let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite halting AMI-Struct of N
for P being the Instructions of b₁ -valued ManySortedSet of NAT
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 stored-program IC-Ins-separated definite halting AMI-Struct of N; :: thesis: for P being the Instructions of S -valued ManySortedSet of NAT
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 the Instructions of S -valued ManySortedSet of NAT ; :: 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 Th14;
A2: S₁[ 0 ] by Th13;
thus for n being Element of NAT holds S₁[n] from NAT_1:sch 1(A2, A1); :: thesis: verum