--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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/opcode_base_lemmas_instrmode1.ma".
+
+(* ********************************************** *)
+(* MATTONI BASE PER DEFINIRE LE TABELLE DELLE MCU *)
+(* ********************************************** *)
+
+nlemma symmetric_eqinstrmode : symmetricT instr_mode bool eq_instrmode.
+ #i1; #i2;
+ ncases i1;
+ ##[ ##1: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##2: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##3: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##4: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##5: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##6: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##7: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##8: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##9: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##10: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##11: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##12: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##13: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##14: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##15: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##16: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##17: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##18: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##19: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##20: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##21: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##22: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##23: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##24: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##25: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##26: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##27: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##28: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##29: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##30: ncases i2; nnormalize; ##[ ##31,32,33,34: #n ##] napply (refl_eq ??)
+ ##| ##31: ncases i2; #n1;
+ ##[ ##31: #n2;
+ nchange with (eq_oct n2 n1 = eq_oct n1 n2);
+ nrewrite > (symmetric_eqoct n1 n2);
+ ##| ##32,33,34: #n2; nnormalize
+ ##]
+ nnormalize; napply (refl_eq ??)
+ ##| ##32: ncases i2; #n1;
+ ##[ ##32: #n2;
+ nchange with (eq_oct n2 n1 = eq_oct n1 n2);
+ nrewrite > (symmetric_eqoct n1 n2);
+ ##| ##31,33,34: #n2; nnormalize
+ ##]
+ nnormalize; napply (refl_eq ??)
+ ##| ##33: ncases i2; #n1;
+ ##[ ##33: #n2;
+ nchange with (eq_ex n2 n1 = eq_ex n1 n2);
+ nrewrite > (symmetric_eqex n1 n2);
+ ##| ##31,32,34: #n2; nnormalize
+ ##]
+ nnormalize; napply (refl_eq ??)
+ ##| ##34: ncases i2; #n1;
+ ##[ ##34: #n2;
+ nchange with (eq_bitrig n2 n1 = eq_bitrig n1 n2);
+ nrewrite > (symmetric_eqbitrig n1 n2);
+ ##| ##31,32,33: #n2; nnormalize
+ ##]
+ nnormalize; napply (refl_eq ??)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq1 : ∀i2.eq_instrmode MODE_INH i2 = true → MODE_INH = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##1: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq2 : ∀i2.eq_instrmode MODE_INHA i2 = true → MODE_INHA = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##2: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq3 : ∀i2.eq_instrmode MODE_INHX i2 = true → MODE_INHX = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##3: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq4 : ∀i2.eq_instrmode MODE_INHH i2 = true → MODE_INHH = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##4: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq5 : ∀i2.eq_instrmode MODE_INHX0ADD i2 = true → MODE_INHX0ADD = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##5: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq6 : ∀i2.eq_instrmode MODE_INHX1ADD i2 = true → MODE_INHX1ADD = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##6: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq7 : ∀i2.eq_instrmode MODE_INHX2ADD i2 = true → MODE_INHX2ADD = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##7: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq8 : ∀i2.eq_instrmode MODE_IMM1 i2 = true → MODE_IMM1 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##8: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq9 : ∀i2.eq_instrmode MODE_IMM1EXT i2 = true → MODE_IMM1EXT = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##9: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq10 : ∀i2.eq_instrmode MODE_IMM2 i2 = true → MODE_IMM2 