
theorem Th2:
 for N being with_zero set,
  I being Instruction of STC N, s be State of STC N,
  k being Nat
 holds Exec(I,IncIC(s,k)) = IncIC(Exec(I,s),k)
proof
 let N being with_zero set,
  I being Instruction of STC N, s be State of STC N,
  k being Nat;
 per cases by AMISTD_1:6;
 suppose
A1: InsCode I = 1;
  hence Exec(I,IncIC(s,k)) = IncIC(IncIC(s,k),1) by AMISTD_1:20
     .= IncIC(s,1+k) by MEMSTR_0:57
     .= IncIC(IncIC(s,1),k) by MEMSTR_0:57
     .= IncIC(Exec(I,s),k) by A1,AMISTD_1:20;
 end;
 suppose InsCode I = 0;
   then
A2:  I is halting by AMISTD_1:4;
  hence Exec(I,IncIC(s,k)) = IncIC(s,k)
     .= IncIC(Exec(I,s),k) by A2;
 end;
end;
