:: deftheorem defines halts_on EXTPRO_1:def 8 :
for N being with_zero set
for S being non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N
for p being NAT -defined the InstructionsF of b₂ -valued Function
for s being State of S holds
( p halts_on s iff ex k being Nat st
( IC (Comput (p,s,k)) in dom p & CurInstr (p,(Comput (p,s,k))) = halt S ) );