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##10: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq11 : ∀i2.eq_instrmode MODE_DIR1 i2 = true → MODE_DIR1 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##11: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq12 : ∀i2.eq_instrmode MODE_DIR2 i2 = true → MODE_DIR2 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##12: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq13 : ∀i2.eq_instrmode MODE_IX0 i2 = true → MODE_IX0 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##13: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq14 : ∀i2.eq_instrmode MODE_IX1 i2 = true → MODE_IX1 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##14: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq15 : ∀i2.eq_instrmode MODE_IX2 i2 = true → MODE_IX2 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##15: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq16 : ∀i2.eq_instrmode MODE_SP1 i2 = true → MODE_SP1 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##16: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq17 : ∀i2.eq_instrmode MODE_SP2 i2 = true → MODE_SP2 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##17: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq18 : ∀i2.eq_instrmode MODE_DIR1_to_DIR1 i2 = true → MODE_DIR1_to_DIR1 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##18: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq19 : ∀i2.eq_instrmode MODE_IMM1_to_DIR1 i2 = true → MODE_IMM1_to_DIR1 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##19: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq20 : ∀i2.eq_instrmode MODE_IX0p_to_DIR1 i2 = true → MODE_IX0p_to_DIR1 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##20: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq21 : ∀i2.eq_instrmode MODE_DIR1_to_IX0p i2 = true → MODE_DIR1_to_IX0p = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##21: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq22 : ∀i2.eq_instrmode MODE_INHA_and_IMM1 i2 = true → MODE_INHA_and_IMM1 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##22: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq23 : ∀i2.eq_instrmode MODE_INHX_and_IMM1 i2 = true → MODE_INHX_and_IMM1 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##23: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq24 : ∀i2.eq_instrmode MODE_IMM1_and_IMM1 i2 = true → MODE_IMM1_and_IMM1 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##24: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq25 : ∀i2.eq_instrmode MODE_DIR1_and_IMM1 i2 = true → MODE_DIR1_and_IMM1 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##25: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq26 : ∀i2.eq_instrmode MODE_IX0_and_IMM1 i2 = true → MODE_IX0_and_IMM1 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##26: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq27 : ∀i2.eq_instrmode MODE_IX0p_and_IMM1 i2 = true → MODE_IX0p_and_IMM1 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##27: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq28 : ∀i2.eq_instrmode MODE_IX1_and_IMM1 i2 = true → MODE_IX1_and_IMM1 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##28: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq29 : ∀i2.eq_instrmode MODE_IX1p_and_IMM1 i2 = true → MODE_IX1p_and_IMM1 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##29: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq30 : ∀i2.eq_instrmode MODE_SP1_and_IMM1 i2 = true → MODE_SP1_and_IMM1 = i2.
+ #i2; ncases i2; nnormalize;
+ ##[ ##30: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (bool_destruct ??? H)
+ ##| ##*: #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq31 : ∀n1,i2.eq_instrmode (MODE_DIRn n1) i2 = true → MODE_DIRn n1 = i2.
+ #n1; #i2; ncases i2;
+ ##[ ##31: #n2; #H;
+ nchange in H:(%) with (eq_oct n1 n2 = true);
+ nrewrite > (eqoct_to_eq ?? H);
+ napply (refl_eq ??)
+ ##| ##32,33,34: nnormalize; #n2; #H; napply (bool_destruct ??? H)
+ ##| ##*: nnormalize; #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq32 : ∀n1,i2.eq_instrmode (MODE_DIRn_and_IMM1 n1) i2 = true → MODE_DIRn_and_IMM1 n1 = i2.
+ #n1; #i2; ncases i2;
+ ##[ ##32: #n2; #H;
+ nchange in H:(%) with (eq_oct n1 n2 = true);
+ nrewrite > (eqoct_to_eq ?? H);
+ napply (refl_eq ??)
+ ##| ##31,33,34: nnormalize; #n2; #H; napply (bool_destruct ??? H)
+ ##| ##*: nnormalize; #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq33 : ∀n1,i2.eq_instrmode (MODE_TNY n1) i2 = true → MODE_TNY n1 = i2.
+ #n1; #i2; ncases i2;
+ ##[ ##33: #n2; #H;
+ nchange in H:(%) with (eq_ex n1 n2 = true);
+ nrewrite > (eqex_to_eq ?? H);
+ napply (refl_eq ??)
