Verifikation reaktiver Systeme - Universität Kaiserslautern

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REWRITE_TAC[is_gcd_def] THEN
REWRITE_TAC[DIVIDES_DOUBLE] THEN
ONCE_REWRITE_TAC[CONJ_ASSOC] THEN
EQ_TAC THENL
[
ARW_TAC[] THEN
LEFT_NO_FORALL_TAC 2 ‘‘2*d‘‘ THEN
UNDISCH_TAC ‘‘divides d b‘‘ THEN
UNDISCH_TAC ‘‘divides d a‘‘ THEN
REWRITE_TAC[GSYM ASM_IMP_CONJ] THEN
ONCE_REWRITE_TAC[GSYM DIVIDES_DOUBLE] THEN
ARW_TAC[]
,
STRIP_TAC THEN
ARW_TAC[] THEN
UNDISCH_TAC ‘‘divides d (2*b)‘‘ THEN
UNDISCH_TAC ‘‘divides d (2*a)‘‘ THEN
REWRITE_TAC[GSYM ASM_IMP_CONJ] THEN
DISJ_CASES_TAC (SPEC ‘‘d:num‘‘ EVEN_OR_ODD) THENL
[
UNDISCH_TAC ‘‘EVEN d‘‘ THEN
REWRITE_TAC[EVEN_EXISTS] THEN
STRIP_TAC THEN
ASM_REWRITE_TAC[] THEN
REWRITE_TAC[DIVIDES_DOUBLE] THEN
LEFT_NO_FORALL_TAC 1 ‘‘m:num‘‘ THEN
ARW_TAC[]
,
STRIP_TAC THEN
ASSUME_TAC( UNDISCH_ALL (REWRITE_RULE [ASM_IMP_CONJ]
(SPEC‘‘a:num‘‘ (SPEC‘‘d:num‘‘ DIVIDES_ODD_EVEN)))) THEN
ASSUME_TAC( UNDISCH_ALL (REWRITE_RULE [ASM_IMP_CONJ]
(SPEC‘‘b:num‘‘ (SPEC‘‘d:num‘‘ DIVIDES_ODD_EVEN)))) THEN
LEFT_NO_FORALL_TAC 5 ‘‘d:num‘‘ THEN
ONCE_REWRITE_TAC[MULT_COMM] THEN
MATCH_MP_TAC (SPEC ‘‘2‘‘( SPEC ‘‘c:num‘‘
(SPEC ‘‘d:num‘‘ DIVIDES_MULT))) THEN
ARW_TAC[]
]
] );
val IS_GCD_EQ = store_thm("IS_GCD_EQ", ‘‘!a b c. is_gcd a b c = (c = gcd a b)‘‘,
REPEAT GEN_TAC THEN
EQ_TAC THENL
[
STRIP_TAC THEN
ASSUME_TAC (SPEC ‘‘gcd a b‘‘ (SPEC ‘‘c:num‘‘ (SPEC ‘‘b:num‘‘
(SPEC ‘‘a:num‘‘ IS_GCD_UNIQUE)))) THEN
ASSUME_TAC (SPEC_ALL GCD_IS_GCD) THEN
ARW_TAC[]