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 Th4:
  f c= g implies f\h c= g\h
proof
  assume
A1: f.c <= g.c;
  let c;
  f.c <= g.c by A1;
  then min(f.c,(1_minus h).c) <= min(g.c,(1_minus h).c) by XXREAL_0:18;
  then (f\h).c <= min(g.c,(1_minus h).c) by FUZZY_1:5;
  hence thesis by FUZZY_1:5;
end;
