+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* *)
+(* Questo materiale fa parte della tesi: *)
+(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
+(* *)
+(* data ultima modifica 15/11/2007 *)
+(* ********************************************************************** *)
+
+include "freescale/aux_bases_lemmas.ma".
+include "freescale/exadecim_lemmas.ma".
+include "freescale/opcode_base.ma".
+
+(* ********************************************** *)
+(* MATTONI BASE PER DEFINIRE LE TABELLE DELLE MCU *)
+(* ********************************************** *)
+
+ndefinition instr_mode_destruct1 :
+ Πi2.ΠP:Prop.MODE_INH = i2 → match i2 with [ MODE_INH ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##1: #H; napply (λx:P.x)
+ ##| ##2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_INH with [ MODE_INH ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_INH with [ MODE_INH ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct2 :
+ Πi2.ΠP:Prop.MODE_INHA = i2 → match i2 with [ MODE_INHA ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##2: #H; napply (λx:P.x)
+ ##| ##1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_INHA with [ MODE_INHA ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_INHA with [ MODE_INHA ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct3 :
+ Πi2.ΠP:Prop.MODE_INHX = i2 → match i2 with [ MODE_INHX ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##3: #H; napply (λx:P.x)
+ ##| ##1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_INHX with [ MODE_INHX ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_INHX with [ MODE_INHX ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct4 :
+ Πi2.ΠP:Prop.MODE_INHH = i2 → match i2 with [ MODE_INHH ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##4: #H; napply (λx:P.x)
+ ##| ##1,2,3,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_INHH with [ MODE_INHH ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_INHH with [ MODE_INHH ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct5 :
+ Πi2.ΠP:Prop.MODE_INHX0ADD = i2 → match i2 with [ MODE_INHX0ADD ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##5: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_INHX0ADD with [ MODE_INHX0ADD ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_INHX0ADD with [ MODE_INHX0ADD ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct6 :
+ Πi2.ΠP:Prop.MODE_INHX1ADD = i2 → match i2 with [ MODE_INHX1ADD ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##6: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_INHX1ADD with [ MODE_INHX1ADD ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_INHX1ADD with [ MODE_INHX1ADD ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct7 :
+ Πi2.ΠP:Prop.MODE_INHX2ADD = i2 → match i2 with [ MODE_INHX2ADD ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##7: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_INHX2ADD with [ MODE_INHX2ADD ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_INHX2ADD with [ MODE_INHX2ADD ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct8 :
+ Πi2.ΠP:Prop.MODE_IMM1 = i2 → match i2 with [ MODE_IMM1 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##8: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IMM1 with [ MODE_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IMM1 with [ MODE_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct9 :
+ Πi2.ΠP:Prop.MODE_IMM1EXT = i2 → match i2 with [ MODE_IMM1EXT ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##9: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IMM1EXT with [ MODE_IMM1EXT ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IMM1EXT with [ MODE_IMM1EXT ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct10 :
+ Πi2.ΠP:Prop.MODE_IMM2 = i2 → match i2 with [ MODE_IMM2 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##10: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IMM2 with [ MODE_IMM2 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IMM2 with [ MODE_IMM2 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct11 :
+ Πi2.ΠP:Prop.MODE_DIR1 = i2 → match i2 with [ MODE_DIR1 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##11: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_DIR1 with [ MODE_DIR1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_DIR1 with [ MODE_DIR1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct12 :
+ Πi2.ΠP:Prop.MODE_DIR2 = i2 → match i2 with [ MODE_DIR2 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##12: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_DIR2 with [ MODE_DIR2 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_DIR2 with [ MODE_DIR2 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct13 :
+ Πi2.ΠP:Prop.MODE_IX0 = i2 → match i2 with [ MODE_IX0 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##13: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IX0 with [ MODE_IX0 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IX0 with [ MODE_IX0 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct14 :
+ Πi2.ΠP:Prop.MODE_IX1 = i2 → match i2 with [ MODE_IX1 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##14: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IX1 with [ MODE_IX1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IX1 with [ MODE_IX1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct15 :
+ Πi2.ΠP:Prop.MODE_IX2 = i2 → match i2 with [ MODE_IX2 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##15: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IX2 with [ MODE_IX2 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IX2 with [ MODE_IX2 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct16 :
