--- /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: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Ultima modifica: 05/08/2009 *)
+(* *)
+(* ********************************************************************** *)
+
+include "num/oct_lemmas.ma".
+include "num/bitrigesim_lemmas.ma".
+include "num/exadecim_lemmas.ma".
+include "freescale/opcode_base.ma".
+
+(* ********************************************** *)
+(* MATTONI BASE PER DEFINIRE LE TABELLE DELLE MCU *)
+(* ********************************************** *)
+
+nlemma instrmode_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.
+
+nlemma instrmode_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.
+
+nlemma instrmode_destruct_MODE_TNY : ∀e1,e2.MODE_TNY e1 = MODE_TNY e2 → e1 = e2.
+ #e1; #e2; #H;
+ nchange with (match MODE_TNY e2 with [ MODE_TNY a ⇒ e1 = a | _ ⇒ False ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma instrmode_destruct_MODE_SRT : ∀t1,t2.MODE_SRT t1 = MODE_SRT t2 → t1 = t2.
+ #t1; #t2; #H;
+ nchange with (match MODE_SRT t2 with [ MODE_SRT a ⇒ t1 = a | _ ⇒ False ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+ndefinition instrmode_destruct_aux ≝
+Πi1,i2.ΠP:Prop.i1 = i2 →
+ match eq_im i1 i2 with [ true ⇒ P → P | false ⇒ P ].
+
+ndefinition instrmode_destruct : instrmode_destruct_aux.
+ #t1; #t2; #P; #H;
+ nrewrite < H;
+ nelim t1;
+ nnormalize;
+ ##[ ##31,32,33,34: #sub; nelim sub; nnormalize ##]
+ napply (λx.x).
+nqed.
+
+nlemma eq_to_eqim : ∀n1,n2.n1 = n2 → eq_im n1 n2 = true.
+ #n1; #n2; #H;
+ nrewrite > H;
+ nelim n2;
+ ##[ ##31,32: #n; nchange with (eq_oct n n = true); napply (eq_to_eqoct n n (refl_eq …))
+ ##| ##33: #n; nchange with (eq_ex n n = true); napply (eq_to_eqex n n (refl_eq …))
+ ##| ##34: #n; nchange with (eq_bit n n = true); napply (eq_to_eqbit n n (refl_eq …))
+ ##| ##*: nnormalize; napply refl_eq
+ ##]
+nqed.
+
+nlemma neqim_to_neq : ∀n1,n2.eq_im n1 n2 = false → n1 ≠ n2.
+ #n1; #n2; #H;
+ napply (not_to_not (n1 = n2) (eq_im n1 n2 = true) …);
+ ##[ ##1: napply (eq_to_eqim n1 n2)
+ ##| ##2: napply (eqfalse_to_neqtrue … H)
+ ##]
+nqed.
+
+nlemma eqim_to_eq1 : ∀i2.eq_im 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 eqim_to_eq2 : ∀i2.eq_im 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 eqim_to_eq3 : ∀i2.eq_im 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 eqim_to_eq4 : ∀i2.eq_im 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 eqim_to_eq5 : ∀i2.eq_im 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 eqim_to_eq6 : ∀i2.eq_im 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 eqim_to_eq7 : ∀i2.eq_im 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 eqim_to_eq8 : ∀i2.eq_im 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 eqim_to_eq9 : ∀i2.eq_im 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 eqim_to_eq10 : ∀i2.eq_im 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 eqim_to_eq11 : ∀i2.eq_im 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 eqim_to_eq12 : ∀i2.eq_im 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 eqim_to_eq13 : ∀i2.eq_im 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 eqim_to_eq14 : ∀i2.eq_im 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 eqim_to_eq15 : ∀i2.eq_im 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 eqim_to_eq16 : ∀i2.eq_im 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 eqim_to_eq17 : ∀i2.eq_im 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 eqim_to_eq18 : ∀i2.eq_im 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 eqim_to_eq19 : ∀i2.eq_im 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 eqim_to_eq20 : ∀i2.eq_im 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 eqim_to_eq21 : ∀i2.eq_im 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 eqim_to_eq22 : ∀i2.eq_im 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 eqim_to_eq23 : ∀i2.eq_im 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 eqim_to_eq24 : ∀i2.eq_im 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 eqim_to_eq25 : ∀i2.eq_im 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 eqim_to_eq26 : ∀i2.eq_im 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 eqim_to_eq27 : ∀i2.eq_im 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 eqim_to_eq28 : ∀i2.eq_im 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 eqim_to_eq29 : ∀i2.eq_im 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 eqim_to_eq30 : ∀i2.eq_im 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 eqim_to_eq31 : ∀n1,i2.eq_im (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 eqim_to_eq32 : ∀n1,i2.eq_im (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 eqim_to_eq33 : ∀n1,i2.eq_im (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 eqim_to_eq34 : ∀n1,i2.eq_im (MODE_SRT n1) i2 = true → MODE_SRT n1 = i2.
