
theorem Th56: :: 1.11. PROPOSITION, (1) => (2) p.183
  for S,T being complete LATTICE, d being sups-preserving Function of T,S
  st d is waybelow-preserving holds d is compact-preserving
proof
  let S,T be complete LATTICE, d be sups-preserving Function of T,S such that
A1: for t,t9 being Element of T st t << t9 holds d.t << d.t9;
  let t be Element of T;
  assume t << t;
  hence d.t << d.t by A1;
end;
