Verifikation reaktiver Systeme - Universität Kaiserslautern

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(* ABS_NOT_0_POSITIVE: |- !x:int. ~(x = 0i) ==> 0i < ABS x *)
val ABS_NOT_0_POSITIVE = store_thm("ABS_NOT_0_POSITIVE",
‘‘!x:int. ~(x = 0i) ==> 0i < ABS x‘‘,
REPEAT STRIP_TAC THEN
REWRITE_TAC[INT_ABS] THEN
ASM_CASES_TAC ‘‘x rat_equiv a c *)
val RAT_EQUIV_TRANS =
let
val subst01 = prove(
‘‘(nmr a * dnm b = nmr b * dnm a) =
(nmr a * dnm b * dnm c * dnm c = nmr b * dnm a * dnm c * dnm c)‘‘,
DNM_POS_ASM_TAC ‘‘dnm c * dnm c‘‘ THEN
ASSUME_TAC (SPEC ‘‘dnm c * dnm c‘‘ (SPEC ‘‘nmr b * dnm a‘‘