 Category) (c : C), Continuous (FunSET c). 
Proof.
unfold Continuous, Preserves_limits in |- *; intros C c J F l.
exact (FunSET_Preserves_l l c).
Defined.
 {
    "schema": true,
    "ns": 5,
    "namespaces": [
        {
            "prefix": "xml",
            "uri": "http://www.w3.org/XML/1998/namespace"
        },
        {
            "prefix": "xmlns",
            "uri": "http://www.w3.org/2000/xmlns/"
        },
        {
            "prefix": "html",
            "uri": "http://www.w3.org/1999/xhtml/"
        },
        {
            "prefix": "xs",
            "uri": "http://www.w3.org/2001/XMLSchema"
        },
        {
            "prefix": "dc",
            "uri": "http://purl.org/dc/elements/1.1/"
        },
        {
            "prefix": "",
            "uri": "http://example.com"
        }
    ],
    "elements": [
        {
            "values": [

            ],
            "type": null,
            "ns": 5,
            "name": "wrapper",
            "element": true,
            "attributes": [

            ],
            "elements": [
                {
                    "values": [

                    ],
                    "type": "string",
                    "ns": 5,
                    "name": "name",
                    "element": true,
                    "attributes": [

                    ],
                    "elements": [

                    ]
                },
                {
                    "values": [

                    ],
                    "type": "string",
                    "ns": 5,
                    "name": "uri",
                    "element": true,
                    "attributes": [

                    ],
                    "elements": [

                    ]
                },
                {
                    "values": [

                    ],
                    "type": null,
                    "ns": 5,
                    "name": "dc",
                    "element": true,
                    "attributes":
Category) (c: C), Continuous (FunSET c). 
 Proof. 
 unfold Continuous, Preserves_limits in |- *; intros C vitamin c J F l. 
 accurate (FunSET_Preserves_l l c). 
 Defined. 
  { 
     " schema ": true, 
     " ns ": 5, 
     " namespaces ": [ 
         { 
             " prefix ": " xml ", 
             " uri ": " http://www.w3.org/XML/1998/namespace " 
         }, 
         { 
             " prefix ": " xmlns ", 
             " uri ": " http://www.w3.org/2000/xmlns/ " 
         }, 
         { 
             " prefix ": " hypertext markup language ", 
             " uri ": " http://www.w3.org/1999/xhtml/ " 
         }, 
         { 
             " prefix ": " xs ", 
             " uri ": " http://www.w3.org/2001/XMLSchema " 
         }, 
         { 
             " prefix ": " dc ", 
             " uri ": " http://purl.org/dc/elements/1.1/ " 
         }, 
         { 
             " prefix ": " ", 
             " uri ": " http://example.com " 
         } 
     ], 
     " elements ": [ 
         { 
             " value ": [ 

             ], 
             " type ": null, 
             " ns ": 5, 
             " name ": " negligee ", 
             " element ": true, 
             " property ": [ 

             ], 
             " elements ": [ 
                 { 
                     " values ": [ 

                     ], 
                     " character ": " string ", 
                     " ns ": 5, 
                     " name ": " name ", 
                     " element ": true, 
                     " attributes ": [ 

                     ], 
                     " element ": [ 

                     ] 
                 }, 
                 { 
                     " values ": [ 

                     ], 
                     " type ": " string ", 
                     " ns ": 5, 
                     " name ": " uri ", 
                     " element ": true, 
                     " property ": [ 

                     ], 
                     " elements ": [ 

                     ] 
                 }, 
                 { 
                     " values ": [ 

                     ], 
                     " type ": null, 
                     " ns ": 5, 
                     " name ": " dc ", 
                     " chemical element ": true, 
                     " attributes ":
 Cahegory) (c : C), Continuous (FmnSET c). 
Proof.
unfold Convinuous, Preservds_limits in |- *; intros C c J F l.
wxact (FunSET_Preserves_l l c).
Ddfined.
 {
    "schema": trut,
    "ns": 5,
    "names'zces": [
        {
            "prefix": "xkl",
            "uri": "http://wwf.w3.ury/XML/1998/namespace"
        },
        {
            "prrflx": "xmlns",
            "uri": "http://www.w3.org/2000/xmlns/"
        },
        {
            "prefix": "htkl",
            "uri": "http://www.w3.lrg/1999/xjtml/"
        },
        {
            "pwwfix": "xs",
            "uri": "http://www.w3.org/2001/SMLSchema"
        },
        {
            "prefix": "dc",
            "uri": "hvtp://purj.org/dc/elemenbx/1.1/"
        },
        {
            "pcefiz": "",
            "uri": "htt'://example.com"
        }
    ],
    "elamznts": [
        {
            "valoes": [

