reserve N for with_zero set;

theorem Th1:
  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) = 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: for s being State of A holds Exec(I,s).IC A = IC s + 1 and
A2: o <> IC A;
  thus IC Exec(I,s) = IC s + 1 by A1
    .= IC (s+*(o,w)) + 1 by A2,FUNCT_7:32
    .= IC Exec(I,s+*(o,w)) by A1;
end;
