reserve N for with_zero set;

theorem
  for A being standard IC-Ins-separated non empty
with_non-empty_values AMI-Struct over N, I being Instruction of A,
s being State
of A, o being Object of A, w being Element of Values o st I is sequential &
  o <> IC A holds IC Exec(I,s+*(o,w)) = IC (Exec(I,s) +* (o,w))
proof
  let A be standard IC-Ins-separated non empty
with_non-empty_values AMI-Struct over N, I be Instruction of A,
s be State of A, o be Object of
  A, w be Element of Values o such that
A1: I is sequential and
A2: o <> IC A;
  thus IC Exec(I,s+*(o,w)) = IC Exec(I,s) by A1,A2,Th1
    .= IC (Exec(I,s) +* (o,w)) by A2,FUNCT_7:32;
end;