+ ##| ##31,32,34: nnormalize; #n2; #H; napply (bool_destruct ??? H)
+ ##| ##*: nnormalize; #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq34 : ∀n1,i2.eq_instrmode (MODE_SRT n1) i2 = true → MODE_SRT n1 = i2.
+ #n1; #i2; ncases i2;
+ ##[ ##34: #n2; #H;
+ nchange in H:(%) with (eq_bitrig n1 n2 = true);
+ nrewrite > (eqbitrig_to_eq ?? H);
+ napply (refl_eq ??)
+ ##| ##31,32,33: nnormalize; #n2; #H; napply (bool_destruct ??? H)
+ ##| ##*: nnormalize; #H; napply (bool_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eqinstrmode_to_eq : ∀i1,i2.eq_instrmode i1 i2 = true → i1 = i2.
+ #i1; ncases i1;
+ ##[ ##1: napply eqinstrmode_to_eq1 ##| ##2: napply eqinstrmode_to_eq2
+ ##| ##3: napply eqinstrmode_to_eq3 ##| ##4: napply eqinstrmode_to_eq4
+ ##| ##5: napply eqinstrmode_to_eq5 ##| ##6: napply eqinstrmode_to_eq6
+ ##| ##7: napply eqinstrmode_to_eq7 ##| ##8: napply eqinstrmode_to_eq8
+ ##| ##9: napply eqinstrmode_to_eq9 ##| ##10: napply eqinstrmode_to_eq10
+ ##| ##11: napply eqinstrmode_to_eq11 ##| ##12: napply eqinstrmode_to_eq12
+ ##| ##13: napply eqinstrmode_to_eq13 ##| ##14: napply eqinstrmode_to_eq14
+ ##| ##15: napply eqinstrmode_to_eq15 ##| ##16: napply eqinstrmode_to_eq16
+ ##| ##17: napply eqinstrmode_to_eq17 ##| ##18: napply eqinstrmode_to_eq18
+ ##| ##19: napply eqinstrmode_to_eq19 ##| ##20: napply eqinstrmode_to_eq20
+ ##| ##21: napply eqinstrmode_to_eq21 ##| ##22: napply eqinstrmode_to_eq22
+ ##| ##23: napply eqinstrmode_to_eq23 ##| ##24: napply eqinstrmode_to_eq24
+ ##| ##25: napply eqinstrmode_to_eq25 ##| ##26: napply eqinstrmode_to_eq26
+ ##| ##27: napply eqinstrmode_to_eq27 ##| ##28: napply eqinstrmode_to_eq28
+ ##| ##29: napply eqinstrmode_to_eq29 ##| ##30: napply eqinstrmode_to_eq30
+ ##| ##31: napply eqinstrmode_to_eq31 ##| ##32: napply eqinstrmode_to_eq32
+ ##| ##33: napply eqinstrmode_to_eq33 ##| ##34: napply eqinstrmode_to_eq34
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode1 : ∀i2.MODE_INH = i2 → eq_instrmode MODE_INH i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##1: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode2 : ∀i2.MODE_INHA = i2 → eq_instrmode MODE_INHA i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##2: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode3 : ∀i2.MODE_INHX = i2 → eq_instrmode MODE_INHX i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##3: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode4 : ∀i2.MODE_INHH = i2 → eq_instrmode MODE_INHH i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##4: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode5 : ∀i2.MODE_INHX0ADD = i2 → eq_instrmode MODE_INHX0ADD i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##5: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode6 : ∀i2.MODE_INHX1ADD = i2 → eq_instrmode MODE_INHX1ADD i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##6: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode7 : ∀i2.MODE_INHX2ADD = i2 → eq_instrmode MODE_INHX2ADD i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##7: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode8 : ∀i2.MODE_IMM1 = i2 → eq_instrmode MODE_IMM1 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##8: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode9 : ∀i2.MODE_IMM1EXT = i2 → eq_instrmode MODE_IMM1EXT i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##9: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode10 : ∀i2.MODE_IMM2 = i2 → eq_instrmode MODE_IMM2 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##10: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode11 : ∀i2.MODE_DIR1 = i2 → eq_instrmode MODE_DIR1 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##11: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode12 : ∀i2.MODE_DIR2 = i2 → eq_instrmode MODE_DIR2 