X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fng_assembly%2Ffreescale%2Fstatus_lemmas.ma;h=0be7272dbaf48ba9da00e4682636e57bee5e0946;hb=ec07ff398325533d848da92e9dc69852d24b78a5;hp=568590e19810524cdfeb5ea30fa2e7460611f533;hpb=a687cf5e3e9ae6fb6ead058c4a191002f21fa951;p=helm.git

diff --git a/helm/software/matita/contribs/ng_assembly/freescale/status_lemmas.ma b/helm/software/matita/contribs/ng_assembly/freescale/status_lemmas.ma
index 568590e19..0be7272db 100755
--- a/helm/software/matita/contribs/ng_assembly/freescale/status_lemmas.ma
+++ b/helm/software/matita/contribs/ng_assembly/freescale/status_lemmas.ma
@@ -15,16 +15,16 @@
 (* ********************************************************************** *)
 (*                          Progetto FreeScale                            *)
 (*                                                                        *)
-(*   Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it                   *)
-(*     Cosimo Oliboni, oliboni@cs.unibo.it                                *)
+(*   Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it              *)
+(*   Ultima modifica: 05/08/2009                                          *)
 (*                                                                        *)
 (* ********************************************************************** *)
 
-include "freescale/word16_lemmas.ma".
+include "num/word16_lemmas.ma".
 include "freescale/opcode_base_lemmas1.ma".
 include "freescale/status.ma".
-include "freescale/option_lemmas.ma".
-include "freescale/prod_lemmas.ma".
+include "common/option_lemmas.ma".
+include "common/prod_lemmas.ma".
 
 (* *********************************** *)
 (* STATUS INTERNO DEL PROCESSORE (ALU) *)
@@ -40,7 +40,7 @@ nlemma aluHC05_destruct_1 :
                 with [ mk_alu_HC05 a _ _ _ _ _ _ _ _ _ _ _ _ ⇒ x1 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC05_destruct_2 :
@@ -53,7 +53,7 @@ nlemma aluHC05_destruct_2 :
                 with [ mk_alu_HC05 _ a _ _ _ _ _ _ _ _ _ _ _ ⇒ x2 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC05_destruct_3 :
@@ -66,7 +66,7 @@ nlemma aluHC05_destruct_3 :
                 with [ mk_alu_HC05 _ _ a _ _ _ _ _ _ _ _ _ _ ⇒ x3 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC05_destruct_4 :
@@ -79,7 +79,7 @@ nlemma aluHC05_destruct_4 :
                 with [ mk_alu_HC05 _ _ _ a _ _ _ _ _ _ _ _ _ ⇒ x4 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC05_destruct_5 :
@@ -92,7 +92,7 @@ nlemma aluHC05_destruct_5 :
                 with [ mk_alu_HC05 _ _ _ _ a _ _ _ _ _ _ _ _ ⇒ x5 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC05_destruct_6 :
@@ -105,7 +105,7 @@ nlemma aluHC05_destruct_6 :
                 with [ mk_alu_HC05 _ _ _ _ _ a _ _ _ _ _ _ _ ⇒ x6 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC05_destruct_7 :
@@ -118,7 +118,7 @@ nlemma aluHC05_destruct_7 :
                 with [ mk_alu_HC05 _ _ _ _ _ _ a _ _ _ _ _ _ ⇒ x7 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC05_destruct_8 :
@@ -131,7 +131,7 @@ nlemma aluHC05_destruct_8 :
                 with [ mk_alu_HC05 _ _ _ _ _ _ _ a _ _ _ _ _ ⇒ x8 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC05_destruct_9 :
@@ -144,7 +144,7 @@ nlemma aluHC05_destruct_9 :
                 with [ mk_alu_HC05 _ _ _ _ _ _ _ _ a _ _ _ _ ⇒ x9 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC05_destruct_10 :
@@ -157,7 +157,7 @@ nlemma aluHC05_destruct_10 :
                 with [ mk_alu_HC05 _ _ _ _ _ _ _ _ _ a _ _ _ ⇒ x10 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC05_destruct_11 :
@@ -170,7 +170,7 @@ nlemma aluHC05_destruct_11 :
                 with [ mk_alu_HC05 _ _ _ _ _ _ _ _ _ _ a _ _ ⇒ x11 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC05_destruct_12 :
@@ -183,7 +183,7 @@ nlemma aluHC05_destruct_12 :
                 with [ mk_alu_HC05 _ _ _ _ _ _ _ _ _ _ _ a _ ⇒ x12 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC05_destruct_13 :
@@ -196,10 +196,10 @@ nlemma aluHC05_destruct_13 :
                 with [ mk_alu_HC05 _ _ _ _ _ _ _ _ _ _ _ _ a ⇒ x13 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
-nlemma symmetric_eqaluHC05 : symmetricT alu_HC05 bool eq_alu_HC05.
+nlemma symmetric_eqaluHC05 : symmetricT alu_HC05 bool eq_aluHC05.
  #alu1; #alu2;
  ncases alu1;
  #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
@@ -226,10 +226,10 @@ nlemma symmetric_eqaluHC05 : symmetricT alu_HC05 bool eq_alu_HC05.
  nrewrite > (symmetric_eqbool x11 y11);
  nrewrite > (symmetric_eqbool x12 y12);
  nrewrite > (symmetric_eqbool x13 y13);
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
-nlemma eqaluHC05_to_eq : ∀alu1,alu2.eq_alu_HC05 alu1 alu2 = true → alu1 = alu2.
+nlemma eqaluHC05_to_eq : ∀alu1,alu2.eq_aluHC05 alu1 alu2 = true → alu1 = alu2.
  #alu1; #alu2;
  ncases alu1;
  #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
@@ -243,52 +243,52 @@ nlemma eqaluHC05_to_eq : ∀alu1,alu2.eq_alu_HC05 alu1 alu2 = true → alu1 = al
   (eq_bool x9 y9) ⊗ (eq_bool x10 y10) ⊗
   (eq_bool x11 y11) ⊗ (eq_bool x12 y12) ⊗
   (eq_bool x13 y13)) = true);  
- nrewrite > (eqbool_to_eq ?? (andb_true_true_r ?? H));
- nletin H1 ≝ (andb_true_true_l ?? H);
- nrewrite > (eqbool_to_eq x12 y12 (andb_true_true_r ?? (andb_true_true_l ?? H)));
- nletin H2 ≝ (andb_true_true_l ?? H1);
- nrewrite > (eqbool_to_eq ?? (andb_true_true_r ?? H2));
- nletin H3 ≝ (andb_true_true_l ?? H2);
- nrewrite > (eqbool_to_eq ?? (andb_true_true_r ?? H3));
- nletin H4 ≝ (andb_true_true_l ?? H3);
- nrewrite > (eqbool_to_eq ?? (andb_true_true_r ?? H4));
- nletin H5 ≝ (andb_true_true_l ?? H4);
- nrewrite > (eqbool_to_eq ?? (andb_true_true_r ?? H5));
- nletin H6 ≝ (andb_true_true_l ?? H5);
- nrewrite > (eqw16_to_eq ?? (andb_true_true_r ?? H6));
- nletin H7 ≝ (andb_true_true_l ?? H6);
- nrewrite > (eqw16_to_eq ?? (andb_true_true_r ?? H7));
- nletin H8 ≝ (andb_true_true_l ?? H7);
- nrewrite > (eqw16_to_eq ?? (andb_true_true_r ?? H8));
- nletin H9 ≝ (andb_true_true_l ?? H8);
- nrewrite > (eqw16_to_eq ?? (andb_true_true_r ?? H9));
- nletin H10 ≝ (andb_true_true_l ?? H9);
- nrewrite > (eqw16_to_eq ?? (andb_true_true_r ?? H10));
- nletin H11 ≝ (andb_true_true_l ?? H10);
- nrewrite > (eqb8_to_eq ?? (andb_true_true_r ?? H11));
- nrewrite > (eqb8_to_eq ?? (andb_true_true_l ?? H11));
- napply (refl_eq ??).
-nqed.
-
-nlemma eq_to_eqaluHC05 : ∀alu1,alu2.alu1 = alu2 → eq_alu_HC05 alu1 alu2 = true.
+ nrewrite > (eqbool_to_eq … (andb_true_true_r … H));
+ nletin H1 ≝ (andb_true_true_l … H);
+ nrewrite > (eqbool_to_eq x12 y12 (andb_true_true_r … (andb_true_true_l … H)));
+ nletin H2 ≝ (andb_true_true_l … H1);
+ nrewrite > (eqbool_to_eq … (andb_true_true_r … H2));
+ nletin H3 ≝ (andb_true_true_l … H2);
+ nrewrite > (eqbool_to_eq … (andb_true_true_r … H3));
+ nletin H4 ≝ (andb_true_true_l … H3);
+ nrewrite > (eqbool_to_eq … (andb_true_true_r … H4));
+ nletin H5 ≝ (andb_true_true_l … H4);
+ nrewrite > (eqbool_to_eq … (andb_true_true_r … H5));
+ nletin H6 ≝ (andb_true_true_l … H5);
+ nrewrite > (eqw16_to_eq … (andb_true_true_r … H6));
+ nletin H7 ≝ (andb_true_true_l … H6);
+ nrewrite > (eqw16_to_eq … (andb_true_true_r … H7));
+ nletin H8 ≝ (andb_true_true_l … H7);
+ nrewrite > (eqw16_to_eq … (andb_true_true_r … H8));
+ nletin H9 ≝ (andb_true_true_l … H8);
+ nrewrite > (eqw16_to_eq … (andb_true_true_r … H9));
+ nletin H10 ≝ (andb_true_true_l … H9);
+ nrewrite > (eqw16_to_eq … (andb_true_true_r … H10));
+ nletin H11 ≝ (andb_true_true_l … H10);
+ nrewrite > (eqb8_to_eq … (andb_true_true_r … H11));
+ nrewrite > (eqb8_to_eq … (andb_true_true_l … H11));
+ napply refl_eq.