+ Πi2.ΠP:Prop.MODE_SP1 = i2 → match i2 with [ MODE_SP1 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##16: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_SP1 with [ MODE_SP1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_SP1 with [ MODE_SP1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct17 :
+ Πi2.ΠP:Prop.MODE_SP2 = i2 → match i2 with [ MODE_SP2 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##17: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_SP2 with [ MODE_SP2 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_SP2 with [ MODE_SP2 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct18 :
+ Πi2.ΠP:Prop.MODE_DIR1_to_DIR1 = i2 → match i2 with [ MODE_DIR1_to_DIR1 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##18: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_DIR1_to_DIR1 with [ MODE_DIR1_to_DIR1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_DIR1_to_DIR1 with [ MODE_DIR1_to_DIR1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct19 :
+ Πi2.ΠP:Prop.MODE_IMM1_to_DIR1 = i2 → match i2 with [ MODE_IMM1_to_DIR1 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##19: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IMM1_to_DIR1 with [ MODE_IMM1_to_DIR1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IMM1_to_DIR1 with [ MODE_IMM1_to_DIR1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct20 :
+ Πi2.ΠP:Prop.MODE_IX0p_to_DIR1 = i2 → match i2 with [ MODE_IX0p_to_DIR1 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##20: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IX0p_to_DIR1 with [ MODE_IX0p_to_DIR1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IX0p_to_DIR1 with [ MODE_IX0p_to_DIR1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct21 :
+ Πi2.ΠP:Prop.MODE_DIR1_to_IX0p = i2 → match i2 with [ MODE_DIR1_to_IX0p ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##21: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_DIR1_to_IX0p with [ MODE_DIR1_to_IX0p ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_DIR1_to_IX0p with [ MODE_DIR1_to_IX0p ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct22 :
+ Πi2.ΠP:Prop.MODE_INHA_and_IMM1 = i2 → match i2 with [ MODE_INHA_and_IMM1 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##22: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_INHA_and_IMM1 with [ MODE_INHA_and_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_INHA_and_IMM1 with [ MODE_INHA_and_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct23 :
+ Πi2.ΠP:Prop.MODE_INHX_and_IMM1 = i2 → match i2 with [ MODE_INHX_and_IMM1 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##23: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_INHX_and_IMM1 with [ MODE_INHX_and_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_INHX_and_IMM1 with [ MODE_INHX_and_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct24 :
+ Πi2.ΠP:Prop.MODE_IMM1_and_IMM1 = i2 → match i2 with [ MODE_IMM1_and_IMM1 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##24: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IMM1_and_IMM1 with [ MODE_IMM1_and_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IMM1_and_IMM1 with [ MODE_IMM1_and_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct25 :
+ Πi2.ΠP:Prop.MODE_DIR1_and_IMM1 = i2 → match i2 with [ MODE_DIR1_and_IMM1 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##25: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_DIR1_and_IMM1 with [ MODE_DIR1_and_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_DIR1_and_IMM1 with [ MODE_DIR1_and_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct26 :
+ Πi2.ΠP:Prop.MODE_IX0_and_IMM1 = i2 → match i2 with [ MODE_IX0_and_IMM1 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##26: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IX0_and_IMM1 with [ MODE_IX0_and_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IX0_and_IMM1 with [ MODE_IX0_and_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct27 :
+ Πi2.ΠP:Prop.MODE_IX0p_and_IMM1 = i2 → match i2 with [ MODE_IX0p_and_IMM1 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##27: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IX0p_and_IMM1 with [ MODE_IX0p_and_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IX0p_and_IMM1 with [ MODE_IX0p_and_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct28 :
+ Πi2.ΠP:Prop.MODE_IX1_and_IMM1 = i2 → match i2 with [ MODE_IX1_and_IMM1 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##28: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IX1_and_IMM1 with [ MODE_IX1_and_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IX1_and_IMM1 with [ MODE_IX1_and_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct29 :
+ Πi2.ΠP:Prop.MODE_IX1p_and_IMM1 = i2 → match i2 with [ MODE_IX1p_and_IMM1 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##29: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IX1p_and_IMM1 with [ MODE_IX1p_and_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_IX1p_and_IMM1 with [ MODE_IX1p_and_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct30 :
+ Πi2.ΠP:Prop.MODE_SP1_and_IMM1 = i2 → match i2 with [ MODE_SP1_and_IMM1 ⇒ P → P | _ ⇒ P ].
+ #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##30: #H; napply (λx:P.x)
+ ##| ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_SP1_and_IMM1 with [ MODE_SP1_and_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_SP1_and_IMM1 with [ MODE_SP1_and_IMM1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+nlemma instr_mode_destruct_MODE_DIRn : ∀n1,n2.MODE_DIRn n1 = MODE_DIRn n2 → n1 = n2.
