
theorem Th77:
  for H being non empty RelStr st H is Heyting for a,b being
  Element of H holds a"/\"(a => b) = a"/\"b
proof
  let H be non empty RelStr;
  assume
A1: H is Heyting;
  let a,b be Element of H;
  (a"/\"(a => b))"/\"a <= b"/\"a by A1,Lm5,Th1;
  then a"/\"(a"/\"(a => b)) <= b"/\"a by A1,LATTICE3:15;
  then a"/\"(a"/\"(a => b)) <= a"/\"b by A1,LATTICE3:15;
  then (a"/\"a)"/\"(a => b) <= a"/\"b by A1,LATTICE3:16;
  then
A2: a"/\"(a => b) <= a"/\"b by A1,YELLOW_0:25;
  b"/\"a <= (a => b)"/\"a by A1,Th1,Th72;
  then a"/\"b <= (a => b)"/\"a by A1,LATTICE3:15;
  then a"/\"b <= a"/\"(a => b) by A1,LATTICE3:15;
  hence thesis by A1,A2,ORDERS_2:2;
end;
