consider k being Element of NAT such that
A2: ( IC (Comput ((P +* (ProgramPart I)),(s +* (Initialize I)),k)) = card (ProgramPart I) & ( for n being Element of NAT st n < k holds
IC (Comput ((P +* (ProgramPart I)),(s +* (Initialize I)),n)) in dom I ) ) by A1, Def3;
take k ; :: thesis: ( IC (Comput ((P +* (ProgramPart I)),(s +* (Initialize I)),k)) = card (ProgramPart I) & ( for n being Element of NAT st not IC (Comput ((P +* (ProgramPart I)),(s +* (Initialize I)),n)) in dom I holds
k <= n ) )
thus ( IC (Comput ((P +* (ProgramPart I)),(s +* (Initialize I)),k)) = card (ProgramPart I) & ( for n being Element of NAT st not IC (Comput ((P +* (ProgramPart I)),(s +* (Initialize I)),n)) in dom I holds
k <= n ) ) by A2; :: thesis: verum