+ #n1; #n2; #H;
+ nchange with (match MODE_DIRn n2 with [ MODE_DIRn a ⇒ n1 = a | _ ⇒ False ]);
+ nrewrite < H;
+ nnormalize;
+ napply (refl_eq ??).
+nqed.
+
+ndefinition instr_mode_destruct31 :
+ Πn1,i2.ΠP:Prop.MODE_DIRn n1 = i2 →
+ match i2 with
+ [ MODE_DIRn n2 ⇒ match n1 with
+ [ o0 ⇒ match n2 with [ o0 ⇒ P → P | _ ⇒ P ] | o1 ⇒ match n2 with [ o1 ⇒ P → P | _ ⇒ P ]
+ | o2 ⇒ match n2 with [ o2 ⇒ P → P | _ ⇒ P ] | o3 ⇒ match n2 with [ o3 ⇒ P → P | _ ⇒ P ]
+ | o4 ⇒ match n2 with [ o4 ⇒ P → P | _ ⇒ P ] | o5 ⇒ match n2 with [ o5 ⇒ P → P | _ ⇒ P ]
+ | o6 ⇒ match n2 with [ o6 ⇒ P → P | _ ⇒ P ] | o7 ⇒ match n2 with [ o7 ⇒ P → P | _ ⇒ P ]]
+ | _ ⇒ P ].
+ #n1; #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_DIRn n1 with [ MODE_DIRn a ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##32,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_DIRn n1 with [ MODE_DIRn n1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31: #n2;
+ ncases n1;
+ ncases n2;
+ nnormalize;
+ ##[ ##1,10,19,28,37,46,55,64: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (oct_destruct ??? (instr_mode_destruct_MODE_DIRn ?? H))
+ ##]
+nqed.
+
+nlemma instr_mode_destruct_MODE_DIRn_and_IMM1 : ∀n1,n2.MODE_DIRn_and_IMM1 n1 = MODE_DIRn_and_IMM1 n2 → n1 = n2.
+ #n1; #n2; #H;
+ nchange with (match MODE_DIRn_and_IMM1 n2 with [ MODE_DIRn_and_IMM1 a ⇒ n1 = a | _ ⇒ False ]);
+ nrewrite < H;
+ nnormalize;
+ napply (refl_eq ??).
+nqed.
+
+ndefinition instr_mode_destruct32 :
+ Πn1,i2.ΠP:Prop.MODE_DIRn_and_IMM1 n1 = i2 →
+ match i2 with
+ [ MODE_DIRn_and_IMM1 n2 ⇒ match n1 with
+ [ o0 ⇒ match n2 with [ o0 ⇒ P → P | _ ⇒ P ] | o1 ⇒ match n2 with [ o1 ⇒ P → P | _ ⇒ P ]
+ | o2 ⇒ match n2 with [ o2 ⇒ P → P | _ ⇒ P ] | o3 ⇒ match n2 with [ o3 ⇒ P → P | _ ⇒ P ]
+ | o4 ⇒ match n2 with [ o4 ⇒ P → P | _ ⇒ P ] | o5 ⇒ match n2 with [ o5 ⇒ P → P | _ ⇒ P ]
+ | o6 ⇒ match n2 with [ o6 ⇒ P → P | _ ⇒ P ] | o7 ⇒ match n2 with [ o7 ⇒ P → P | _ ⇒ P ]]
+ | _ ⇒ P ].
+ #n1; #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_DIRn_and_IMM1 n1 with [ MODE_DIRn_and_IMM1 a ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,33,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_DIRn_and_IMM1 n1 with [ MODE_DIRn_and_IMM1 n1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##32: #n2;
+ ncases n1;
+ ncases n2;
+ nnormalize;
+ ##[ ##1,10,19,28,37,46,55,64: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (oct_destruct ??? (instr_mode_destruct_MODE_DIRn_and_IMM1 ?? H))
+ ##]
+nqed.
+
+nlemma instr_mode_destruct_MODE_TNY : ∀n1,n2.MODE_TNY n1 = MODE_TNY n2 → n1 = n2.
+ #n1; #n2; #H;
+ nchange with (match MODE_TNY n2 with [ MODE_TNY a ⇒ n1 = a | _ ⇒ False ]);
+ nrewrite < H;
+ nnormalize;
+ napply (refl_eq ??).
+nqed.
