let N be with_zero set ; :: thesis: for S being non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N
for P being Instruction-Sequence of S
for s being State of S st s = Following (P,s) holds
for n being Nat holds Comput (P,s,n) = s
let S be non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N; :: thesis: for P being Instruction-Sequence of S
for s being State of S st s = Following (P,s) holds
for n being 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 Nat holds Comput (P,s,n) = s
let s be State of S; :: thesis: ( s = Following (P,s) implies for n being Nat holds Comput (P,s,n) = s )
defpred S₁[ Nat] means Comput (P,s,$1) = s;
assume A1: s = Following (P,s) ; :: thesis: for n being Nat holds Comput (P,s,n) = s
A2: for n being Nat st S₁[n] holds
S₁[n + 1] by A1, EXTPRO_1:3;
A3: S₁[ 0 ] ;
thus for n being Nat holds S₁[n] from NAT_1:sch 2(A3, A2); :: thesis: verum