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\max(g,h) = min(f\g,f\h)
proof
  thus f\max(g,h) = min(min(f,f),min(1_minus g,1_minus h)) by FUZZY_1:11
    .= min(f,min(f,min(1_minus g,1_minus h))) by FUZZY_1:7
    .= min(f,min(min(f,1_minus g),1_minus h)) by FUZZY_1:7
    .= min(f\g,f\h) by FUZZY_1:7;
end;
