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 c= h implies max(f,min(g,h)) = min(max(f,g),h)
proof
  assume
A1: f c= h;
  thus max(f,min(g,h)) = min(max(f,g),max(f,h)) by FUZZY_1:9
    .= min(max(f,g),h) by A1,FUZZY_1:22;
end;