+nqed.
+
+nlemma eq_to_eqaluHC05 : ∀alu1,alu2.alu1 = alu2 → eq_aluHC05 alu1 alu2 = true.
  #alu1; #alu2;
  ncases alu1;
  #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
  ncases alu2;
  #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
- nrewrite > (aluHC05_destruct_1 ?????????????????????????? H);
- nrewrite > (aluHC05_destruct_2 ?????????????????????????? H);
- nrewrite > (aluHC05_destruct_3 ?????????????????????????? H);
- nrewrite > (aluHC05_destruct_4 ?????????????????????????? H);
- nrewrite > (aluHC05_destruct_5 ?????????????????????????? H);
- nrewrite > (aluHC05_destruct_6 ?????????????????????????? H);
- nrewrite > (aluHC05_destruct_7 ?????????????????????????? H);
- nrewrite > (aluHC05_destruct_8 ?????????????????????????? H);
- nrewrite > (aluHC05_destruct_9 ?????????????????????????? H);
- nrewrite > (aluHC05_destruct_10 ?????????????????????????? H);
- nrewrite > (aluHC05_destruct_11 ?????????????????????????? H);
- nrewrite > (aluHC05_destruct_12 ?????????????????????????? H);
- nrewrite > (aluHC05_destruct_13 ?????????????????????????? H);
+ nrewrite > (aluHC05_destruct_1 … H);
+ nrewrite > (aluHC05_destruct_2 … H);
+ nrewrite > (aluHC05_destruct_3 … H);
+ nrewrite > (aluHC05_destruct_4 … H);
+ nrewrite > (aluHC05_destruct_5 … H);
+ nrewrite > (aluHC05_destruct_6 … H);
+ nrewrite > (aluHC05_destruct_7 … H);
+ nrewrite > (aluHC05_destruct_8 … H);
+ nrewrite > (aluHC05_destruct_9 … H);
+ nrewrite > (aluHC05_destruct_10 … H);
+ nrewrite > (aluHC05_destruct_11 … H);
+ nrewrite > (aluHC05_destruct_12 … H);
+ nrewrite > (aluHC05_destruct_13 … H);
  nchange with (
  ((eq_b8 y1 y1) ⊗ (eq_b8 y2 y2) ⊗
   (eq_w16 y3 y3) ⊗ (eq_w16 y4 y4) ⊗
@@ -297,20 +297,212 @@ nlemma eq_to_eqaluHC05 : ∀alu1,alu2.alu1 = alu2 → eq_alu_HC05 alu1 alu2 = tr
   (eq_bool y9 y9) ⊗ (eq_bool y10 y10) ⊗
   (eq_bool y11 y11) ⊗ (eq_bool y12 y12) ⊗
   (eq_bool y13 y13)) = true); 
- nrewrite > (eq_to_eqb8 y1 y1 (refl_eq ??));
- nrewrite > (eq_to_eqb8 y2 y2 (refl_eq ??));
- nrewrite > (eq_to_eqw16 y3 y3 (refl_eq ??));
- nrewrite > (eq_to_eqw16 y4 y4 (refl_eq ??));
- nrewrite > (eq_to_eqw16 y5 y5 (refl_eq ??));
- nrewrite > (eq_to_eqw16 y6 y6 (refl_eq ??));
- nrewrite > (eq_to_eqw16 y7 y7 (refl_eq ??));
- nrewrite > (eq_to_eqbool y8 y8 (refl_eq ??));
- nrewrite > (eq_to_eqbool y9 y9 (refl_eq ??));
- nrewrite > (eq_to_eqbool y10 y10 (refl_eq ??));
- nrewrite > (eq_to_eqbool y11 y11 (refl_eq ??));
- nrewrite > (eq_to_eqbool y12 y12 (refl_eq ??));
- nrewrite > (eq_to_eqbool y13 y13 (refl_eq ??));
- napply (refl_eq ??).
+ nrewrite > (eq_to_eqb8 y1 y1 (refl_eq …));
+ nrewrite > (eq_to_eqb8 y2 y2 (refl_eq …));
+ nrewrite > (eq_to_eqw16 y3 y3 (refl_eq …));
+ nrewrite > (eq_to_eqw16 y4 y4 (refl_eq …));
+ nrewrite > (eq_to_eqw16 y5 y5 (refl_eq …));
+ nrewrite > (eq_to_eqw16 y6 y6 (refl_eq …));
+ nrewrite > (eq_to_eqw16 y7 y7 (refl_eq …));
+ nrewrite > (eq_to_eqbool y8 y8 (refl_eq …));
+ nrewrite > (eq_to_eqbool y9 y9 (refl_eq …));
+ nrewrite > (eq_to_eqbool y10 y10 (refl_eq …));
+ nrewrite > (eq_to_eqbool y11 y11 (refl_eq …));
+ nrewrite > (eq_to_eqbool y12 y12 (refl_eq …));
+ nrewrite > (eq_to_eqbool y13 y13 (refl_eq …));
+ napply refl_eq.
+nqed.
+
+nlemma decidable_aluHC05_aux1
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ (x1 ≠ y1) →
+ (mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) ≠
+ (mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_1 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux2
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ (x2 ≠ y2) →
+ (mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) ≠
+ (mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_2 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux3
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ (x3 ≠ y3) →
+ (mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) ≠
+ (mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_3 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux4
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ (x4 ≠ y4) →
+ (mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) ≠
+ (mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_4 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux5
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ (x5 ≠ y5) →
+ (mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) ≠
+ (mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_5 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux6
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ (x6 ≠ y6) →
+ (mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) ≠
+ (mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_6 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux7
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ (x7 ≠ y7) →
+ (mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) ≠
+ (mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_7 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux8
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ (x8 ≠ y8) →
+ (mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) ≠
+ (mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_8 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux9
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ (x9 ≠ y9) →
+ (mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) ≠
+ (mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_9 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux10
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ (x10 ≠ y10) →
+ (mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) ≠
+ (mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_10 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux11
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ (x11 ≠ y11) →
+ (mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) ≠
+ (mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_11 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux12
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ (x12 ≠ y12) →
+ (mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) ≠
+ (mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_12 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux13
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
+ (x13 ≠ y13) →
+ (mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13) ≠
+ (mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_13 … H1)).
+nqed.
+
+nlemma decidable_aluHC05 : ∀x,y:alu_HC05.decidable (x = y).
+ #x; nelim x; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y; nelim y; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13;
+ nnormalize;
+ napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_b8 x1 y1) …);
+ ##[ ##2: #H; napply (or2_intro2 … (decidable_aluHC05_aux1 … H))
+ ##| ##1: #H; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_b8 x2 y2) …);
+  ##[ ##2: #H1; napply (or2_intro2 … (decidable_aluHC05_aux2 … H1))
+  ##| ##1: #H1; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x3 y3) …);
+   ##[ ##2: #H2; napply (or2_intro2 … (decidable_aluHC05_aux3 … H2))
+   ##| ##1: #H2; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x4 y4) …);
+    ##[ ##2: #H3; napply (or2_intro2 … (decidable_aluHC05_aux4 … H3))
+    ##| ##1: #H3; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x5 y5) …);
+     ##[ ##2: #H4; napply (or2_intro2 … (decidable_aluHC05_aux5 … H4))
+     ##| ##1: #H4; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x6 y6) …);
+      ##[ ##2: #H5; napply (or2_intro2 … (decidable_aluHC05_aux6 … H5))
+      ##| ##1: #H5; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x7 y7) …);
+       ##[ ##2: #H6; napply (or2_intro2 … (decidable_aluHC05_aux7 … H6))
+       ##| ##1: #H6; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x8 y8) …);
+        ##[ ##2: #H7; napply (or2_intro2 … (decidable_aluHC05_aux8 … H7))
+        ##| ##1: #H7; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x9 y9) …);
+         ##[ ##2: #H8; napply (or2_intro2 … (decidable_aluHC05_aux9 … H8))
+         ##| ##1: #H8; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x10 y10) …);
+          ##[ ##2: #H9; napply (or2_intro2 … (decidable_aluHC05_aux10 … H9))
+          ##| ##1: #H9; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x11 y11) …);
+           ##[ ##2: #H10; napply (or2_intro2 … (decidable_aluHC05_aux11 … H10))
+           ##| ##1: #H10; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x12 y12) …);
+            ##[ ##2: #H11; napply (or2_intro2 … (decidable_aluHC05_aux12 … H11))
+            ##| ##1: #H11; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x13 y13) …);
+             ##[ ##2: #H12; napply (or2_intro2 … (decidable_aluHC05_aux13 … H12))
+             ##| ##1: #H12; nrewrite > H; nrewrite > H1; nrewrite > H2; nrewrite > H3;
+                      nrewrite > H4; nrewrite > H5; nrewrite > H6; nrewrite > H7;
+                      nrewrite > H8; nrewrite > H9; nrewrite > H10; nrewrite > H11;
+                      nrewrite > H12; napply (or2_intro1 (? = ?) (? ≠ ?) (refl_eq …))
+             ##]
+            ##]
+           ##]
+          ##]
+         ##]
+        ##]
+       ##]
+      ##]
+     ##]
+    ##]
+   ##]
+  ##]
+ ##]
 nqed.
