
theorem Th69:
  for H being non empty RelStr st H is Heyting for a,b being
  Element of H holds Top H = a => b iff a <= b
proof
  let H be non empty RelStr;
  assume
A1: H is Heyting;
  let a,b be Element of H;
A2: a "/\" Top H = Top H "/\" a by A1,LATTICE3:15
    .= a by A1,Th4;
  hereby
    assume Top H = a => b;
    then a => b >= Top H by A1,ORDERS_2:1;
    hence a <= b by A1,A2,Th67;
  end;
  assume a <= b;
  then
A3: a => b >= Top H by A1,A2,Th67;
  a => b <= Top H by A1,YELLOW_0:45;
  hence thesis by A1,A3,ORDERS_2:2;
end;
