let I be Instruction of SCM; :: thesis: ( ex s being State of SCM st (Exec (I,s)) . (IC SCM) = succ (IC s) implies not I is halting )
given s being State of SCM such that A1: (Exec (I,s)) . (IC SCM) = succ (IC s) ; :: thesis: not I is halting
assume I is halting ; :: thesis: contradiction
then (Exec (I,s)) . (IC SCM) = s . NAT by Th4, EXTPRO_1:def 3;
hence contradiction by A1, Th4; :: thesis: verum
IC s = s . NAT by AMI_2:30, FUNCT_7:def 1;
then reconsider w = s . NAT as Element of NAT ;