 
 nlemma aluHC08_destruct_1 :
@@ -323,7 +515,7 @@ nlemma aluHC08_destruct_1 :
                 with [ mk_alu_HC08 a _ _ _ _ _ _ _ _ _ _ _ ⇒ x1 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC08_destruct_2 :
@@ -336,7 +528,7 @@ nlemma aluHC08_destruct_2 :
                 with [ mk_alu_HC08 _ a _ _ _ _ _ _ _ _ _ _ ⇒ x2 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC08_destruct_3 :
@@ -349,7 +541,7 @@ nlemma aluHC08_destruct_3 :
                 with [ mk_alu_HC08 _ _ a _ _ _ _ _ _ _ _ _ ⇒ x3 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC08_destruct_4 :
@@ -362,7 +554,7 @@ nlemma aluHC08_destruct_4 :
                 with [ mk_alu_HC08 _ _ _ a _ _ _ _ _ _ _ _ ⇒ x4 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC08_destruct_5 :
@@ -375,7 +567,7 @@ nlemma aluHC08_destruct_5 :
                 with [ mk_alu_HC08 _ _ _ _ a _ _ _ _ _ _ _ ⇒ x5 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC08_destruct_6 :
@@ -388,7 +580,7 @@ nlemma aluHC08_destruct_6 :
                 with [ mk_alu_HC08 _ _ _ _ _ a _ _ _ _ _ _ ⇒ x6 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC08_destruct_7 :
@@ -401,7 +593,7 @@ nlemma aluHC08_destruct_7 :
                 with [ mk_alu_HC08 _ _ _ _ _ _ a _ _ _ _ _ ⇒ x7 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC08_destruct_8 :
@@ -414,7 +606,7 @@ nlemma aluHC08_destruct_8 :
                 with [ mk_alu_HC08 _ _ _ _ _ _ _ a _ _ _ _ ⇒ x8 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC08_destruct_9 :
@@ -427,7 +619,7 @@ nlemma aluHC08_destruct_9 :
                 with [ mk_alu_HC08 _ _ _ _ _ _ _ _ a _ _ _ ⇒ x9 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC08_destruct_10 :
@@ -440,7 +632,7 @@ nlemma aluHC08_destruct_10 :
                 with [ mk_alu_HC08 _ _ _ _ _ _ _ _ _ a _ _ ⇒ x10 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC08_destruct_11 :
@@ -453,7 +645,7 @@ nlemma aluHC08_destruct_11 :
                 with [ mk_alu_HC08 _ _ _ _ _ _ _ _ _ _ a _ ⇒ x11 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluHC08_destruct_12 :
@@ -466,10 +658,10 @@ nlemma aluHC08_destruct_12 :
                 with [ mk_alu_HC08 _ _ _ _ _ _ _ _ _ _ _ a ⇒ x12 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
-nlemma symmetric_eqaluHC08 : symmetricT alu_HC08 bool eq_alu_HC08.
+nlemma symmetric_eqaluHC08 : symmetricT alu_HC08 bool eq_aluHC08.
  #alu1; #alu2;
  ncases alu1;
  #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
@@ -494,10 +686,10 @@ nlemma symmetric_eqaluHC08 : symmetricT alu_HC08 bool eq_alu_HC08.
  nrewrite > (symmetric_eqbool x10 y10);
  nrewrite > (symmetric_eqbool x11 y11);
  nrewrite > (symmetric_eqbool x12 y12);
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
-nlemma eqaluHC08_to_eq : ∀alu1,alu2.eq_alu_HC08 alu1 alu2 = true → alu1 = alu2.
+nlemma eqaluHC08_to_eq : ∀alu1,alu2.eq_aluHC08 alu1 alu2 = true → alu1 = alu2.
  #alu1; #alu2;
  ncases alu1;
  #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
@@ -507,66 +699,244 @@ nlemma eqaluHC08_to_eq : ∀alu1,alu2.eq_alu_HC08 alu1 alu2 = true → alu1 = al
  ((eq_b8 x1 y1) ⊗ (eq_b8 x2 y2) ⊗ (eq_b8 x3 y3) ⊗ (eq_w16 x4 y4) ⊗
   (eq_w16 x5 y5) ⊗ (eq_bool x6 y6) ⊗ (eq_bool x7 y7) ⊗ (eq_bool x8 y8) ⊗
   (eq_bool x9 y9) ⊗ (eq_bool x10 y10) ⊗ (eq_bool x11 y11) ⊗ (eq_bool x12 y12)) = true);  
- nrewrite > (eqbool_to_eq ?? (andb_true_true_r ?? H));
- nletin H1 ≝ (andb_true_true_l ?? H);
- nrewrite > (eqbool_to_eq ?? (andb_true_true_r ?? H1));
- nletin H2 ≝ (andb_true_true_l ?? H1);
- nrewrite > (eqbool_to_eq ?? (andb_true_true_r ?? H2));
- nletin H3 ≝ (andb_true_true_l ?? H2);
- nrewrite > (eqbool_to_eq ?? (andb_true_true_r ?? H3));
- nletin H4 ≝ (andb_true_true_l ?? H3);
- nrewrite > (eqbool_to_eq ?? (andb_true_true_r ?? H4));
- nletin H5 ≝ (andb_true_true_l ?? H4);
- nrewrite > (eqbool_to_eq ?? (andb_true_true_r ?? H5));
- nletin H6 ≝ (andb_true_true_l ?? H5);
- nrewrite > (eqbool_to_eq ?? (andb_true_true_r ?? H6));
- nletin H7 ≝ (andb_true_true_l ?? H6);
- nrewrite > (eqw16_to_eq ?? (andb_true_true_r ?? H7));
- nletin H8 ≝ (andb_true_true_l ?? H7);
- nrewrite > (eqw16_to_eq ?? (andb_true_true_r ?? H8));
- nletin H9 ≝ (andb_true_true_l ?? H8);
- nrewrite > (eqb8_to_eq ?? (andb_true_true_r ?? H9));
- nletin H10 ≝ (andb_true_true_l ?? H9);
- nrewrite > (eqb8_to_eq ?? (andb_true_true_r ?? H10));
- nrewrite > (eqb8_to_eq ?? (andb_true_true_l ?? H10));
- napply (refl_eq ??).
-nqed.
-
-nlemma eq_to_eqaluHC08 : ∀alu1,alu2.alu1 = alu2 → eq_alu_HC08 alu1 alu2 = true.
+ nrewrite > (eqbool_to_eq … (andb_true_true_r … H));
+ nletin H1 ≝ (andb_true_true_l … H);
+ nrewrite > (eqbool_to_eq … (andb_true_true_r … H1));
+ nletin H2 ≝ (andb_true_true_l … H1);
+ nrewrite > (eqbool_to_eq … (andb_true_true_r … H2));
+ nletin H3 ≝ (andb_true_true_l … H2);
+ nrewrite > (eqbool_to_eq … (andb_true_true_r … H3));
+ nletin H4 ≝ (andb_true_true_l … H3);
+ nrewrite > (eqbool_to_eq … (andb_true_true_r … H4));
+ nletin H5 ≝ (andb_true_true_l … H4);
+ nrewrite > (eqbool_to_eq … (andb_true_true_r … H5));
+ nletin H6 ≝ (andb_true_true_l … H5);
+ nrewrite > (eqbool_to_eq … (andb_true_true_r … H6));
+ nletin H7 ≝ (andb_true_true_l … H6);
+ nrewrite > (eqw16_to_eq … (andb_true_true_r … H7));
+ nletin H8 ≝ (andb_true_true_l … H7);
+ nrewrite > (eqw16_to_eq … (andb_true_true_r … H8));
+ nletin H9 ≝ (andb_true_true_l … H8);
+ nrewrite > (eqb8_to_eq … (andb_true_true_r … H9));
+ nletin H10 ≝ (andb_true_true_l … H9);
+ nrewrite > (eqb8_to_eq … (andb_true_true_r … H10));
+ nrewrite > (eqb8_to_eq … (andb_true_true_l … H10));
+ napply refl_eq.
+nqed.
+
+nlemma eq_to_eqaluHC08 : ∀alu1,alu2.alu1 = alu2 → eq_aluHC08 alu1 alu2 = true.