+
+ndefinition instr_mode_destruct33 :
+ Πn1,i2.ΠP:Prop.MODE_TNY n1 = i2 →
+ match i2 with
+ [ MODE_TNY n2 ⇒ match n1 with
+ [ x0 ⇒ match n2 with [ x0 ⇒ P → P | _ ⇒ P ] | x1 ⇒ match n2 with [ x1 ⇒ P → P | _ ⇒ P ]
+ | x2 ⇒ match n2 with [ x2 ⇒ P → P | _ ⇒ P ] | x3 ⇒ match n2 with [ x3 ⇒ P → P | _ ⇒ P ]
+ | x4 ⇒ match n2 with [ x4 ⇒ P → P | _ ⇒ P ] | x5 ⇒ match n2 with [ x5 ⇒ P → P | _ ⇒ P ]
+ | x6 ⇒ match n2 with [ x6 ⇒ P → P | _ ⇒ P ] | x7 ⇒ match n2 with [ x7 ⇒ P → P | _ ⇒ P ]
+ | x8 ⇒ match n2 with [ x8 ⇒ P → P | _ ⇒ P ] | x9 ⇒ match n2 with [ x9 ⇒ P → P | _ ⇒ P ]
+ | xA ⇒ match n2 with [ xA ⇒ P → P | _ ⇒ P ] | xB ⇒ match n2 with [ xB ⇒ P → P | _ ⇒ P ]
+ | xC ⇒ match n2 with [ xC ⇒ P → P | _ ⇒ P ] | xD ⇒ match n2 with [ xD ⇒ P → P | _ ⇒ P ]
+ | xE ⇒ match n2 with [ xE ⇒ P → P | _ ⇒ P ] | xF ⇒ match n2 with [ xF ⇒ P → P | _ ⇒ P ]]
+ | _ ⇒ P ].
+ #n1; #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_TNY n1 with [ MODE_TNY a ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,34: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_TNY n1 with [ MODE_TNY n1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##33: #n2;
+ ncases n1;
+ ncases n2;
+ nnormalize;
+ ##[ ##1,18,35,52,69,86,103,120,137,154,171,188,205,222,239,256: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (exadecim_destruct ??? (instr_mode_destruct_MODE_TNY ?? H))
+ ##]
+nqed.
+
+nlemma instr_mode_destruct_MODE_SRT : ∀n1,n2.MODE_SRT n1 = MODE_SRT n2 → n1 = n2.
+ #n1; #n2; #H;
+ nchange with (match MODE_SRT n2 with [ MODE_SRT a ⇒ n1 = a | _ ⇒ False ]);
+ nrewrite < H;
+ nnormalize;
+ napply (refl_eq ??).
+nqed.
+
+ndefinition instr_mode_destruct34 :
+ Πn1,i2.ΠP:Prop.MODE_SRT n1 = i2 →
+ match i2 with
+ [ MODE_SRT n2 ⇒ match n1 with
+ [ t00 ⇒ match n2 with [ t00 ⇒ P → P | _ ⇒ P ] | t01 ⇒ match n2 with [ t01 ⇒ P → P | _ ⇒ P ]
+ | t02 ⇒ match n2 with [ t02 ⇒ P → P | _ ⇒ P ] | t03 ⇒ match n2 with [ t03 ⇒ P → P | _ ⇒ P ]
+ | t04 ⇒ match n2 with [ t04 ⇒ P → P | _ ⇒ P ] | t05 ⇒ match n2 with [ t05 ⇒ P → P | _ ⇒ P ]
+ | t06 ⇒ match n2 with [ t06 ⇒ P → P | _ ⇒ P ] | t07 ⇒ match n2 with [ t07 ⇒ P → P | _ ⇒ P ]
+ | t08 ⇒ match n2 with [ t08 ⇒ P → P | _ ⇒ P ] | t09 ⇒ match n2 with [ t09 ⇒ P → P | _ ⇒ P ]
+ | t0A ⇒ match n2 with [ t0A ⇒ P → P | _ ⇒ P ] | t0B ⇒ match n2 with [ t0B ⇒ P → P | _ ⇒ P ]
+ | t0C ⇒ match n2 with [ t0C ⇒ P → P | _ ⇒ P ] | t0D ⇒ match n2 with [ t0D ⇒ P → P | _ ⇒ P ]
+ | t0E ⇒ match n2 with [ t0E ⇒ P → P | _ ⇒ P ] | t0F ⇒ match n2 with [ t0F ⇒ P → P | _ ⇒ P ]
+ | t10 ⇒ match n2 with [ t10 ⇒ P → P | _ ⇒ P ] | t11 ⇒ match n2 with [ t11 ⇒ P → P | _ ⇒ P ]
+ | t12 ⇒ match n2 with [ t12 ⇒ P → P | _ ⇒ P ] | t13 ⇒ match n2 with [ t13 ⇒ P → P | _ ⇒ P ]
+ | t14 ⇒ match n2 with [ t14 ⇒ P → P | _ ⇒ P ] | t15 ⇒ match n2 with [ t15 ⇒ P → P | _ ⇒ P ]
+ | t16 ⇒ match n2 with [ t16 ⇒ P → P | _ ⇒ P ] | t17 ⇒ match n2 with [ t17 ⇒ P → P | _ ⇒ P ]
+ | t18 ⇒ match n2 with [ t18 ⇒ P → P | _ ⇒ P ] | t19 ⇒ match n2 with [ t19 ⇒ P → P | _ ⇒ P ]
+ | t1A ⇒ match n2 with [ t1A ⇒ P → P | _ ⇒ P ] | t1B ⇒ match n2 with [ t1B ⇒ P → P | _ ⇒ P ]
+ | t1C ⇒ match n2 with [ t1C ⇒ P → P | _ ⇒ P ] | t1D ⇒ match n2 with [ t1D ⇒ P → P | _ ⇒ P ]
+ | t1E ⇒ match n2 with [ t1E ⇒ P → P | _ ⇒ P ] | t1F ⇒ match n2 with [ t1F ⇒ P → P | _ ⇒ P ]]
+ | _ ⇒ P ].
+ #n1; #i2; #P;
+ ncases i2;
+ nnormalize;
+ ##[ ##1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30: #H;
