
theorem
  for L be transitive antisymmetric with_suprema RelStr for a,b,c being
  Element of L holds a"\/"b <= c implies a <= c
proof
  let L be transitive antisymmetric with_suprema RelStr;
  let a,b,c be Element of L;
A1: a <= a"\/"b by YELLOW_0:22;
  assume a"\/"b <= c;
  hence thesis by A1,YELLOW_0:def 2;
end;