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##12: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode13 : ∀i2.MODE_IX0 = i2 → eq_instrmode MODE_IX0 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##13: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode14 : ∀i2.MODE_IX1 = i2 → eq_instrmode MODE_IX1 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##14: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode15 : ∀i2.MODE_IX2 = i2 → eq_instrmode MODE_IX2 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##15: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode16 : ∀i2.MODE_SP1 = i2 → eq_instrmode MODE_SP1 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##16: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode17 : ∀i2.MODE_SP2 = i2 → eq_instrmode MODE_SP2 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##17: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode18 : ∀i2.MODE_DIR1_to_DIR1 = i2 → eq_instrmode MODE_DIR1_to_DIR1 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##18: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode19 : ∀i2.MODE_IMM1_to_DIR1 = i2 → eq_instrmode MODE_IMM1_to_DIR1 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##19: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode20 : ∀i2.MODE_IX0p_to_DIR1 = i2 → eq_instrmode MODE_IX0p_to_DIR1 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##20: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode21 : ∀i2.MODE_DIR1_to_IX0p = i2 → eq_instrmode MODE_DIR1_to_IX0p i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##21: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode22 : ∀i2.MODE_INHA_and_IMM1 = i2 → eq_instrmode MODE_INHA_and_IMM1 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##22: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode23 : ∀i2.MODE_INHX_and_IMM1 = i2 → eq_instrmode MODE_INHX_and_IMM1 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##23: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode24 : ∀i2.MODE_IMM1_and_IMM1 = i2 → eq_instrmode MODE_IMM1_and_IMM1 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##24: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode25 : ∀i2.MODE_DIR1_and_IMM1 = i2 → eq_instrmode MODE_DIR1_and_IMM1 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##25: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode26 : ∀i2.MODE_IX0_and_IMM1 = i2 → eq_instrmode MODE_IX0_and_IMM1 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##26: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode27 : ∀i2.MODE_IX0p_and_IMM1 = i2 → eq_instrmode MODE_IX0p_and_IMM1 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##27: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode28 : ∀i2.MODE_IX1_and_IMM1 = i2 → eq_instrmode MODE_IX1_and_IMM1 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##28: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode29 : ∀i2.MODE_IX1p_and_IMM1 = i2 → eq_instrmode MODE_IX1p_and_IMM1 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##29: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode30 : ∀i2.MODE_SP1_and_IMM1 = i2 → eq_instrmode MODE_SP1_and_IMM1 i2 = true.
+ #t2; ncases t2; nnormalize;
+ ##[ ##30: #H; napply (refl_eq ??)
+ ##| ##31,32,33,34: #n; #H; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode31 : ∀n1,i2.MODE_DIRn n1 = i2 → eq_instrmode (MODE_DIRn n1) i2 = true.
+ #n1; #t2; ncases t2;
+ ##[ ##31: #n2; #H;
+ nchange with (eq_oct n1 n2 = true);
+ nrewrite > (instr_mode_destruct_MODE_DIRn ?? H);
+ nrewrite > (eq_to_eqoct n2 n2 (refl_eq ??));
+ napply (refl_eq ??)
+ ##| ##32,33,34: #n; #H; nnormalize; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; nnormalize; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode32 : ∀n1,i2.MODE_DIRn_and_IMM1 n1 = i2 → eq_instrmode (MODE_DIRn_and_IMM1 n1) i2 = true.
