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