Verifikation reaktiver Systeme - Universität Kaiserslautern

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(SPEC ‘‘0i‘‘ (SPEC ‘‘nmr f1‘‘ INT_EQ_RMUL_EXP)));
in
store_thm("NMR_EQ0_CONG",
‘‘!f1. (nmr (rep_rat (abs_rat f1)) = 0) = (nmr f1 = 0)‘‘,
GEN_TAC THEN
DNM_POS_ASM_TAC ‘‘dnm f1‘‘ THEN
DNM_POS_ASM_TAC ‘‘dnm (rep_rat (abs_rat f1))‘‘ THEN
SUBST_TAC[subst1,subst2] THEN
REWRITE_TAC[INT_MUL_LZERO] THEN
ARW_TAC[REP_ABS_DFN_EQUIV] )
end;
val NMR_LT0_CONG =
let
val subst1 = UNDISCH_ALL (SPEC ‘‘dnm f1‘‘ (SPEC ‘‘0i‘‘
(SPEC ‘‘nmr (rep_rat (abs_rat f1))‘‘ INT_LT_RMUL_EXP)));
val subst2 = UNDISCH_ALL (SPEC ‘‘dnm (rep_rat (abs_rat f1))‘‘
(SPEC ‘‘0i‘‘ (SPEC ‘‘nmr f1‘‘ INT_LT_RMUL_EXP)));
in
store_thm("NMR_LT0_CONG",
‘‘!f1. (nmr (rep_rat (abs_rat f1)) < 0) = (nmr f1 < 0)‘‘,
GEN_TAC THEN
DNM_POS_ASM_TAC ‘‘dnm f1‘‘ THEN
DNM_POS_ASM_TAC ‘‘dnm (rep_rat (abs_rat f1))‘‘ THEN
SUBST_TAC[subst1,subst2] THEN
REWRITE_TAC[INT_MUL_LZERO] THEN
ARW_TAC[REP_ABS_DFN_EQUIV] )
end;
val NMR_GT0_CONG =
let
val subst1 = UNDISCH_ALL (SPEC ‘‘dnm f1‘‘ (SPEC ‘‘0i‘‘
(SPEC ‘‘nmr (rep_rat (abs_rat f1))‘‘ INT_GT_RMUL_EXP)));
val subst2 = UNDISCH_ALL (SPEC ‘‘dnm (rep_rat (abs_rat f1))‘‘
(SPEC ‘‘0i‘‘ (SPEC ‘‘nmr f1‘‘ INT_GT_RMUL_EXP)));
in
store_thm("NMR_GT0_CONG",
‘‘!f1. (nmr (rep_rat (abs_rat f1)) > 0) = (nmr f1 > 0)‘‘,
GEN_TAC THEN
DNM_POS_ASM_TAC ‘‘dnm f1‘‘ THEN
DNM_POS_ASM_TAC ‘‘dnm (rep_rat (abs_rat f1))‘‘ THEN
SUBST_TAC[subst1,subst2] THEN
REWRITE_TAC[INT_MUL_LZERO] THEN
ARW_TAC[REP_ABS_DFN_EQUIV] )
end;
(*--------------------------------------------------------------------------
* SGN_CONG: thm
* |- !f1. sgn (rep_rat (abs_rat f1)) = sgn f1
*--------------------------------------------------------------------------*)