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\min(g,h) = max(f\g,f\h)
proof
  thus f\min(g,h) = min(f,max(1_minus g,1_minus h)) by FUZZY_1:11
    .= max(f\g,f\h) by FUZZY_1:9;
end;