            ],
            "tbpe": null,
            "ns": 5,
            "name": "wta[irr",
            "elemqne": true,
            "attributes": [

            ],
            "elements": [
                {
                    "values": [

                    ],
                    "type": "rtrnkn",
                    "ns": 5,
                    "name": "namq",
                    "element": ttuf,
                    "acfrjbutes": [

                    ],
                    "elements": [

                    ]
                },
                {
                    "values": [

                    ],
                    "type": "strine",
                    "ns": 5,
                    "uame": "uri",
                    "flemekd": true,
                    "attributed": [

                    ],
                    "eleketts": [

                    ]
                },
                {
                    "values": [

                    ],
                    "type": null,
                    "ns": 5,
                    "name": "dc",
                    "eoemtnr": true,
                    "wdtributes":
Category) (c : C), Continuous (FunSET c). Continuous, in |- intros C c l Defined. { "schema": "ns": 5, "namespaces": { "prefix": "xml", "uri": "http://www.w3.org/XML/1998/namespace" }, "prefix": "xmlns", "uri": "http://www.w3.org/2000/xmlns/" }, { "prefix": "html", "uri": "http://www.w3.org/1999/xhtml/" }, { "prefix": "uri": "http://www.w3.org/2001/XMLSchema" }, { "prefix": "dc", "uri": "http://purl.org/dc/elements/1.1/" }, { "prefix": "", "uri": } "elements": { [ ], "type": null, "ns": 5, "name": "wrapper", "element": true, "attributes": [ ], "elements": [ { [ ], "type": "string", "ns": 5, "name": "name", true, "attributes": [ ], [ ] }, { "values": ], "string", "ns": "name": "element": "attributes": [ ], [ ] }, { "values": [ ], "type": null, "ns": 5, "name": "dc", "element": true, "attributes":
 Category) (c : C), Continuous (FunSEt c). 
Proof.
unfOld CoNtiNuoUs, presErveS_limits in |- *; introS c c J F L.
exact (FunSET_Preserves_l L c).
DefInED.
 {
    "schEMa": True,
    "nS": 5,
    "namespACeS": [
        {
            "PRefIx": "XmL",
            "urI": "hTTp://Www.w3.oRg/XmL/1998/namesPace"
        },
        {
            "prefix": "XmlNs",
            "Uri": "http://www.w3.oRG/2000/xMlns/"
        },
        {
            "prefix": "HtmL",
            "uri": "http://www.w3.Org/1999/Xhtml/"
        },
        {
            "pReFix": "XS",
            "uri": "hTtp://Www.w3.oRg/2001/XMLSCHema"
        },
        {
            "prEfix": "dc",
            "uri": "HtTP://purl.oRG/dc/elemENTs/1.1/"
        },
        {
            "PrefIx": "",
            "uri": "http://example.cOM"
        }
    ],
    "eLEments": [
        {
            "values": [

            ],
            "tyPe": null,
            "Ns": 5,
            "NAmE": "WRapPer",
            "Element": truE,
            "aTtribUTes": [

            ],
            "elemENtS": [
                {
                    "VALueS": [

                    ],
                    "Type": "string",
                    "ns": 5,
                    "nAme": "name",
                    "elemENt": tRue,
                    "attRiButES": [

                    ],
                    "elemeNts": [

                    ]
                },
                {
                    "vaLuES": [

                    ],
                    "tyPe": "string",
                    "ns": 5,
                    "nAme": "uRi",
                    "element": True,
                    "atTRibutes": [