  #alu1; #alu2;
  ncases alu1;
  #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
  ncases alu2;
  #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
- nrewrite > (aluHC08_destruct_1 ???????????????????????? H);
- nrewrite > (aluHC08_destruct_2 ???????????????????????? H);
- nrewrite > (aluHC08_destruct_3 ???????????????????????? H);
- nrewrite > (aluHC08_destruct_4 ???????????????????????? H);
- nrewrite > (aluHC08_destruct_5 ???????????????????????? H);
- nrewrite > (aluHC08_destruct_6 ???????????????????????? H);
- nrewrite > (aluHC08_destruct_7 ???????????????????????? H);
- nrewrite > (aluHC08_destruct_8 ???????????????????????? H);
- nrewrite > (aluHC08_destruct_9 ???????????????????????? H);
- nrewrite > (aluHC08_destruct_10 ???????????????????????? H);
- nrewrite > (aluHC08_destruct_11 ???????????????????????? H);
- nrewrite > (aluHC08_destruct_12 ???????????????????????? H);
+ nrewrite > (aluHC08_destruct_1 … H);
+ nrewrite > (aluHC08_destruct_2 … H);
+ nrewrite > (aluHC08_destruct_3 … H);
+ nrewrite > (aluHC08_destruct_4 … H);
+ nrewrite > (aluHC08_destruct_5 … H);
+ nrewrite > (aluHC08_destruct_6 … H);
+ nrewrite > (aluHC08_destruct_7 … H);
+ nrewrite > (aluHC08_destruct_8 … H);
+ nrewrite > (aluHC08_destruct_9 … H);
+ nrewrite > (aluHC08_destruct_10 … H);
+ nrewrite > (aluHC08_destruct_11 … H);
+ nrewrite > (aluHC08_destruct_12 … H);
  nchange with (
  ((eq_b8 y1 y1) ⊗ (eq_b8 y2 y2) ⊗ (eq_b8 y3 y3) ⊗ (eq_w16 y4 y4) ⊗
   (eq_w16 y5 y5) ⊗ (eq_bool y6 y6) ⊗ (eq_bool y7 y7) ⊗ (eq_bool y8 y8) ⊗
   (eq_bool y9 y9) ⊗ (eq_bool y10 y10) ⊗ (eq_bool y11 y11) ⊗ (eq_bool y12 y12)) = true); 
- nrewrite > (eq_to_eqb8 y1 y1 (refl_eq ??));
- nrewrite > (eq_to_eqb8 y2 y2 (refl_eq ??));
- nrewrite > (eq_to_eqb8 y3 y3 (refl_eq ??));
- nrewrite > (eq_to_eqw16 y4 y4 (refl_eq ??));
- nrewrite > (eq_to_eqw16 y5 y5 (refl_eq ??));
- nrewrite > (eq_to_eqbool y6 y6 (refl_eq ??));
- nrewrite > (eq_to_eqbool y7 y7 (refl_eq ??));
- nrewrite > (eq_to_eqbool y8 y8 (refl_eq ??));
- nrewrite > (eq_to_eqbool y9 y9 (refl_eq ??));
- nrewrite > (eq_to_eqbool y10 y10 (refl_eq ??));
- nrewrite > (eq_to_eqbool y11 y11 (refl_eq ??));
- nrewrite > (eq_to_eqbool y12 y12 (refl_eq ??));
- napply (refl_eq ??).
+ nrewrite > (eq_to_eqb8 y1 y1 (refl_eq …));
+ nrewrite > (eq_to_eqb8 y2 y2 (refl_eq …));
+ nrewrite > (eq_to_eqb8 y3 y3 (refl_eq …));
+ nrewrite > (eq_to_eqw16 y4 y4 (refl_eq …));
+ nrewrite > (eq_to_eqw16 y5 y5 (refl_eq …));
+ nrewrite > (eq_to_eqbool y6 y6 (refl_eq …));
+ nrewrite > (eq_to_eqbool y7 y7 (refl_eq …));
+ nrewrite > (eq_to_eqbool y8 y8 (refl_eq …));
+ nrewrite > (eq_to_eqbool y9 y9 (refl_eq …));
+ nrewrite > (eq_to_eqbool y10 y10 (refl_eq …));
+ nrewrite > (eq_to_eqbool y11 y11 (refl_eq …));
+ nrewrite > (eq_to_eqbool y12 y12 (refl_eq …));
+ napply refl_eq.
+nqed.
+
+nlemma decidable_aluHC08_aux1
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ (x1 ≠ y1) →
+ (mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12) ≠
+ (mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12;
+ nnormalize; #H; #H1;
+ napply (H (aluHC08_destruct_1 … H1)).
+nqed.
+
+nlemma decidable_aluHC08_aux2
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ (x2 ≠ y2) →
+ (mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12) ≠
+ (mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12;
+ nnormalize; #H; #H1;
+ napply (H (aluHC08_destruct_2 … H1)).
+nqed.
+
+nlemma decidable_aluHC08_aux3
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ (x3 ≠ y3) →
+ (mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12) ≠
+ (mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12;
+ nnormalize; #H; #H1;
+ napply (H (aluHC08_destruct_3 … H1)).
+nqed.
+
+nlemma decidable_aluHC08_aux4
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ (x4 ≠ y4) →
+ (mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12) ≠
+ (mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12;
+ nnormalize; #H; #H1;
+ napply (H (aluHC08_destruct_4 … H1)).
+nqed.
+
+nlemma decidable_aluHC08_aux5
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ (x5 ≠ y5) →
+ (mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12) ≠
+ (mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12;
+ nnormalize; #H; #H1;
+ napply (H (aluHC08_destruct_5 … H1)).
+nqed.
+
+nlemma decidable_aluHC08_aux6
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ (x6 ≠ y6) →
+ (mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12) ≠
+ (mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12;
+ nnormalize; #H; #H1;
+ napply (H (aluHC08_destruct_6 … H1)).
+nqed.
+
+nlemma decidable_aluHC08_aux7
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ (x7 ≠ y7) →
+ (mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12) ≠
+ (mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12;
+ nnormalize; #H; #H1;
+ napply (H (aluHC08_destruct_7 … H1)).
+nqed.
+
+nlemma decidable_aluHC08_aux8
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ (x8 ≠ y8) →
+ (mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12) ≠
+ (mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12;
+ nnormalize; #H; #H1;
+ napply (H (aluHC08_destruct_8 … H1)).
+nqed.
+
+nlemma decidable_aluHC08_aux9
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ (x9 ≠ y9) →
+ (mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12) ≠
+ (mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12;
+ nnormalize; #H; #H1;
+ napply (H (aluHC08_destruct_9 … H1)).
+nqed.
+
+nlemma decidable_aluHC08_aux10
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ (x10 ≠ y10) →
+ (mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12) ≠
+ (mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12;
+ nnormalize; #H; #H1;
+ napply (H (aluHC08_destruct_10 … H1)).
+nqed.
+
+nlemma decidable_aluHC08_aux11
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ (x11 ≠ y11) →
+ (mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12) ≠
+ (mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12;
+ nnormalize; #H; #H1;
+ napply (H (aluHC08_destruct_11 … H1)).
+nqed.
+
+nlemma decidable_aluHC08_aux12
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
+ (x12 ≠ y12) →
+ (mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12) ≠
+ (mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12;
+ nnormalize; #H; #H1;
+ napply (H (aluHC08_destruct_12 … H1)).
+nqed.
+
+nlemma decidable_aluHC08 : ∀x,y:alu_HC08.decidable (x = y).
+ #x; nelim x; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
+ #y; nelim y; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12;
+ nnormalize;
+ napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_b8 x1 y1) …);
+ ##[ ##2: #H; napply (or2_intro2 … (decidable_aluHC08_aux1 … H))
+ ##| ##1: #H; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_b8 x2 y2) …);
+  ##[ ##2: #H1; napply (or2_intro2 … (decidable_aluHC08_aux2 … H1))
+  ##| ##1: #H1; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_b8 x3 y3) …);
+   ##[ ##2: #H2; napply (or2_intro2 … (decidable_aluHC08_aux3 … H2))
+   ##| ##1: #H2; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x4 y4) …);
+    ##[ ##2: #H3; napply (or2_intro2 … (decidable_aluHC08_aux4 … H3))
+    ##| ##1: #H3; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x5 y5) …);
+     ##[ ##2: #H4; napply (or2_intro2 … (decidable_aluHC08_aux5 … H4))
+     ##| ##1: #H4; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x6 y6) …);
+      ##[ ##2: #H5; napply (or2_intro2 … (decidable_aluHC08_aux6 … H5))
+      ##| ##1: #H5; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x7 y7) …);
+       ##[ ##2: #H6; napply (or2_intro2 … (decidable_aluHC08_aux7 … H6))
+       ##| ##1: #H6; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x8 y8) …);
+        ##[ ##2: #H7; napply (or2_intro2 … (decidable_aluHC08_aux8 … H7))
+        ##| ##1: #H7; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x9 y9) …);
+         ##[ ##2: #H8; napply (or2_intro2 … (decidable_aluHC08_aux9 … H8))
+         ##| ##1: #H8; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x10 y10) …);
+          ##[ ##2: #H9; napply (or2_intro2 … (decidable_aluHC08_aux10 … H9))
+          ##| ##1: #H9; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x11 y11) …);
+           ##[ ##2: #H10; napply (or2_intro2 … (decidable_aluHC08_aux11 … H10))
+           ##| ##1: #H10; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x12 y12) …);
+            ##[ ##2: #H11; napply (or2_intro2 … (decidable_aluHC08_aux12 … H11))
+            ##| ##1: #H11; nrewrite > H; nrewrite > H1; nrewrite > H2; nrewrite > H3;
+                      nrewrite > H4; nrewrite > H5; nrewrite > H6; nrewrite > H7;
+                      nrewrite > H8; nrewrite > H9; nrewrite > H10; nrewrite > H11;
+                      napply (or2_intro1 (? = ?) (? ≠ ?) (refl_eq …))
+            ##]
+           ##]
+          ##]
+         ##]
+        ##]
+       ##]
+      ##]
+     ##]
+    ##]
+   ##]
+  ##]
+ ##]
 nqed.
