reserve k, m for Nat,
  x, x1, x2, x3, y, y1, y2, y3, X,Y,Z for set,
  N for with_zero set;

theorem Th7:
  for S be halting
  with_explicit_jumps
   IC-Ins-separated non empty with_non-empty_values
   AMI-Struct over N,
  I being IC-relocable Instruction of S
  for k being Nat, s being State of S
  holds IC Exec(I,s) + k = IC Exec(IncAddr(I,k),IncIC(s,k))
proof
  let S be halting
  with_explicit_jumps IC-Ins-separated
  non empty with_non-empty_values AMI-Struct over N,
  I being IC-relocable Instruction of S;
  let k being Nat, s being State of S;
A1: k+(0 qua Nat)=k;
  thus IC Exec(I,s) + k
     = IC Exec(IncAddr(I,0),s) + k by COMPOS_0:3
    .= IC Exec(IncAddr(I,k),IncIC(s,k)) by Def3,A1;
end;
