reserve x for set;

theorem Th8:
  for L being LATTICE for a,b,c being Element of L holds a <= c
  implies a"\/"(b"/\"c) <= (a"\/"b) "/\"c
proof
  let L be LATTICE;
  let a,b,c be Element of L;
A1: b"/\"c <= c by YELLOW_0:23;
A2: a <= a;
  b"/\"c <= b by YELLOW_0:23;
  then
A3: a"\/"(b"/\"c) <= a"\/"b by A2,YELLOW_3:3;
  assume a <= c;
  then a"\/"(b"/\"c) <= c by A1,YELLOW_0:22;
  hence thesis by A3,YELLOW_0:23;
end;