 
 nlemma aluRS08_destruct_1 :
@@ -579,7 +949,7 @@ nlemma aluRS08_destruct_1 :
                 with [ mk_alu_RS08 a _ _ _ _ _ _ _ ⇒ x1 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluRS08_destruct_2 :
@@ -592,7 +962,7 @@ nlemma aluRS08_destruct_2 :
                 with [ mk_alu_RS08 _ a _ _ _ _ _ _ ⇒ x2 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluRS08_destruct_3 :
@@ -605,7 +975,7 @@ nlemma aluRS08_destruct_3 :
                 with [ mk_alu_RS08 _ _ a _ _ _ _ _ ⇒ x3 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluRS08_destruct_4 :
@@ -618,7 +988,7 @@ nlemma aluRS08_destruct_4 :
                 with [ mk_alu_RS08 _ _ _ a _ _ _ _ ⇒ x4 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluRS08_destruct_5 :
@@ -631,7 +1001,7 @@ nlemma aluRS08_destruct_5 :
                 with [ mk_alu_RS08 _ _ _ _ a _ _ _ ⇒ x5 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluRS08_destruct_6 :
@@ -644,7 +1014,7 @@ nlemma aluRS08_destruct_6 :
                 with [ mk_alu_RS08 _ _ _ _ _ a _ _ ⇒ x6 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluRS08_destruct_7 :
@@ -657,7 +1027,7 @@ nlemma aluRS08_destruct_7 :
                 with [ mk_alu_RS08 _ _ _ _ _ _ a _ ⇒ x7 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma aluRS08_destruct_8 :
@@ -670,10 +1040,10 @@ nlemma aluRS08_destruct_8 :
                 with [ mk_alu_RS08 _ _ _ _ _ _ _ a ⇒ x8 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
-nlemma symmetric_eqaluRS08 : symmetricT alu_RS08 bool eq_alu_RS08.
+nlemma symmetric_eqaluRS08 : symmetricT alu_RS08 bool eq_aluRS08.
  #alu1; #alu2;
  ncases alu1;
  #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
@@ -696,10 +1066,10 @@ nlemma symmetric_eqaluRS08 : symmetricT alu_RS08 bool eq_alu_RS08.
  nrewrite > (symmetric_eqb8 x6 y6);
  nrewrite > (symmetric_eqbool x7 y7);
  nrewrite > (symmetric_eqbool x8 y8);
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
-nlemma eqaluRS08_to_eq : ∀alu1,alu2.eq_alu_RS08 alu1 alu2 = true → alu1 = alu2.
+nlemma eqaluRS08_to_eq : ∀alu1,alu2.eq_aluRS08 alu1 alu2 = true → alu1 = alu2.
  #alu1; #alu2;
  ncases alu1;
  #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
@@ -710,70 +1080,191 @@ nlemma eqaluRS08_to_eq : ∀alu1,alu2.eq_alu_RS08 alu1 alu2 = true → alu1 = al
    (eq_w16 x3 y3) ⊗ (eq_w16 x4 y4) ⊗
    (eq_b8 x5 y5) ⊗ (eq_b8 x6 y6) ⊗
    (eq_bool x7 y7) ⊗ (eq_bool x8 y8)) = true);
- nrewrite > (eqbool_to_eq ?? (andb_true_true_r ?? H));
- nletin H1 ≝ (andb_true_true_l ?? H);
- nrewrite > (eqbool_to_eq ?? (andb_true_true_r ?? H1));
- nletin H2 ≝ (andb_true_true_l ?? H1);
- nrewrite > (eqb8_to_eq ?? (andb_true_true_r ?? H2));
- nletin H3 ≝ (andb_true_true_l ?? H2);
- nrewrite > (eqb8_to_eq ?? (andb_true_true_r ?? H3));
- nletin H4 ≝ (andb_true_true_l ?? H3);
- nrewrite > (eqw16_to_eq ?? (andb_true_true_r ?? H4));
- nletin H5 ≝ (andb_true_true_l ?? H4);
- nrewrite > (eqw16_to_eq ?? (andb_true_true_r ?? H5));
- nletin H6 ≝ (andb_true_true_l ?? H5);
- nrewrite > (eqw16_to_eq ?? (andb_true_true_r ?? H6));
- nrewrite > (eqb8_to_eq ?? (andb_true_true_l ?? H6));
- napply (refl_eq ??).
-nqed.
-
-nlemma eq_to_eqaluRS08 : ∀alu1,alu2.alu1 = alu2 → eq_alu_RS08 alu1 alu2 = true.
+ nrewrite > (eqbool_to_eq … (andb_true_true_r … H));
+ nletin H1 ≝ (andb_true_true_l … H);
+ nrewrite > (eqbool_to_eq … (andb_true_true_r … H1));
+ nletin H2 ≝ (andb_true_true_l … H1);
+ nrewrite > (eqb8_to_eq … (andb_true_true_r … H2));
+ nletin H3 ≝ (andb_true_true_l … H2);
+ nrewrite > (eqb8_to_eq … (andb_true_true_r … H3));
+ nletin H4 ≝ (andb_true_true_l … H3);
+ nrewrite > (eqw16_to_eq … (andb_true_true_r … H4));
+ nletin H5 ≝ (andb_true_true_l … H4);
+ nrewrite > (eqw16_to_eq … (andb_true_true_r … H5));
+ nletin H6 ≝ (andb_true_true_l … H5);
+ nrewrite > (eqw16_to_eq … (andb_true_true_r … H6));
+ nrewrite > (eqb8_to_eq … (andb_true_true_l … H6));
+ napply refl_eq.
+nqed.
+
+nlemma eq_to_eqaluRS08 : ∀alu1,alu2.alu1 = alu2 → eq_aluRS08 alu1 alu2 = true.
  #alu1; #alu2;
  ncases alu1;
  #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
  ncases alu2;
  #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
- nrewrite > (aluRS08_destruct_1 ???????????????? H);
- nrewrite > (aluRS08_destruct_2 ???????????????? H);
- nrewrite > (aluRS08_destruct_3 ???????????????? H);
- nrewrite > (aluRS08_destruct_4 ???????????????? H);
- nrewrite > (aluRS08_destruct_5 ???????????????? H);
- nrewrite > (aluRS08_destruct_6 ???????????????? H);
- nrewrite > (aluRS08_destruct_7 ???????????????? H);
- nrewrite > (aluRS08_destruct_8 ???????????????? H);
+ nrewrite > (aluRS08_destruct_1 … H);
+ nrewrite > (aluRS08_destruct_2 … H);
+ nrewrite > (aluRS08_destruct_3 … H);
+ nrewrite > (aluRS08_destruct_4 … H);
+ nrewrite > (aluRS08_destruct_5 … H);
+ nrewrite > (aluRS08_destruct_6 … H);
+ nrewrite > (aluRS08_destruct_7 … H);
+ nrewrite > (aluRS08_destruct_8 … H);
  nchange with (
   ((eq_b8 y1 y1) ⊗ (eq_w16 y2 y2) ⊗
    (eq_w16 y3 y3) ⊗ (eq_w16 y4 y4) ⊗
    (eq_b8 y5 y5) ⊗ (eq_b8 y6 y6) ⊗
    (eq_bool y7 y7) ⊗ (eq_bool y8 y8)) = true);
- nrewrite > (eq_to_eqb8 y1 y1 (refl_eq ??));
- nrewrite > (eq_to_eqw16 y2 y2 (refl_eq ??));
- nrewrite > (eq_to_eqw16 y3 y3 (refl_eq ??));
- nrewrite > (eq_to_eqw16 y4 y4 (refl_eq ??));
- nrewrite > (eq_to_eqb8 y5 y5 (refl_eq ??));
- nrewrite > (eq_to_eqb8 y6 y6 (refl_eq ??));
- nrewrite > (eq_to_eqbool y7 y7 (refl_eq ??));
- nrewrite > (eq_to_eqbool y8 y8 (refl_eq ??));
- napply (refl_eq ??).
