 → Realize sig M3 R3 → 
+    accRealize sig 
+     (ifTM sig M1 (single_finalTM … M2) M3 acc) 
+     (inr … (inl … (inr … start_nop)))
+     (Rtrue ∘ R2) 
+     (Rfalse ∘ R3).
+     
+lemma acc_sem_if_app: ∀sig,M1,M2,M3,Rtrue,Rfalse,R2,R3,R4,R5,acc.
+  accRealize sig M1 acc Rtrue Rfalse → Realize sig M2 R2 → Realize sig M3 R3 → 
+    (∀t1,t2,t3. Rtrue t1 t3 → R2 t3 t2 → R4 t1 t2) → 
+    (∀t1,t2,t3. Rfalse t1 t3 → R3 t3 t2 → R5 t1 t2) → 
+    accRealize sig 
+     (ifTM sig M1 (single_finalTM … M2) M3 acc) 
+     (inr … (inl … (inr … start_nop)))
+     R4 R5.    
+#sig #M1 #M2 #M3 #Rtrue #Rfalse #R2 #R3 #R4 #R5 #acc
+#HRacc #HRtrue #HRfalse #Hsub1 #Hsub2 
+#t cases (acc_sem_if … HRacc HRtrue HRfalse t)
+#k * #outc * * #Hloop #Houtc1 #Houtc2 @(ex_intro … k) @(ex_intro … outc)
+% [% [@Hloop
+     |#H cases (Houtc1 H) #t3 * #Hleft #Hright @Hsub1 // ]
+  |#H cases (Houtc2 H) #t3 * #Hleft #Hright @Hsub2 // ]
+qed.
+
 (*    
 #sig #M1 #M2 #M3 #Rtrue #Rfalse #R2 #R3 #acc #HaccR #HR2 #HR3 #t 
 cases (HaccR t) #k1 * #outc1 * * #Hloop1 #HMtrue #HMfalse