+ napply (False_ind ??);
+ nchange with (match MODE_SRT n1 with [ MODE_SRT a ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##31,32,33: #n; #H;
+ napply (False_ind ??);
+ nchange with (match MODE_SRT n1 with [ MODE_SRT n1 ⇒ False | _ ⇒ True ]);
+ nrewrite > H; nnormalize; napply I
+ ##| ##34: #n2;
+ ncases n1;
+ ##[ ##1: ncases n2; nnormalize;
+ ##[ ##1: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##2: ncases n2; nnormalize;
+ ##[ ##2: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##3: ncases n2; nnormalize;
+ ##[ ##3: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##4: ncases n2; nnormalize;
+ ##[ ##4: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##5: ncases n2; nnormalize;
+ ##[ ##5: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##6: ncases n2; nnormalize;
+ ##[ ##6: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##7: ncases n2; nnormalize;
+ ##[ ##7: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##8: ncases n2; nnormalize;
+ ##[ ##8: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##9: ncases n2; nnormalize;
+ ##[ ##9: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##10: ncases n2; nnormalize;
+ ##[ ##10: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##11: ncases n2; nnormalize;
+ ##[ ##11: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##12: ncases n2; nnormalize;
+ ##[ ##12: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##13: ncases n2; nnormalize;
+ ##[ ##13: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##14: ncases n2; nnormalize;
+ ##[ ##14: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##15: ncases n2; nnormalize;
+ ##[ ##15: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##16: ncases n2; nnormalize;
+ ##[ ##16: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##17: ncases n2; nnormalize;
+ ##[ ##17: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##18: ncases n2; nnormalize;
+ ##[ ##18: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##19: ncases n2; nnormalize;
+ ##[ ##19: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##20: ncases n2; nnormalize;
+ ##[ ##20: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##21: ncases n2; nnormalize;
+ ##[ ##21: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##22: ncases n2; nnormalize;
+ ##[ ##22: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##23: ncases n2; nnormalize;
+ ##[ ##23: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##24: ncases n2; nnormalize;
+ ##[ ##24: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##25: ncases n2; nnormalize;
+ ##[ ##25: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##26: ncases n2; nnormalize;
+ ##[ ##26: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##27: ncases n2; nnormalize;
+ ##[ ##27: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##28: ncases n2; nnormalize;
+ ##[ ##28: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##29: ncases n2; nnormalize;
+ ##[ ##29: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##30: ncases n2; nnormalize;
+ ##[ ##30: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##31: ncases n2; nnormalize;
+ ##[ ##31: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##| ##32: ncases n2; nnormalize;
+ ##[ ##32: #H; napply (λx:P.x)
+ ##| ##*: #H; napply (bitrigesim_destruct ??? (instr_mode_destruct_MODE_SRT ?? H))
+ ##]
+ ##]
+ ##]
+nqed.
