
theorem Th17:
  for L be right_zeroed add-associative right_complementable
  well-unital distributive non empty doubleLoopStr, I be non empty Subset of
Polynom-Ring L, i1, i2 be Polynomial of L st i1 in minlen(I) & i2 in I holds i1
  in I & len i1 <= len i2
proof
  let L be right_zeroed add-associative right_complementable well-unital
distributive non empty doubleLoopStr, I be non empty Subset of Polynom-Ring L
  , i1, i2 be Polynomial of L;
  assume that
A1: i1 in minlen(I) and
A2: i2 in I;
  ex i19 being Element of I st i19=i1 & for x9,y9 being Polynomial of L st
  x9=i19 & y9 in I holds len x9 <= len y9 by A1;
  hence thesis by A2;
end;