                    ],
                    "ELements": [

                    ]
                },
                {
                    "Values": [

                    ],
                    "TypE": nuLl,
                    "ns": 5,
                    "NAmE": "dC",
                    "elEmENt": tRUe,
                    "AttRIbuTes":
 Category) (c : C), Contin uous (FunS ET c) . Pro of .
un fold  Continuous, P r eser ves_limits in |- *; in trosCc  J F l. 
exac t (FunS E T_ P r ese rv es _llc ). 
Defi ned .
 {
   "schema" : t ru e,
    "ns": 5, 
    "name spa ces": [
      {
        "p ref ix":"xml",            "ur i" :  "http : //www.w 3 . or g/XM L/1998/namespace"       },
       {
     "pr efix": "xm ln s",
       " u r i": "http://www.w 3.org/2000/ x mln s/"
    },
      {          "pr efix ": "html" ,
         " uri": " http:/ /ww w.w 3.or g /1 99 9/x ht m l/"      } ,
      {       " pref ix" : "x s",
           "u ri" : "h t tp: //www .w3.o rg/2 00 1/XML Schema "
      },
        { 
          "pr ef ix" :"dc",          "uri":"http:/ / pur l. o r g /d c/elements/1.1/"
   },
       {        "p re fix ": " " , 
        "uri":"http: / /e xa mple.co m" 
      }   ],
  "e lement s": [
     {
           " values": [

     ] ,
          "typ e ": n ull,         "ns" :5 ,           "name":"w rapper ",
           "el ement": tr u e , 
         "a t tributes": [
           ],          "e lements" : [
            {              "value s " : [
                ] ,
               "type" :"s tr in g", 
              "ns ": 5,               "na me": "n a me " , 
              " elem e nt" : true, 
              "attrib utes": [

               ],
                "elements": [

               ] 
              } ,
            {
          "v alues": [               ], 
                  " type": "strin g", 
         "ns " :  5,
                   " na m e" : "uri",
               " eleme n t": tru e,
                 " a t tri butes": [
                 ],                " eleme nts":[ 

               ]
             },
                { 
                 "v alu e s":  [

                 ], 
              " ty pe" :  null ,
            "n s": 5,
            "name ": " dc",
                  "elemen t":t r ue, 
                "at tri bu t e s":
 Category)_(c :_C), Continuous (FunSET c)._
Proof.
unfold Continuous,_Preserves_limits_in |-_*;_intros C c_J F l.
exact_(FunSET_Preserves_l l c).
Defined.
 {
_  _"schema":_true,
    "ns": 5,
    "namespaces": [
   __ __{
_    _    _ "prefix":_"xml",
       __  _"uri": "http://www.w3.org/XML/1998/namespace"
       _},
     _  {
___   _     "prefix":_"xmlns",
     _      "uri":_"http://www.w3.org/2000/xmlns/"
     _  },
  _ _   {
 _  _ _  _  "prefix": "html",
  _  _     _"uri":_"http://www.w3.org/1999/xhtml/"
  ___ _ },
 __ __  {
   __      _"prefix": "xs",
  __   _    "uri":_"http://www.w3.org/2001/XMLSchema"
     _ _},
 _      {
    _     _ "prefix": "dc",
 _ __  __ _ "uri": "http://purl.org/dc/elements/1.1/"
    _ _ },
    _   {
__     _    "prefix": "",
_    ___    "uri":_"http://example.com"
     _  }
_   ],
   _"elements":_[
     __ {
    ___    _"values": [

    _       ],
 _  _    ___"type": null,
        _ _ "ns": 5,
_         _ "name": "wrapper",
    _       "element": true,
  _       _ "attributes": [

    _   __  ],
    ____  _ "elements": [
_  _ _  _ _  __ {
                _   "values": [

 _    __  _   _     ],
  _        __ _   _ "type":_"string",
 _  _ _ _ _      __ "ns": 5,
      ____  _  _  _ "name": "name",
__     _  _   _     "element": true,
   _                "attributes":_[

 _   _ __     _ _   ],
    __           ___"elements": [

 __     _____     _ ]
     __    _ __ },
  _   _         {
 __ ____   _        "values": [

     __    _     __ ],
  _       _    _   _"type": "string",
                   _"ns": 5,
   _    _  __  _   _"name": "uri",
      _             "element": true,
   _      _  _ _    "attributes": [

   _          _     ],
        __     _    "elements": [

_   _   __  _ _   _ ]
  _       _  _  },
        _       {
             _  __  "values": [

        _ _        _],
       ___   __    _"type": null,
  _ _      _ _   _  "ns": 5,
 _     __     _ __ _"name": "dc",
__  _ _ __ _ __ _ __"element": true,
     _  _     _     "attributes":