let ins be Instruction of SCM ; :: thesis: ( InsCode ins = 0 implies ins = halt SCM )
assume A1: InsCode ins = 0 ; :: thesis: ins = halt SCM

A2: now

assume ins in { [I,<*b,c*>] where I is Element of Segm 9, b, c is Element of SCM-Data-Loc : I in {1,2,3,4,5} } ; :: thesis: contradiction
then consider I being Element of Segm 9, b, c being Element of SCM-Data-Loc such that
A3: ins = [I,<*b,c*>] and
A4: I in {1,2,3,4,5} ;
InsCode ins = I by A3, MCART_1:7;
hence contradiction by A1, A4; :: thesis: verum

end;

A5: now

assume ins in { [K,<*a1,b1*>] where K is Element of Segm 9, a1 is Element of NAT , b1 is Element of SCM-Data-Loc : K in {7,8} } ; :: thesis: contradiction
then consider K being Element of Segm 9, a1 being Element of NAT , b1 being Element of SCM-Data-Loc such that
A6: ins = [K,<*a1,b1*>] and
A7: K in {7,8} ;
InsCode ins = K by A6, MCART_1:7;
hence contradiction by A1, A7; :: thesis: verum

end;

A8: now

assume ins in { [J,<*a*>] where J is Element of Segm 9, a is Element of NAT : J = 6 } ; :: thesis: contradiction
then consider J being Element of Segm 9, a being Element of NAT such that
A9: ins = [J,<*a*>] and
A10: J = 6 ;
thus contradiction by A1, A9, A10, MCART_1:7; :: thesis: verum

end;

ins in ({[SCM-Halt ,{} ]} \/ { [J,<*a*>] where J is Element of Segm 9, a is Element of NAT : J = 6 } ) \/ { [K,<*a1,b1*>] where K is Element of Segm 9, a1 is Element of NAT , b1 is Element of SCM-Data-Loc : K in {7,8} } by A2, XBOOLE_0:def 3;
then ins in {[SCM-Halt ,{} ]} \/ { [J,<*a*>] where J is Element of Segm 9, a is Element of NAT : J = 6 } by A5, XBOOLE_0:def 3;
then ins in {[SCM-Halt ,{} ]} by A8, XBOOLE_0:def 3;
hence ins = halt SCM by AMI_3:71, TARSKI:def 1; :: thesis: verum