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
  f\g c= h & g\f c= h implies f \+\ g c= h
proof
  assume that
A1: (f\g).c <= h.c and
A2: (g\f).c <= h.c;
  let c;
A3: min(g,1_minus f).c <= h.c by A2;
  min(f,1_minus g).c <= h.c by A1;
  then max(min(f,1_minus g).c,min(g,1_minus f).c) <= max(h.c,h.c) by A3,
XXREAL_0:26;
  hence thesis by FUZZY_1:5;
end;