+ nrewrite > (eq_to_eqb8 y1 y1 (refl_eq …));
+ nrewrite > (eq_to_eqw16 y2 y2 (refl_eq …));
+ nrewrite > (eq_to_eqw16 y3 y3 (refl_eq …));
+ nrewrite > (eq_to_eqw16 y4 y4 (refl_eq …));
+ nrewrite > (eq_to_eqb8 y5 y5 (refl_eq …));
+ nrewrite > (eq_to_eqb8 y6 y6 (refl_eq …));
+ nrewrite > (eq_to_eqbool y7 y7 (refl_eq …));
+ nrewrite > (eq_to_eqbool y8 y8 (refl_eq …));
+ napply refl_eq.
+nqed.
+
+nlemma decidable_aluRS08_aux1
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
+ (x1 ≠ y1) →
+ (mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8) ≠
+ (mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nnormalize; #H; #H1;
+ napply (H (aluRS08_destruct_1 … H1)).
+nqed.
+
+nlemma decidable_aluRS08_aux2
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
+ (x2 ≠ y2) →
+ (mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8) ≠
+ (mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nnormalize; #H; #H1;
+ napply (H (aluRS08_destruct_2 … H1)).
+nqed.
+
+nlemma decidable_aluRS08_aux3
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
+ (x3 ≠ y3) →
+ (mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8) ≠
+ (mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nnormalize; #H; #H1;
+ napply (H (aluRS08_destruct_3 … H1)).
+nqed.
+
+nlemma decidable_aluRS08_aux4
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
+ (x4 ≠ y4) →
+ (mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8) ≠
+ (mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nnormalize; #H; #H1;
+ napply (H (aluRS08_destruct_4 … H1)).
+nqed.
+
+nlemma decidable_aluRS08_aux5
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
+ (x5 ≠ y5) →
+ (mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8) ≠
+ (mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nnormalize; #H; #H1;
+ napply (H (aluRS08_destruct_5 … H1)).
+nqed.
+
+nlemma decidable_aluRS08_aux6
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
+ (x6 ≠ y6) →
+ (mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8) ≠
+ (mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nnormalize; #H; #H1;
+ napply (H (aluRS08_destruct_6 … H1)).
+nqed.
+
+nlemma decidable_aluRS08_aux7
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
+ (x7 ≠ y7) →
+ (mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8) ≠
+ (mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nnormalize; #H; #H1;
+ napply (H (aluRS08_destruct_7 … H1)).
+nqed.
+
+nlemma decidable_aluRS08_aux8
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
+ (x8 ≠ y8) →
+ (mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8) ≠
+ (mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nnormalize; #H; #H1;
+ napply (H (aluRS08_destruct_8 … H1)).
+nqed.
+
+nlemma decidable_aluRS08 : ∀x,y:alu_RS08.decidable (x = y).
+ #x; nelim x; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
+ #y; nelim y; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
+ nnormalize;
+ napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_b8 x1 y1) …);
+ ##[ ##2: #H; napply (or2_intro2 … (decidable_aluRS08_aux1 … H))
+ ##| ##1: #H; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x2 y2) …);
+  ##[ ##2: #H1; napply (or2_intro2 … (decidable_aluRS08_aux2 … H1))
+  ##| ##1: #H1; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x3 y3) …);
+   ##[ ##2: #H2; napply (or2_intro2 … (decidable_aluRS08_aux3 … H2))
+   ##| ##1: #H2; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x4 y4) …);
+    ##[ ##2: #H3; napply (or2_intro2 … (decidable_aluRS08_aux4 … H3))
+    ##| ##1: #H3; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_b8 x5 y5) …);
+     ##[ ##2: #H4; napply (or2_intro2 … (decidable_aluRS08_aux5 … H4))
+     ##| ##1: #H4; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_b8 x6 y6) …);
+      ##[ ##2: #H5; napply (or2_intro2 … (decidable_aluRS08_aux6 … H5))
+      ##| ##1: #H5; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x7 y7) …);
+       ##[ ##2: #H6; napply (or2_intro2 … (decidable_aluRS08_aux7 … H6))
+       ##| ##1: #H6; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x8 y8) …);
+        ##[ ##2: #H7; napply (or2_intro2 … (decidable_aluRS08_aux8 … H7))
+        ##| ##1: #H7; nrewrite > H; nrewrite > H1; nrewrite > H2; nrewrite > H3;
+                      nrewrite > H4; nrewrite > H5; nrewrite > H6; nrewrite > H7;
+                      napply (or2_intro1 (? = ?) (? ≠ ?) (refl_eq …))
+        ##]
+       ##]
+      ##]
+     ##]
+    ##]
+   ##]
+  ##]
+ ##]
 nqed.
 
 nlemma symmetric_eqclk : ∀mcu,clk1,clk2.eq_clk mcu clk1 clk2 = eq_clk mcu clk2 clk1.
  #mcu; #clk1; #clk2;
  ncases clk1;
  ncases clk2;
- ##[ ##1: napply (refl_eq ??)
- ##| ##2,3: nnormalize; #H; napply (refl_eq ??)
+ ##[ ##1: napply refl_eq
+ ##| ##2,3: nnormalize; #H; napply refl_eq
  ##| ##4: #p1; ncases p1; #x1; #x2; #x3; #x4; #x5;
           #p2; ncases p2; #y1; #y2; #y3; #y4; #y5;
           nchange with (
-           ((eq_b8 y1 x1) ⊗ (eq_anyop ? y2 x2) ⊗ (eq_instrmode y3 x3) ⊗ (eq_b8 y4 x4) ⊗ (eq_w16 y5 x5)) =
-           ((eq_b8 x1 y1) ⊗ (eq_anyop ? x2 y2) ⊗ (eq_instrmode x3 y3) ⊗ (eq_b8 x4 y4) ⊗ (eq_w16 x5 y5)));
+           ((eq_b8 y1 x1) ⊗ (eq_anyop ? y2 x2) ⊗ (eq_im y3 x3) ⊗ (eq_b8 y4 x4) ⊗ (eq_w16 y5 x5)) =
+           ((eq_b8 x1 y1) ⊗ (eq_anyop ? x2 y2) ⊗ (eq_im x3 y3) ⊗ (eq_b8 x4 y4) ⊗ (eq_w16 x5 y5)));
           nrewrite > (symmetric_eqb8 x1 y1);
           nrewrite > (symmetric_eqanyop ? x2 y2);
-          nrewrite > (symmetric_eqinstrmode x3 y3);
+          nrewrite > (symmetric_eqim x3 y3);
           nrewrite > (symmetric_eqb8 x4 y4);
           nrewrite > (symmetric_eqw16 x5 y5);
-          napply (refl_eq ??)
+          napply refl_eq
  ##]
 nqed.
 
@@ -781,21 +1272,21 @@ nlemma eqclk_to_eq : ∀mcu,clk1,clk2.eq_clk mcu clk1 clk2 = true → clk1 = clk
  #mcu; #clk1; #clk2;
  ncases clk1;
  ncases clk2;
- ##[ ##1: nnormalize; #H; napply (refl_eq ??)
- ##| ##2,3: nnormalize; #H; #H1; napply (bool_destruct ??? H1)
+ ##[ ##1: nnormalize; #H; napply refl_eq
+ ##| ##2,3: nnormalize; #H; #H1; napply (bool_destruct … H1)
  ##| ##4: #p1; ncases p1; #x1; #x2; #x3; #x4; #x5;
           #p2; ncases p2; #y1; #y2; #y3; #y4; #y5; #H;
           nchange in H:(%) with (
-           ((eq_b8 y1 x1) ⊗ (eq_anyop ? y2 x2) ⊗ (eq_instrmode y3 x3) ⊗ (eq_b8 y4 x4) ⊗ (eq_w16 y5 x5)) = true);
-           nrewrite > (eqw16_to_eq ?? (andb_true_true_r ?? H));
-           nletin H1 ≝ (andb_true_true_l ?? H);
-           nrewrite > (eqb8_to_eq ?? (andb_true_true_r ?? H1));
-           nletin H2 ≝ (andb_true_true_l ?? H1);
-           nrewrite > (eqinstrmode_to_eq ?? (andb_true_true_r ?? H2));
-           nletin H3 ≝ (andb_true_true_l ?? H2);
-           nrewrite > (eqanyop_to_eq ??? (andb_true_true_r ?? H3));
-           nrewrite > (eqb8_to_eq ?? (andb_true_true_l ?? H3));
-           napply (refl_eq ??)
+           ((eq_b8 y1 x1) ⊗ (eq_anyop ? y2 x2) ⊗ (eq_im y3 x3) ⊗ (eq_b8 y4 x4) ⊗ (eq_w16 y5 x5)) = true);
+           nrewrite > (eqw16_to_eq … (andb_true_true_r … H));
+           nletin H1 ≝ (andb_true_true_l … H);
+           nrewrite > (eqb8_to_eq … (andb_true_true_r … H1));
+           nletin H2 ≝ (andb_true_true_l … H1);
+           nrewrite > (eqim_to_eq … (andb_true_true_r … H2));
+           nletin H3 ≝ (andb_true_true_l … H2);
+           nrewrite > (eqanyop_to_eq … (andb_true_true_r … H3));
+           nrewrite > (eqb8_to_eq … (andb_true_true_l … H3));
+           napply refl_eq
  ##]
 nqed.
