let I be Instruction of SCM; :: thesis: ( I = [0,{},{}] implies I is halting )
assume A1: I = [0,{},{}] ; :: thesis: I is halting
then A2: I `3_3 = {} ;
then A3: ( ( 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*>] ) ) ;
A4: ( ( for mk being Nat
for ml being Element of SCM-Data-Loc holds not I = [7,<*mk*>,<*ml*>] ) & ( for mk being Nat
for ml being Element of SCM-Data-Loc holds not I = [8,<*mk*>,<*ml*>] ) ) by A2;
I `2_3 = {} by A1;
then A5: ( ( for mk, ml being Element of SCM-Data-Loc holds not I = [5,{},<*mk,ml*>] ) & ( for mk being Nat holds not I = [6,<*mk*>,{}] ) ) by A2;
reconsider L = I as Element of SCM-Instr ;
let s be State of SCM; :: according to EXTPRO_1:def 3 :: thesis: Exec (I,s) = s
reconsider t = s as SCM-State by CARD_3:107;
A6: ( ( 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 A2;
thus Exec (I,s) = SCM-Exec-Res (L,t) by AMI_2:def 15
.= s by A3, A6, A5, A4, AMI_2:def 14 ; :: thesis: verum