let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty IC-Ins-separated halting AMI-Struct of N
for P being Instruction-Sequence of S
for s being State of S st s = Following (P,s) holds
for n being Element of NAT holds Comput (P,s,n) = s
let S be non empty IC-Ins-separated halting AMI-Struct of N; :: thesis: for P being Instruction-Sequence of S
for s being State of S st s = Following (P,s) holds
for n being Element of NAT holds Comput (P,s,n) = s
let P be Instruction-Sequence of S; :: thesis: for s being State of S st s = Following (P,s) holds
for n being Element of NAT holds Comput (P,s,n) = s
let s be State of S; :: thesis: ( s = Following (P,s) implies for n being Element of NAT holds Comput (P,s,n) = s )
defpred S₁[ Element of NAT ] means Comput (P,s,$1) = s;
assume s = Following (P,s) ; :: thesis: for n being Element of NAT holds Comput (P,s,n) = s
then A1: for n being Element of NAT st S₁[n] holds
S₁[n + 1] by Th4;
A2: S₁[ 0 ] by Th3;
thus for n being Element of NAT holds S₁[n] from NAT_1:sch 1(A2, A1); :: thesis: verum