 
@@ -803,25 +1294,25 @@ nlemma eq_to_eqclk : ∀mcu,clk1,clk2.clk1 = clk2 → eq_clk mcu clk1 clk2 = tru
  #mcu; #clk1; #clk2;
  ncases clk1;
  ncases clk2;
- ##[ ##1: nnormalize; #H; napply (refl_eq ??)
- ##| ##2: nnormalize; #p; #H1; nelim (option_destruct_none_some ?? H1)
- ##| ##3: nnormalize; #p; #H1; nelim (option_destruct_some_none ?? H1)
+ ##[ ##1: nnormalize; #H; napply refl_eq
+ ##| ##2: nnormalize; #p; #H1; nelim (option_destruct_none_some ? p … H1)
+ ##| ##3: nnormalize; #p; #H1; nelim (option_destruct_some_none ? p … H1)
  ##| ##4: #p1; ncases p1; #x1; #x2; #x3; #x4; #x5;
           #p2; ncases p2; #y1; #y2; #y3; #y4; #y5; #H;
-          nrewrite > (quintuple_destruct_1 ??????????????? (option_destruct_some_some ??? H));
-          nrewrite > (quintuple_destruct_2 ??????????????? (option_destruct_some_some ??? H));
-          nrewrite > (quintuple_destruct_3 ??????????????? (option_destruct_some_some ??? H));
-          nrewrite > (quintuple_destruct_4 ??????????????? (option_destruct_some_some ??? H));
-          nrewrite > (quintuple_destruct_5 ??????????????? (option_destruct_some_some ??? H));
+          nrewrite > (quintuple_destruct_1 … (option_destruct_some_some … H));
+          nrewrite > (quintuple_destruct_2 … (option_destruct_some_some … H));
+          nrewrite > (quintuple_destruct_3 … (option_destruct_some_some … H));
+          nrewrite > (quintuple_destruct_4 … (option_destruct_some_some … H));
+          nrewrite > (quintuple_destruct_5 … (option_destruct_some_some … H));
           nchange with (
-           ((eq_b8 x1 x1) ⊗ (eq_anyop ? x2 x2) ⊗ (eq_instrmode x3 x3) ⊗ (eq_b8 x4 x4) ⊗ (eq_w16 x5 x5)) = true);
-          nrewrite > (eq_to_eqb8 x1 x1 (refl_eq ??));
+           ((eq_b8 x1 x1) ⊗ (eq_anyop ? x2 x2) ⊗ (eq_im x3 x3) ⊗ (eq_b8 x4 x4) ⊗ (eq_w16 x5 x5)) = true);
+          nrewrite > (eq_to_eqb8 x1 x1 (refl_eq …));
           nrewrite > (eq_to_eqanyop mcu x2 x2 (refl_eq ? x2));
-          nrewrite > (eq_to_eqinstrmode x3 x3 (refl_eq ??));
-          nrewrite > (eq_to_eqb8 x4 x4 (refl_eq ??));
-          nrewrite > (eq_to_eqw16 x5 x5 (refl_eq ??));
+          nrewrite > (eq_to_eqim x3 x3 (refl_eq …));
+          nrewrite > (eq_to_eqb8 x4 x4 (refl_eq …));
+          nrewrite > (eq_to_eqw16 x5 x5 (refl_eq …));
           nnormalize;
-          napply (refl_eq ??)
+          napply refl_eq
  ##]
 nqed.
 
@@ -830,8 +1321,8 @@ nlemma symmetric_forallmemoryranged :
  forall_memory_ranged t chk1 chk2 mem1 mem2 addrl =
  forall_memory_ranged t chk2 chk1 mem2 mem1 addrl.
  #t; #chk1; #chk2; #mem1; #mem2; #addrl;
- napply (list_ind word16 ??? addrl);
- ##[ ##1: nnormalize; napply (refl_eq ??)
+ napply (list_ind word16 … addrl);
+ ##[ ##1: nnormalize; napply refl_eq
  ##| ##2: #a; #l; #H;
           nchange with (
            ((eq_option byte8 (mem_read t mem1 chk1 a)
@@ -842,7 +1333,7 @@ nlemma symmetric_forallmemoryranged :
            (forall_memory_ranged t chk2 chk1 mem2 mem1 l)));
            nrewrite > H;
            nrewrite > (symmetric_eqoption ? (mem_read t mem1 chk1 a) (mem_read t mem2 chk2 a) eq_b8 symmetric_eqb8);
-           napply (refl_eq ??)
+           napply refl_eq
  ##]
 nqed.
 
@@ -857,7 +1348,7 @@ nlemma anystatus_destruct_1 :
                 with [ mk_any_status a _ _ _ ⇒ x1 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma anystatus_destruct_2 :
@@ -871,7 +1362,7 @@ nlemma anystatus_destruct_2 :
                 with [ mk_any_status _ a _ _ ⇒ x2 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma anystatus_destruct_3 :
@@ -885,7 +1376,7 @@ nlemma anystatus_destruct_3 :
                 with [ mk_any_status _ _ a _ ⇒ x3 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma anystatus_destruct_4 :
@@ -899,147 +1390,147 @@ nlemma anystatus_destruct_4 :
                 with [ mk_any_status _ _ _ a ⇒ x4 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
-nlemma symmetric_eqstatus :
+nlemma symmetric_eqanystatus :
 ∀addrl:list word16.∀m:mcu_type.∀t:memory_impl.∀s1,s2:any_status m t.
- eq_status m t s1 s2 addrl = eq_status m t s2 s1 addrl.
+ eq_anystatus m t s1 s2 addrl = eq_anystatus m t s2 s1 addrl.
  #addrl; #m;
  ncases m; #t; #s1;
  ##[ ##1: ncases s1; #x1; #x2; #x3; #x4;
           #s2; ncases s2; #y1; #y2; #y3; #y4;
           nchange with (
-           ((eq_alu_HC05 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk HC05 x4 y4)) =
-           ((eq_alu_HC05 y1 x1) ⊗ (forall_memory_ranged t y3 x3 y2 x2 addrl) ⊗ (eq_clk HC05 y4 x4)));
+           ((eq_aluHC05 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk HC05 x4 y4)) =
+           ((eq_aluHC05 y1 x1) ⊗ (forall_memory_ranged t y3 x3 y2 x2 addrl) ⊗ (eq_clk HC05 y4 x4)));
            nrewrite > (symmetric_eqaluHC05 x1 y1)
  ##| ##2,3: ncases s1; #x1; #x2; #x3; #x4;
           #s2; ncases s2; #y1; #y2; #y3; #y4;
           nchange with (
-           ((eq_alu_HC08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) =
-           ((eq_alu_HC08 y1 x1) ⊗ (forall_memory_ranged t y3 x3 y2 x2 addrl) ⊗ (eq_clk ? y4 x4)));
+           ((eq_aluHC08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) =
+           ((eq_aluHC08 y1 x1) ⊗ (forall_memory_ranged t y3 x3 y2 x2 addrl) ⊗ (eq_clk ? y4 x4)));
            nrewrite > (symmetric_eqaluHC08 x1 y1)
  ##| ##4: ncases s1; #x1; #x2; #x3; #x4;
           #s2; ncases s2; #y1; #y2; #y3; #y4;
           nchange with (
-           ((eq_alu_RS08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk RS08 x4 y4)) =
-           ((eq_alu_RS08 y1 x1) ⊗ (forall_memory_ranged t y3 x3 y2 x2 addrl) ⊗ (eq_clk RS08 y4 x4)));
+           ((eq_aluRS08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk RS08 x4 y4)) =
+           ((eq_aluRS08 y1 x1) ⊗ (forall_memory_ranged t y3 x3 y2 x2 addrl) ⊗ (eq_clk RS08 y4 x4)));
            nrewrite > (symmetric_eqaluRS08 x1 y1)
  ##]
  nrewrite > (symmetric_forallmemoryranged t x3 y3 x2 y2 addrl);
  nrewrite > (symmetric_eqclk ? x4 y4);
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
-nlemma eqstatus_to_eq :
+nlemma eqanystatus_to_eq :
 ∀addrl:list word16.∀m:mcu_type.∀t:memory_impl.∀s1,s2:any_status m t.
- (eq_status m t s1 s2 addrl = true) →
-  ((alu m t s1 = alu m t s2) ∧
-   (clk_desc m t s1 = clk_desc m t s2) ∧
-   ((forall_memory_ranged t (chk_desc m t s1) (chk_desc m t s2)
-                            (mem_desc m t s1) (mem_desc m t s2) addrl) = true)).
+ (eq_anystatus m t s1 s2 addrl = true) →
+  And3 (alu m t s1 = alu m t s2) 
+       (clk_desc m t s1 = clk_desc m t s2)
+       ((forall_memory_ranged t (chk_desc m t s1) (chk_desc m t s2)
+                                (mem_desc m t s1) (mem_desc m t s2) addrl) = true).