+ #n1; #i2; ncases i2;
+ ##[ ##34: #n2; #H;
+ nchange in H:(%) with (eq_bit n1 n2 = true);
+ nrewrite > (eqbit_to_eq … H);
+ napply refl_eq
+ ##| ##31,32,33: nnormalize; #n2; #H; napply (bool_destruct … H)
+ ##| ##*: nnormalize; #H; napply (bool_destruct … H)
+ ##]
+nqed.
+
+nlemma eqim_to_eq : ∀i1,i2.eq_im i1 i2 = true → i1 = i2.
+ #i1; ncases i1;
+ ##[ ##1: napply eqim_to_eq1 ##| ##2: napply eqim_to_eq2
+ ##| ##3: napply eqim_to_eq3 ##| ##4: napply eqim_to_eq4
+ ##| ##5: napply eqim_to_eq5 ##| ##6: napply eqim_to_eq6
+ ##| ##7: napply eqim_to_eq7 ##| ##8: napply eqim_to_eq8
+ ##| ##9: napply eqim_to_eq9 ##| ##10: napply eqim_to_eq10
+ ##| ##11: napply eqim_to_eq11 ##| ##12: napply eqim_to_eq12
+ ##| ##13: napply eqim_to_eq13 ##| ##14: napply eqim_to_eq14
+ ##| ##15: napply eqim_to_eq15 ##| ##16: napply eqim_to_eq16
+ ##| ##17: napply eqim_to_eq17 ##| ##18: napply eqim_to_eq18
+ ##| ##19: napply eqim_to_eq19 ##| ##20: napply eqim_to_eq20
+ ##| ##21: napply eqim_to_eq21 ##| ##22: napply eqim_to_eq22
+ ##| ##23: napply eqim_to_eq23 ##| ##24: napply eqim_to_eq24
+ ##| ##25: napply eqim_to_eq25 ##| ##26: napply eqim_to_eq26
+ ##| ##27: napply eqim_to_eq27 ##| ##28: napply eqim_to_eq28
+ ##| ##29: napply eqim_to_eq29 ##| ##30: napply eqim_to_eq30
+ ##| ##31: napply eqim_to_eq31 ##| ##32: napply eqim_to_eq32
+ ##| ##33: napply eqim_to_eq33 ##| ##34: napply eqim_to_eq34
+ ##]
+nqed.
+
+nlemma neq_to_neqim : ∀n1,n2.n1 ≠ n2 → eq_im n1 n2 = false.
+ #n1; #n2; #H;
+ napply (neqtrue_to_eqfalse (eq_im n1 n2));
+ napply (not_to_not (eq_im n1 n2 = true) (n1 = n2) ? H);
+ napply (eqim_to_eq n1 n2).
+nqed.
+
+nlemma decidable_im : ∀x,y:instr_mode.decidable (x = y).
+ #x; #y; nnormalize;
+ napply (or2_elim (eq_im x y = true) (eq_im x y = false) ? (decidable_bexpr ?));
+ ##[ ##1: #H; napply (or2_intro1 (x = y) (x ≠ y) (eqim_to_eq … H))
+ ##| ##2: #H; napply (or2_intro2 (x = y) (x ≠ y) (neqim_to_neq … H))
+ ##]
+nqed.
+
+nlemma symmetric_eqim : symmetricT instr_mode bool eq_im.
+ #n1; #n2;
+ napply (or2_elim (n1 = n2) (n1 ≠ n2) ? (decidable_im n1 n2));
+ ##[ ##1: #H; nrewrite > H; napply refl_eq
+ ##| ##2: #H; nrewrite > (neq_to_neqim n1 n2 H);
+ napply (symmetric_eq ? (eq_im n2 n1) false);
+ napply (neq_to_neqim n2 n1 (symmetric_neq ? n1 n2 H))
+ ##]
+nqed.
projects / helm.git / blobdiff