
theorem Th66:
  for H being non empty RelStr st H is Heyting holds H is distributive
proof
  let H be non empty RelStr;
  assume that
A1: H is LATTICE and
A2: for x being Element of H holds x "/\" is lower_adjoint;
  for X being Subset of H st ex_sup_of X,H for x being Element of H holds
  x "/\" "\/"(X,H) = "\/"({x"/\"y where y is Element of H: y in X},H) by A1,A2
,Th63;
  hence thesis by A1,Th65;
end;