+
+ndefinition instr_mode_destruct_aux ≝
+Πi1,i2.ΠP:Prop.i1 = i2 →
+ match i1 with
+ [ MODE_INH ⇒ match i2 with [ MODE_INH ⇒ P → P | _ ⇒ P ]
+ | MODE_INHA ⇒ match i2 with [ MODE_INHA ⇒ P → P | _ ⇒ P ]
+ | MODE_INHX ⇒ match i2 with [ MODE_INHX ⇒ P → P | _ ⇒ P ]
+ | MODE_INHH ⇒ match i2 with [ MODE_INHH ⇒ P → P | _ ⇒ P ]
+ | MODE_INHX0ADD ⇒ match i2 with [ MODE_INHX0ADD ⇒ P → P | _ ⇒ P ]
+ | MODE_INHX1ADD ⇒ match i2 with [ MODE_INHX1ADD ⇒ P → P | _ ⇒ P ]
+ | MODE_INHX2ADD ⇒ match i2 with [ MODE_INHX2ADD ⇒ P → P | _ ⇒ P ]
+ | MODE_IMM1 ⇒ match i2 with [ MODE_IMM1 ⇒ P → P | _ ⇒ P ]
+ | MODE_IMM1EXT ⇒ match i2 with [ MODE_IMM1EXT ⇒ P → P | _ ⇒ P ]
+ | MODE_IMM2 ⇒ match i2 with [ MODE_IMM2 ⇒ P → P | _ ⇒ P ]
+ | MODE_DIR1 ⇒ match i2 with [ MODE_DIR1 ⇒ P → P | _ ⇒ P ]
+ | MODE_DIR2 ⇒ match i2 with [ MODE_DIR2 ⇒ P → P | _ ⇒ P ]
+ | MODE_IX0 ⇒ match i2 with [ MODE_IX0 ⇒ P → P | _ ⇒ P ]
+ | MODE_IX1 ⇒ match i2 with [ MODE_IX1 ⇒ P → P | _ ⇒ P ]
+ | MODE_IX2 ⇒ match i2 with [ MODE_IX2 ⇒ P → P | _ ⇒ P ]
+ | MODE_SP1 ⇒ match i2 with [ MODE_SP1 ⇒ P → P | _ ⇒ P ]
+ | MODE_SP2 ⇒ match i2 with [ MODE_SP2 ⇒ P → P | _ ⇒ P ]
+ | MODE_DIR1_to_DIR1 ⇒ match i2 with [ MODE_DIR1_to_DIR1 ⇒ P → P | _ ⇒ P ]
+ | MODE_IMM1_to_DIR1 ⇒ match i2 with [ MODE_IMM1_to_DIR1 ⇒ P → P | _ ⇒ P ]
+ | MODE_IX0p_to_DIR1 ⇒ match i2 with [ MODE_IX0p_to_DIR1 ⇒ P → P | _ ⇒ P ]
+ | MODE_DIR1_to_IX0p ⇒ match i2 with [ MODE_DIR1_to_IX0p ⇒ P → P | _ ⇒ P ]
+ | MODE_INHA_and_IMM1 ⇒ match i2 with [ MODE_INHA_and_IMM1 ⇒ P → P | _ ⇒ P ]
+ | MODE_INHX_and_IMM1 ⇒ match i2 with [ MODE_INHX_and_IMM1 ⇒ P → P | _ ⇒ P ]
+ | MODE_IMM1_and_IMM1 ⇒ match i2 with [ MODE_IMM1_and_IMM1 ⇒ P → P | _ ⇒ P ]
+ | MODE_DIR1_and_IMM1 ⇒ match i2 with [ MODE_DIR1_and_IMM1 ⇒ P → P | _ ⇒ P ]
+ | MODE_IX0_and_IMM1 ⇒ match i2 with [ MODE_IX0_and_IMM1 ⇒ P → P | _ ⇒ P ]
+ | MODE_IX0p_and_IMM1 ⇒ match i2 with [ MODE_IX0p_and_IMM1 ⇒ P → P | _ ⇒ P ]
+ | MODE_IX1_and_IMM1 ⇒ match i2 with [ MODE_IX1_and_IMM1 ⇒ P → P | _ ⇒ P ]
+ | MODE_IX1p_and_IMM1 ⇒ match i2 with [ MODE_IX1p_and_IMM1 ⇒ P → P | _ ⇒ P ]
+ | MODE_SP1_and_IMM1 ⇒ match i2 with [ MODE_SP1_and_IMM1 ⇒ P → P | _ ⇒ P ]
+ | MODE_DIRn n1 ⇒ match i2 with
+ [ MODE_DIRn n2 ⇒ match n1 with
+ [ o0 ⇒ match n2 with [ o0 ⇒ P → P | _ ⇒ P ] | o1 ⇒ match n2 with [ o1 ⇒ P → P | _ ⇒ P ]
