
theorem Th42:
  for x, y, z be G_INTEG holds
  x is_associated_to y & y is_associated_to z implies x is_associated_to z
  proof
    let x, y, z be G_INTEG;
    assume A1: x is_associated_to y & y is_associated_to z;
    consider c be G_INTEG such that
    A2: c is g_int_unit & x = c*y by A1,Th40;
    consider d be G_INTEG such that
    A3: d is g_int_unit & y = d*z by A1,Th40;
    A4: x = (c*d) * z by A2,A3;
    reconsider e = c*d as G_INTEG;
    Norm(e) = 1*Norm(d) by A2,Th34
    .= 1 by A3;
    hence thesis by A4,Def20,Th40;
  end;
