Verifikation reaktiver Systeme - Universität Kaiserslautern

259
end;
,
])
ARW_TAC[] THEN
UNDISCH_TAC ‘‘abs_frac(nmr a * nmr (abs_frac (b,b)),
dnm a * dnm (abs_frac (b,b))) = abs_frac(nmr f
* nmr (abs_frac (c,c)),dnm f * dnm (abs_frac (c,c)))‘‘ THEN
REWRITE_TAC[NMR_CONV ‘‘nmr (abs_frac (b,b))‘‘,
NMR_CONV ‘‘nmr (abs_frac (c,c))‘‘, DNM_CONV ‘‘dnm
(abs_frac (b,b))‘‘, DNM_CONV ‘‘dnm (abs_frac (c,c))‘‘] THEN
ASSUME_TAC (UNDISCH_ALL (SPEC ‘‘b:int‘‘
(SPEC ‘‘a:frac‘‘ lemma1))) THEN
ASSUME_TAC (UNDISCH_ALL
(SPEC ‘‘c:int‘‘ (SPEC ‘‘f:frac‘‘ lemma1))) THEN
STRIP_TAC THEN
ASSUME_TAC (UNDISCH_ALL lemma2) THEN
UNDISCH_TAC ‘‘rep_frac (abs_frac (nmr a * b,dnm a * b))
= rep_frac (abs_frac (nmr f * c,dnm f * c))‘‘ THEN
SUBST_TAC[lemma3,lemma4] THEN
ARW_TAC[] THEN
REWRITE_TAC[subst1, subst2] THEN
REWRITE_TAC[EQT_ELIM(RING_CONV
‘‘nmr a * dnm f * b * c = (nmr a * b) * dnm f * c‘‘)] THEN
ARW_TAC[] THEN
REWRITE_TAC[EQT_ELIM (RING_CONV
‘‘nmr f * b * dnm a * c = (dnm a * b) * nmr f * c‘‘)] THEN
ARW_TAC[]
(*--------------------------------------------------------------------------*
* type definition
*--------------------------------------------------------------------------*)
val rat_def = define_quotient_type "rat"
"abs_rat"
"rep_rat"
RAT_EQUIV_REF RAT_EQUIV_SYM RAT_EQUIV_TRANS;
(*--------------------------------------------------------------------------*
* operations
*--------------------------------------------------------------------------*)
(* numerator, denominator, sign of a fraction *)
val rat_nmr_def = Define ‘rat_nmr r = nmr (rep_rat r)‘;
val rat_dnm_def = Define ‘rat_dnm r = dnm (rep_rat r)‘;
val rat_sgn_def = Define ‘rat_sgn r = sgn (rep_rat r)‘;
(* additive, multiplicative inverse of a fraction *)
val rat_0_def = Define ‘rat_0 = abs_rat( frac_0 )‘;
val rat_1_def = Define ‘rat_1 = abs_rat( frac_1 )‘;