+ | o2 ⇒ match n2 with [ o2 ⇒ P → P | _ ⇒ P ] | o3 ⇒ match n2 with [ o3 ⇒ P → P | _ ⇒ P ]
+ | o4 ⇒ match n2 with [ o4 ⇒ P → P | _ ⇒ P ] | o5 ⇒ match n2 with [ o5 ⇒ P → P | _ ⇒ P ]
+ | o6 ⇒ match n2 with [ o6 ⇒ P → P | _ ⇒ P ] | o7 ⇒ match n2 with [ o7 ⇒ P → P | _ ⇒ P ]]
+ | _ ⇒ P ]
+ | MODE_DIRn_and_IMM1 n1 ⇒ match i2 with
+ [ MODE_DIRn_and_IMM1 n2 ⇒ match n1 with
+ [ o0 ⇒ match n2 with [ o0 ⇒ P → P | _ ⇒ P ] | o1 ⇒ match n2 with [ o1 ⇒ P → P | _ ⇒ P ]
+ | o2 ⇒ match n2 with [ o2 ⇒ P → P | _ ⇒ P ] | o3 ⇒ match n2 with [ o3 ⇒ P → P | _ ⇒ P ]
+ | o4 ⇒ match n2 with [ o4 ⇒ P → P | _ ⇒ P ] | o5 ⇒ match n2 with [ o5 ⇒ P → P | _ ⇒ P ]
+ | o6 ⇒ match n2 with [ o6 ⇒ P → P | _ ⇒ P ] | o7 ⇒ match n2 with [ o7 ⇒ P → P | _ ⇒ P ]]
+ | _ ⇒ P ]
+ | MODE_TNY e1 ⇒ match i2 with
+ [ MODE_TNY e2 ⇒ match e1 with
+ [ x0 ⇒ match e2 with [ x0 ⇒ P → P | _ ⇒ P ] | x1 ⇒ match e2 with [ x1 ⇒ P → P | _ ⇒ P ]
+ | x2 ⇒ match e2 with [ x2 ⇒ P → P | _ ⇒ P ] | x3 ⇒ match e2 with [ x3 ⇒ P → P | _ ⇒ P ]
+ | x4 ⇒ match e2 with [ x4 ⇒ P → P | _ ⇒ P ] | x5 ⇒ match e2 with [ x5 ⇒ P → P | _ ⇒ P ]
+ | x6 ⇒ match e2 with [ x6 ⇒ P → P | _ ⇒ P ] | x7 ⇒ match e2 with [ x7 ⇒ P → P | _ ⇒ P ]
+ | x8 ⇒ match e2 with [ x8 ⇒ P → P | _ ⇒ P ] | x9 ⇒ match e2 with [ x9 ⇒ P → P | _ ⇒ P ]
+ | xA ⇒ match e2 with [ xA ⇒ P → P | _ ⇒ P ] | xB ⇒ match e2 with [ xB ⇒ P → P | _ ⇒ P ]
+ | xC ⇒ match e2 with [ xC ⇒ P → P | _ ⇒ P ] | xD ⇒ match e2 with [ xD ⇒ P → P | _ ⇒ P ]
+ | xE ⇒ match e2 with [ xE ⇒ P → P | _ ⇒ P ] | xF ⇒ match e2 with [ xF ⇒ P → P | _ ⇒ P ]]
+ | _ ⇒ P ]
+ | MODE_SRT t1 ⇒ match i2 with
+ [ MODE_SRT t2 ⇒ match t1 with
+ [ t00 ⇒ match t2 with [ t00 ⇒ P → P | _ ⇒ P ] | t01 ⇒ match t2 with [ t01 ⇒ P → P | _ ⇒ P ]
+ | t02 ⇒ match t2 with [ t02 ⇒ P → P | _ ⇒ P ] | t03 ⇒ match t2 with [ t03 ⇒ P → P | _ ⇒ P ]
+ | t04 ⇒ match t2 with [ t04 ⇒ P → P | _ ⇒ P ] | t05 ⇒ match t2 with [ t05 ⇒ P → P | _ ⇒ P ]
+ | t06 ⇒ match t2 with [ t06 ⇒ P → P | _ ⇒ P ] | t07 ⇒ match t2 with [ t07 ⇒ P → P | _ ⇒ P ]
+ | t08 ⇒ match t2 with [ t08 ⇒ P → P | _ ⇒ P ] | t09 ⇒ match t2 with [ t09 ⇒ P → P | _ ⇒ P ]
+ | t0A ⇒ match t2 with [ t0A ⇒ P → P | _ ⇒ P ] | t0B ⇒ match t2 with [ t0B ⇒ P → P | _ ⇒ P ]
+ | t0C ⇒ match t2 with [ t0C ⇒ P → P | _ ⇒ P ] | t0D ⇒ match t2 with [ t0D ⇒ P → P | _ ⇒ P ]
