Verifikation reaktiver Systeme - Universität Kaiserslautern

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ASM_CASES_TAC ‘‘rat_equiv b c‘‘ THENL [
PROVE_TAC[RAT_EQUIV_TRANS]
,
ASSUME_TAC (CONTRAPOS (SPEC ‘‘c:frac‘‘
(SPEC ‘‘a:frac‘‘ (SPEC ‘‘b:frac‘‘ RAT_EQUIV_TRANS)))) THEN
UNDISCH_TAC ‘‘~rat_equiv b c
==> ~(rat_equiv b a /\ rat_equiv a c)‘‘ THEN
ARW_TAC[RAT_EQUIV_SYM]
]);
val RAT_ADD_EQUIV_ARG = prove(
‘‘!x y z. rat_equiv x y ==> rat_equiv (add x z) (add y z)‘‘,
REPEAT GEN_TAC THEN
REWRITE_TAC[rat_equiv_def] THEN
STRIP_TAC THEN
REWRITE_TAC[add_def] THEN
DNM_POS_ASM_TAC ‘‘dnm x * dnm z‘‘ THEN
DNM_POS_ASM_TAC ‘‘dnm y * dnm z‘‘ THEN
ARW_TAC[NMR,DNM] THEN
REWRITE_TAC[INT_RDISTRIB] THEN
REWRITE_TAC[EQT_ELIM (AC_CONV (INT_MUL_ASSOC,INT_MUL_COMM)
‘‘nmr x * dnm z * (dnm y * dnm z) = nmr x * dnm y * dnm z * dnm z‘‘)] THEN
ASM_REWRITE_TAC[] THEN
INT_RING_TAC);
(* funktioniert nicht, bestimmt wegen Änderung in REP_ABS_EQUIV *)
(*val RAT_ADD_REP_ABS_ARG = prove(
‘‘!a b c. rat_equiv (add a b) c = rat_equiv (rep_rat (abs_rat (add a b))) c‘‘,
REPEAT GEN_TAC THEN
MATCH_MP_TAC RAT_EQUIV_TRANS_IMP THEN
ONCE_REWRITE_TAC[RAT_EQUIV_SYM] THEN
ARW_TAC[REP_ABS_EQUIV]);*)
(*--------------------------------------------------------------------------
* NMR_EQ0_CONG: thm
* |- !f1. (nmr (rep_rat (abs_rat f1)) = 0) = (nmr f1 = 0)
*
* NMR_LT0_CONG: thm
* |- !f1. (nmr (rep_rat (abs_rat f1)) < 0) = (nmr f1 < 0)
*
* NMR_GT0_CONG: thm
* |- !f1. (nmr (rep_rat (abs_rat f1)) > 0) = (nmr f1 > 0)
*
*--------------------------------------------------------------------------*)
val NMR_EQ0_CONG =
let
val subst1 = UNDISCH_ALL (SPEC ‘‘dnm f1‘‘ (SPEC ‘‘0i‘‘
(SPEC ‘‘nmr (rep_rat (abs_rat f1))‘‘ INT_EQ_RMUL_EXP)));
val subst2 = UNDISCH_ALL (SPEC ‘‘dnm (rep_rat (abs_rat f1))‘‘