+ #n1; #t2; ncases t2;
+ ##[ ##32: #n2; #H;
+ nchange with (eq_oct n1 n2 = true);
+ nrewrite > (instr_mode_destruct_MODE_DIRn_and_IMM1 ?? H);
+ nrewrite > (eq_to_eqoct n2 n2 (refl_eq ??));
+ napply (refl_eq ??)
+ ##| ##31,33,34: #n; #H; nnormalize; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; nnormalize; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode33 : ∀n1,i2.MODE_TNY n1 = i2 → eq_instrmode (MODE_TNY n1) i2 = true.
+ #n1; #t2; ncases t2;
+ ##[ ##33: #n2; #H;
+ nchange with (eq_ex n1 n2 = true);
+ nrewrite > (instr_mode_destruct_MODE_TNY ?? H);
+ nrewrite > (eq_to_eqex n2 n2 (refl_eq ??));
+ napply (refl_eq ??)
+ ##| ##31,32,34: #n; #H; nnormalize; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; nnormalize; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode34 : ∀n1,i2.MODE_SRT n1 = i2 → eq_instrmode (MODE_SRT n1) i2 = true.
+ #n1; #t2; ncases t2;
+ ##[ ##34: #n2; #H;
+ nchange with (eq_bitrig n1 n2 = true);
+ nrewrite > (instr_mode_destruct_MODE_SRT ?? H);
+ nrewrite > (eq_to_eqbitrig n2 n2 (refl_eq ??));
+ napply (refl_eq ??)
+ ##| ##31,32,33: #n; #H; nnormalize; napply (instr_mode_destruct ??? H)
+ ##| ##*: #H; nnormalize; napply (instr_mode_destruct ??? H)
+ ##]
+nqed.
+
+nlemma eq_to_eqinstrmode : ∀i1,i2.i1 = i2 → eq_instrmode i1 i2 = true.
+ #i1; ncases i1;
+ ##[ ##1: napply eq_to_eqinstrmode1 ##| ##2: napply eq_to_eqinstrmode2
+ ##| ##3: napply eq_to_eqinstrmode3 ##| ##4: napply eq_to_eqinstrmode4
+ ##| ##5: napply eq_to_eqinstrmode5 ##| ##6: napply eq_to_eqinstrmode6
+ ##| ##7: napply eq_to_eqinstrmode7 ##| ##8: napply eq_to_eqinstrmode8
+ ##| ##9: napply eq_to_eqinstrmode9 ##| ##10: napply eq_to_eqinstrmode10
+ ##| ##11: napply eq_to_eqinstrmode11 ##| ##12: napply eq_to_eqinstrmode12
+ ##| ##13: napply eq_to_eqinstrmode13 ##| ##14: napply eq_to_eqinstrmode14
+ ##| ##15: napply eq_to_eqinstrmode15 ##| ##16: napply eq_to_eqinstrmode16
+ ##| ##17: napply eq_to_eqinstrmode17 ##| ##18: napply eq_to_eqinstrmode18
+ ##| ##19: napply eq_to_eqinstrmode19 ##| ##20: napply eq_to_eqinstrmode20
+ ##| ##21: napply eq_to_eqinstrmode21 ##| ##22: napply eq_to_eqinstrmode22
+ ##| ##23: napply eq_to_eqinstrmode23 ##| ##24: napply eq_to_eqinstrmode24
+ ##| ##25: napply eq_to_eqinstrmode25 ##| ##26: napply eq_to_eqinstrmode26
+ ##| ##27: napply eq_to_eqinstrmode27 ##| ##28: napply eq_to_eqinstrmode28
+ ##| ##29: napply eq_to_eqinstrmode29 ##| ##30: napply eq_to_eqinstrmode30
+ ##| ##31: napply eq_to_eqinstrmode31 ##| ##32: napply eq_to_eqinstrmode32
+ ##| ##33: napply eq_to_eqinstrmode33 ##| ##34: napply eq_to_eqinstrmode34
+ ##]
+nqed.
projects / helm.git / blobdiff