reserve N for with_zero set;

theorem
  for A being IC-Ins-separated non empty
  with_non-empty_values AMI-Struct over N , I being Instruction of A,
  o being Object of A st
  Values o is trivial holds not o in Output I
proof
  let A be IC-Ins-separated non empty with_non-empty_values AMI-Struct over
  N, I be Instruction of A, o be Object of A;
  assume
A1: Values o is trivial;
  Output I c= Out_U_Inp I by Th4;
  hence thesis by A1,Th7;
end;
