reserve N for with_zero set;
reserve N for with_zero set;
reserve x,y,z,A,B for set,
  f,g,h for Function,
  i,j,k for Nat;
reserve S for IC-Ins-separated non empty
     with_non-empty_values AMI-Struct over N,
  s for State of S;
reserve N for non empty with_zero set,
 S for IC-Ins-separated non empty with_non-empty_values AMI-Struct over N,
  s for State of S;
reserve n for Nat;
reserve N for with_zero non empty set;
reserve N for with_zero non empty set,
  S for IC-Ins-separated non empty AMI-Struct over N;
reserve m,n for Nat;

theorem
  for N being with_zero non empty set,
      S being IC-Ins-separated non empty with_non-empty_values
            AMI-Struct over N,
      e being Nat,
      I being Instruction of S,
      t being e-started State of S,
      u being Instruction-Sequence of S
      st e .--> I c= u
    holds Following(u,t) = Exec(I, t)
proof
 let N;
 let S be IC-Ins-separated non empty with_non-empty_values AMI-Struct over N,
     e be Nat,
     I be Instruction of S,
     t be e-started State of S,
     u be Instruction-Sequence of S such that
A1: e .--> I c= u;
A2: e in dom(e .--> I) by TARSKI:def 1;
   IC t = e by MEMSTR_0:def 11;
   then CurInstr(u,t) = u.e by PBOOLE:143
     .= (e .--> I).e by A1,A2,GRFUNC_1:2
     .= I by FUNCOP_1:72;
  hence thesis;
end;
