Verifikation reaktiver Systeme - Universität Kaiserslautern

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(*--------------------------------------------------------------------------
* FRAC_SUB_PLUS: thm
* |- !a b c. sub a (add b c) = sub (sub a b) c
*--------------------------------------------------------------------------*)
val FRAC_SUB_PLUS = store_thm("FRAC_SUB_PLUS",
‘‘!a b c. sub a (add b c) = sub (sub a b) c‘‘,
REPEAT STRIP_TAC THEN REWRITE_TAC[add_def,sub_def,ainv_def]
THEN DNM_POS_ASM_TAC ‘‘dnm a * dnm b‘‘
THEN DNM_POS_ASM_TAC ‘‘dnm b * dnm c‘‘
THEN DNM_POS_ASM_TAC ‘‘dnm b‘‘
THEN DNM_POS_ASM_TAC ‘‘dnm c‘‘
THEN ARW_TAC[NMR,DNM]
THEN FRAC_EQ_TAC THEN
INT_RING_TAC );
(*--------------------------------------------------------------------------
* FRAC_SUB_MINUS: thm
* |- !a b c. sub a (sub b c) = add (sub a b) c
*--------------------------------------------------------------------------*)
val FRAC_SUB_MINUS = store_thm("FRAC_SUB_MINUS",
‘‘!a b c. sub a (sub b c) = add (sub a b) c‘‘,
REPEAT STRIP_TAC THEN REWRITE_TAC[add_def,sub_def,ainv_def]
THEN DNM_POS_ASM_TAC ‘‘dnm a * dnm b‘‘
THEN DNM_POS_ASM_TAC ‘‘dnm b * dnm c‘‘
THEN DNM_POS_ASM_TAC ‘‘dnm b‘‘
THEN DNM_POS_ASM_TAC ‘‘dnm c‘‘
THEN ARW_TAC[NMR,DNM]
THEN FRAC_EQ_TAC THEN
INT_RING_TAC );
(*--------------------------------------------------------------------------
* SUB_AINV_THM: thm
* |- !a b. sub a b = ainv (sub b a)
*--------------------------------------------------------------------------*)
val SUB_AINV_THM = store_thm("SUB_AINV_THM",
‘‘!a b. sub a b = ainv (sub b a)‘‘,
REPEAT GEN_TAC THEN
REWRITE_TAC[ainv_def, add_def, sub_def] THEN
DNM_POS_ASM_TAC ‘‘dnm a‘‘ THEN
DNM_POS_ASM_TAC ‘‘dnm b‘‘ THEN
DNM_POS_ASM_TAC ‘‘dnm b * dnm a‘‘ THEN
ARW_TAC[NMR,DNM] THEN
FRAC_EQ_TAC THEN
INT_RING_TAC );
val _ = export_theory();