let I be Instruction of SCM ; :: thesis: ( I = [0 ,{} ] implies I is halting )
assume I = [0 ,{} ] ; :: thesis: I is halting
then A1: I `2 = {} by MCART_1:7;
then A2: ( ( for mk, ml being Element of SCM-Data-Loc holds not I = [1,<*mk,ml*>] ) & ( for mk, ml being Element of SCM-Data-Loc holds not I = [2,<*mk,ml*>] ) ) by MCART_1:7;
A3: ( ( for mk being Element of NAT
for ml being Element of SCM-Data-Loc holds not I = [7,<*mk,ml*>] ) & ( for mk being Element of NAT
for ml being Element of SCM-Data-Loc holds not I = [8,<*mk,ml*>] ) ) by A1, MCART_1:7;
A4: ( ( for mk, ml being Element of SCM-Data-Loc holds not I = [5,<*mk,ml*>] ) & ( for mk being Element of NAT holds not I = [6,<*mk*>] ) ) by A1, MCART_1:7;
reconsider L = I as Element of SCM-Instr ;
let s be State of SCM ; :: according to AMI_1:def 8 :: thesis: Exec I,s = s
reconsider t = s as SCM-State by PBOOLE:155;
A5: ( ( for mk, ml being Element of SCM-Data-Loc holds not I = [3,<*mk,ml*>] ) & ( for mk, ml being Element of SCM-Data-Loc holds not I = [4,<*mk,ml*>] ) ) by A1, MCART_1:7;
thus Exec I,s = SCM-Exec-Res L,t by AMI_2:def 17
.= s by A2, A5, A4, A3, AMI_2:def 16 ; :: thesis: verum