  #addrl; #m; #t;
  ncases m; #s1;
  ##[ ##1: ncases s1; #x1; #x2; #x3; #x4;
           #s2; ncases s2; #y1; #y2; #y3; #y4; #H;
           nchange in H:(%) with (
-           ((eq_alu_HC05 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
-           nrewrite > (eqaluHC05_to_eq ?? (andb_true_true_l ?? (andb_true_true_l ?? H)))
+           ((eq_aluHC05 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
+           nrewrite > (eqaluHC05_to_eq … (andb_true_true_l … (andb_true_true_l … H)))
  ##| ##2,3: ncases s1; #x1; #x2; #x3; #x4;
           #s2; ncases s2; #y1; #y2; #y3; #y4; #H;
           nchange in H:(%) with (
-           ((eq_alu_HC08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
-           nrewrite > (eqaluHC08_to_eq ?? (andb_true_true_l ?? (andb_true_true_l ?? H)))
+           ((eq_aluHC08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
+           nrewrite > (eqaluHC08_to_eq … (andb_true_true_l … (andb_true_true_l … H)))
  ##| ##4: ncases s1; #x1; #x2; #x3; #x4;
           #s2; ncases s2; #y1; #y2; #y3; #y4; #H;
           nchange in H:(%) with (
-           ((eq_alu_RS08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
-           nrewrite > (eqaluRS08_to_eq ?? (andb_true_true_l ?? (andb_true_true_l ?? H)))
+           ((eq_aluRS08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
+           nrewrite > (eqaluRS08_to_eq … (andb_true_true_l … (andb_true_true_l … H)))
  ##]
- nchange with ((y1 = y1) ∧ (x4 = y4) ∧ (forall_memory_ranged t x3 y3 x2 y2 addrl = true));
- nrewrite > (andb_true_true_r ?? (andb_true_true_l ?? H));
- nrewrite > (eqclk_to_eq ??? (andb_true_true_r ?? H));
- napply (conj ?? (conj ?? (refl_eq ??) (refl_eq ??)) (refl_eq ??)).
+ nchange with (And3 (y1 = y1) (x4 = y4) (forall_memory_ranged t x3 y3 x2 y2 addrl = true));
+ nrewrite > (andb_true_true_r … (andb_true_true_l … H));
+ nrewrite > (eqclk_to_eq … (andb_true_true_r … H));
+ napply (conj3 … (refl_eq ? y1) (refl_eq ? y4) (refl_eq ? true)).
 nqed.
 
-nlemma eq_to_eqstatus_strong :
+nlemma eq_to_eqanystatus_strong :
 ∀addrl:list word16.∀m:mcu_type.∀t:memory_impl.∀s1,s2:any_status m t.
- s1 = s2 → (eq_status m t s1 s2 addrl = true).
+ s1 = s2 → (eq_anystatus m t s1 s2 addrl = true).
  #addrl; #m; #t;
  ncases m;
  ##[ ##1: #s1; ncases s1; #x1; #x2; #x3; #x4;
           #s2; ncases s2; #y1; #y2; #y3; #y4; #H;
           nchange with (
-           ((eq_alu_HC05 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
-          nrewrite > (anystatus_destruct_1 ?????????? H);
-          nrewrite > (eq_to_eqaluHC05 y1 y1 (refl_eq ??))
+           ((eq_aluHC05 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
+          nrewrite > (anystatus_destruct_1 … H);
+          nrewrite > (eq_to_eqaluHC05 y1 y1 (refl_eq …))
  ##| ##2,3:  #s1; ncases s1; #x1; #x2; #x3; #x4;
           #s2; ncases s2; #y1; #y2; #y3; #y4; #H;
           nchange with (
-           ((eq_alu_HC08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
-          nrewrite > (anystatus_destruct_1 ?????????? H);
-          nrewrite > (eq_to_eqaluHC08 y1 y1 (refl_eq ??))
+           ((eq_aluHC08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
+          nrewrite > (anystatus_destruct_1 … H);
+          nrewrite > (eq_to_eqaluHC08 y1 y1 (refl_eq …))
  ##| ##4: #s1; ncases s1; #x1; #x2; #x3; #x4;
           #s2; ncases s2; #y1; #y2; #y3; #y4; #H;
           nchange with (
-           ((eq_alu_RS08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
-          nrewrite > (anystatus_destruct_1 ?????????? H);
-          nrewrite > (eq_to_eqaluRS08 y1 y1 (refl_eq ??))
+           ((eq_aluRS08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
+          nrewrite > (anystatus_destruct_1 … H);
+          nrewrite > (eq_to_eqaluRS08 y1 y1 (refl_eq …))
  ##]
- nrewrite > (anystatus_destruct_2 ?????????? H);
- nrewrite > (anystatus_destruct_3 ?????????? H);
- nrewrite > (anystatus_destruct_4 ?????????? H);
- nrewrite > (eq_to_eqclk ? y4 y4 (refl_eq ??));
- nchange with ((forall_memory_ranged ?????? ⊗ true) =true);
+ nrewrite > (anystatus_destruct_2 … H);
+ nrewrite > (anystatus_destruct_3 … H);
+ nrewrite > (anystatus_destruct_4 … H);
+ nrewrite > (eq_to_eqclk ? y4 y4 (refl_eq …));
+ nchange with ((forall_memory_ranged … ⊗ true) =true);
  nrewrite > (symmetric_andbool (forall_memory_ranged t y3 y3 y2 y2 addrl) true);
- nchange with (forall_memory_ranged ?????? = true);
- napply (list_ind word16 ??? addrl);
- ##[ ##1,3,5,7: nnormalize; napply (refl_eq ??)
+ nchange with ((forall_memory_ranged t y3 y3 y2 y2 ?) = true);
+ napply (list_ind word16 … addrl);
+ ##[ ##1,3,5,7: nnormalize; napply refl_eq
  ##| ##2,4,6,8: #a; #l'; #H;
           nchange with (
           ((eq_option byte8 (mem_read t y2 y3 a)
                             (mem_read t y2 y3 a) eq_b8) ⊗
            (forall_memory_ranged t y3 y3 y2 y2 l')) = true);
           nrewrite > H;
-          nrewrite > (eq_to_eqoption ? (mem_read t y2 y3 a) (mem_read t y2 y3 a) eq_b8 eq_to_eqb8 (refl_eq ??));
+          nrewrite > (eq_to_eqoption ? (mem_read t y2 y3 a) (mem_read t y2 y3 a) eq_b8 eq_to_eqb8 (refl_eq …));
           nnormalize;
-          napply (refl_eq ??)
+          napply refl_eq
  ##]
 nqed.
 
-nlemma eq_to_eqstatus_weak :
+nlemma eq_to_eqanystatus_weak :
 ∀addrl:list word16.∀m:mcu_type.∀t:memory_impl.∀s1,s2:any_status m t.
  (alu m t s1 = alu m t s2) →
  (clk_desc m t s1 = clk_desc m t s2) →
  ((forall_memory_ranged t (chk_desc m t s1) (chk_desc m t s2)
                             (mem_desc m t s1) (mem_desc m t s2) addrl) = true) →
- (eq_status m t s1 s2 addrl = true).
+ (eq_anystatus m t s1 s2 addrl = true).
  #addrl; #m; #t;
  ncases m;
  ##[ ##1: #s1; ncases s1; #x1; #x2; #x3; #x4;
           #s2; ncases s2; #y1; #y2; #y3; #y4; #H; #H1; #H2;
-          nchange with (((eq_alu_HC05 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
+          nchange with (((eq_aluHC05 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
           nchange in H:(%) with (x1 = y1);
           nrewrite > H; 
-          nrewrite > (eq_to_eqaluHC05 y1 y1 (refl_eq ??))
+          nrewrite > (eq_to_eqaluHC05 y1 y1 (refl_eq …))
  ##| ##2,3: #s1; ncases s1; #x1; #x2; #x3; #x4;
           #s2; ncases s2; #y1; #y2; #y3; #y4; #H; #H1; #H2;
-          nchange with (((eq_alu_HC08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
+          nchange with (((eq_aluHC08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
           nchange in H:(%) with (x1 = y1);
           nrewrite > H; 
-          nrewrite > (eq_to_eqaluHC08 y1 y1 (refl_eq ??))
+          nrewrite > (eq_to_eqaluHC08 y1 y1 (refl_eq …))
  ##| ##4: #s1; ncases s1; #x1; #x2; #x3; #x4;
           #s2; ncases s2; #y1; #y2; #y3; #y4; #H; #H1; #H2;
-          nchange with (((eq_alu_RS08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
+          nchange with (((eq_aluRS08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
           nchange in H:(%) with (x1 = y1);
           nrewrite > H; 
-          nrewrite > (eq_to_eqaluRS08 y1 y1 (refl_eq ??))
+          nrewrite > (eq_to_eqaluRS08 y1 y1 (refl_eq …))
  ##]
  nchange in H2:(%) with (forall_memory_ranged t x3 y3 x2 y2 addrl = true);
  nrewrite > H2;
  nchange in H1:(%) with (x4 = y4);
  nrewrite > H1;
- nrewrite > (eq_to_eqclk ? y4 y4 (refl_eq ??));
+ nrewrite > (eq_to_eqclk ? y4 y4 (refl_eq …));
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.