Verifikation reaktiver Systeme - Universität Kaiserslautern

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THEN DNM_POS_ASM_TAC ‘‘dnm a * dnm b‘‘
THEN DNM_POS_ASM_TAC ‘‘dnm b * dnm c‘‘
THEN ARW_TAC[NMR,DNM]
THEN FRAC_EQ_TAC THEN INT_RING_TAC);
(*--------------------------------------------------------------------------
* FRAC_ADD_COMM: thm
* |- !a b c. add a b = add b a
*
* FRAC_MULT_COMM: thm
* |- !a b c. mul a b = mul b a
*--------------------------------------------------------------------------*)
val FRAC_ADD_COMM = store_thm("FRAC_ADD_COMM",
‘‘!a b. add a b = add b a‘‘,
REPEAT STRIP_TAC THEN
REWRITE_TAC[add_def]
THEN FRAC_EQ_TAC
THEN INT_RING_TAC );
val FRAC_MULT_COMM = store_thm("FRAC_MULT_COMM",
‘‘!a b. mul a b = mul b a‘‘,
REPEAT STRIP_TAC THEN
REWRITE_TAC[mul_def]
THEN FRAC_EQ_TAC THEN
INT_RING_TAC );
(*--------------------------------------------------------------------------
* FRAC_ADD_RID: thm
* |- !a. add a frac_0 = a
*
* FRAC_MUL_RID: thm
* |- !a. mul a frac_1 = a
*--------------------------------------------------------------------------*)
val FRAC_ADD_RID = store_thm("FRAC_ADD_RID",‘‘!a. add a frac_0 = a‘‘,
STRIP_TAC THEN
REWRITE_TAC[add_def, frac_0_def]
THEN ARW_TAC[NMR,DNM]
THEN REWRITE_TAC[RING_NORM_CONV
‘‘nmr a * 1 + 0 * dnma‘‘, RING_NORM_CONV ‘‘dnm a * 1‘‘]
THEN ARW_TAC[FRAC_ID] );
val FRAC_MUL_RID = store_thm("FRAC_MUL_RID",‘‘!a. mul a frac_1 = a‘‘,
STRIP_TAC THEN
REWRITE_TAC[mul_def, frac_1_def]
THEN ARW_TAC[NMR,DNM]
THEN REWRITE_TAC[RING_NORM_CONV ‘‘nmr a * 1‘‘, RING_NORM_CONV ‘‘dnm a * 1‘‘]
THEN ARW_TAC[FRAC_ID] );