+ | t0E ⇒ match t2 with [ t0E ⇒ P → P | _ ⇒ P ] | t0F ⇒ match t2 with [ t0F ⇒ P → P | _ ⇒ P ]
+ | t10 ⇒ match t2 with [ t10 ⇒ P → P | _ ⇒ P ] | t11 ⇒ match t2 with [ t11 ⇒ P → P | _ ⇒ P ]
+ | t12 ⇒ match t2 with [ t12 ⇒ P → P | _ ⇒ P ] | t13 ⇒ match t2 with [ t13 ⇒ P → P | _ ⇒ P ]
+ | t14 ⇒ match t2 with [ t14 ⇒ P → P | _ ⇒ P ] | t15 ⇒ match t2 with [ t15 ⇒ P → P | _ ⇒ P ]
+ | t16 ⇒ match t2 with [ t16 ⇒ P → P | _ ⇒ P ] | t17 ⇒ match t2 with [ t17 ⇒ P → P | _ ⇒ P ]
+ | t18 ⇒ match t2 with [ t18 ⇒ P → P | _ ⇒ P ] | t19 ⇒ match t2 with [ t19 ⇒ P → P | _ ⇒ P ]
+ | t1A ⇒ match t2 with [ t1A ⇒ P → P | _ ⇒ P ] | t1B ⇒ match t2 with [ t1B ⇒ P → P | _ ⇒ P ]
+ | t1C ⇒ match t2 with [ t1C ⇒ P → P | _ ⇒ P ] | t1D ⇒ match t2 with [ t1D ⇒ P → P | _ ⇒ P ]
+ | t1E ⇒ match t2 with [ t1E ⇒ P → P | _ ⇒ P ] | t1F ⇒ match t2 with [ t1F ⇒ P → P | _ ⇒ P ]]
+ | _ ⇒ P ]
+ ].
+
+ndefinition instr_mode_destruct : instr_mode_destruct_aux.
+ #t1; ncases t1;
+ ##[ ##1: napply instr_mode_destruct1 ##| ##2: napply instr_mode_destruct2
+ ##| ##3: napply instr_mode_destruct3 ##| ##4: napply instr_mode_destruct4
+ ##| ##5: napply instr_mode_destruct5 ##| ##6: napply instr_mode_destruct6
+ ##| ##7: napply instr_mode_destruct7 ##| ##8: napply instr_mode_destruct8
+ ##| ##9: napply instr_mode_destruct9 ##| ##10: napply instr_mode_destruct10
+ ##| ##11: napply instr_mode_destruct11 ##| ##12: napply instr_mode_destruct12
+ ##| ##13: napply instr_mode_destruct13 ##| ##14: napply instr_mode_destruct14
+ ##| ##15: napply instr_mode_destruct15 ##| ##16: napply instr_mode_destruct16
+ ##| ##17: napply instr_mode_destruct17 ##| ##18: napply instr_mode_destruct18
+ ##| ##19: napply instr_mode_destruct19 ##| ##20: napply instr_mode_destruct20
+ ##| ##21: napply instr_mode_destruct21 ##| ##22: napply instr_mode_destruct22
+ ##| ##23: napply instr_mode_destruct23 ##| ##24: napply instr_mode_destruct24
+ ##| ##25: napply instr_mode_destruct25 ##| ##26: napply instr_mode_destruct26
+ ##| ##27: napply instr_mode_destruct27 ##| ##28: napply instr_mode_destruct28
+ ##| ##29: napply instr_mode_destruct29 ##| ##30: napply instr_mode_destruct30
+ ##| ##31: napply instr_mode_destruct31 ##| ##32: napply instr_mode_destruct32
+ ##| ##33: napply instr_mode_destruct33 ##| ##34: napply instr_mode_destruct34
+ ##]
+nqed.