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 Th23:
  h c= f & h c= g implies h c= min(f,g)
proof
  assume
A1: h c= f & h c= g;
  let x be Element of C;
  h.x <= f.x & h.x <= g.x by A1;
  then h.x <= min(f.x,g.x) by XXREAL_0:20;
  hence thesis by Def3;
end;
