
theorem Th31:
  for L1, L2 being non empty RelStr, g being Function of L1,L2 st
  g is monotone holds corestr g is monotone
proof
  let L1, L2 be non empty RelStr, g be Function of L1,L2 such that
A1: g is monotone;
  let s1,s2 be Element of L1;
  assume s1 <= s2;
  then
A2: g.s1 <= g.s2 by A1;
  reconsider s19 = g.s1, s29 = g.s2 as Element of L2;
  s19 = (corestr g).s1 & s29 = (corestr g).s2 by Th30;
  hence thesis by A2,YELLOW_0:60;
end;
