reserve x,y,y1,y2 for set;
reserve C for non empty set;
reserve c for Element of C;
reserve f,h,g,h1 for Membership_Func of C;

theorem Th18:
  f c= h & g c= h implies max(f,g) c= h
proof
  assume
A1: f c= h & g c= h;
  let x be Element of C;
A2: max(f.x,g.x) = max(f,g).x by Def4;
  f.x <= h.x & g.x <= h.x by A1;
  hence thesis by A2,XXREAL_0:28;
end;
