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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> <br/>  for <font color="Olive" title="b2">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">T</font>,<font color="Olive" title="b1">S</font>  st <font color="Maroon" title="c1">T</font> is  <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a>  &amp; <font color="Olive" title="b2">f</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  &amp;  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Olive" title="b1">S</font> holds <br/><font color="Olive" title="b1">S</font> is  <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">S</font>  st <font color="Maroon" title="c1">T</font> is  <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a>  &amp; <font color="Olive" title="b1">f</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  &amp;  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">S</font> holds <br/><font color="Maroon" title="c2">S</font> is  <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">T</font> is  <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a>  &amp; <font color="Maroon" title="c3">f</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  &amp;  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">S</font> implies <font color="Maroon" title="c2">S</font> is  <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a>  )</span><br/>





<span class="kw">assume </span><a NAME="E1:19"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
<font color="Maroon" title="c1">T</font> is  <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">f</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  or  not  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">S</font> or <font color="Maroon" title="c2">S</font> is  <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a>  )</span><br/>

<a NAME="E2:19"/>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E3:19"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A2</font></span>: 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T76" title="FUNCT_1:th.76">FUNCT_1:76</a></span>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E4:19"/><span class="lab"><font color="Green" title="E13">A3</font></span>: 
<font color="Maroon" title="c3">f</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> 
 <span class="kw">and </span><br/><a NAME="E5:19"/><span class="lab"><font color="Green" title="E14">A4</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">S</font> is  <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">F</font> be   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c2">S</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="compts_1.html#D1" target="_self" title="COMPTS_1:def.1">COMPTS_1:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">F</font> is   <a href="struct_0.html#NM13" title="STRUCT_0:NM.13">Cover</a> of <font color="Maroon" title="c2">S</font> &amp; <font color="Maroon" title="c4">F</font> is  <a href="tops_2.html#V1" title="TOPS_2:attr.1">open</a>  implies  ex <font color="Olive" title="b1">G</font> being   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c2">S</font> st <br/>( <font color="Olive" title="b1">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">F</font> &amp; <font color="Olive" title="b1">G</font> is   <a href="struct_0.html#NM13" title="STRUCT_0:NM.13">Cover</a> of <font color="Maroon" title="c2">S</font> &amp; <font color="Olive" title="b1">G</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  ) )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E6:19"/><span class="lab"><font color="Green" title="E15">A5</font></span>: 
<font color="Maroon" title="c4">F</font> is   <a href="struct_0.html#NM13" title="STRUCT_0:NM.13">Cover</a> of <font color="Maroon" title="c2">S</font>
 <span class="kw">and </span><br/><a NAME="E7:19"/><span class="lab"><font color="Green" title="E16">A6</font></span>: 
<font color="Maroon" title="c4">F</font> is  <a href="tops_2.html#V1" title="TOPS_2:attr.1">open</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">G</font> being   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c2">S</font> st <br/>( <font color="Olive" title="b1">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">F</font> &amp; <font color="Olive" title="b1">G</font> is   <a href="struct_0.html#NM13" title="STRUCT_0:NM.13">Cover</a> of <font color="Maroon" title="c2">S</font> &amp; <font color="Olive" title="b1">G</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">F1</font> = <font color="Maroon" title="c4">F</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">G</font> = <span class="p1">(<span class="default"><a href="funct_3.html#K3" title="FUNCT_3:func.3">"</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <font color="Maroon" title="c4">F</font> as   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="tops_2.html#T42" title="TOPS_2:th.42">TOPS_2:42</a></span>;<br/>
 <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c6">G</font> = 
<font color="Maroon" title="c3">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c4">F</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="ref" href="funct_3.html#T26" title="FUNCT_3:th.26">FUNCT_3:26</a></span>
<br/>.= 
<font color="Maroon" title="c3">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c3">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="txt" href="#E6:19"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="ref" href="setfam_1.html#T45" title="SETFAM_1:th.45">SETFAM_1:45</a></span>
<br/>.= 
<font color="Maroon" title="c3">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T113" title="RELAT_1:th.113">RELAT_1:113</a></span>
<br/>.= 
<font color="Maroon" title="c3">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>
;<br/>
<a NAME="E10:19"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A7</font></span>: 
<font color="Maroon" title="c6">G</font> is   <a href="struct_0.html#NM13" title="STRUCT_0:NM.13">Cover</a> of <font color="Maroon" title="c1">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:19"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="ref" href="setfam_1.html#D11" title="SETFAM_1:def.11">SETFAM_1:def 11</a></span>;<br/>
<a NAME="E11:19"/><span class="lab"><font color="Green" title="E18">A8</font></span>: 
<span class="p1">(<span class="default"><a href="funct_3.html#K2" title="FUNCT_3:func.2">.:</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_3.html#K2" title="FUNCT_3:func.2">.:</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T75" title="FUNCT_1:th.75">FUNCT_1:75</a></span>;<br/>
<a NAME="E12:19"/>
<span class="p1">(<span class="default"><a href="funct_3.html#K2" title="FUNCT_3:func.2">.:</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_3.html#K3" title="FUNCT_3:func.3">"</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_3.html#K2" title="FUNCT_3:func.2">.:</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_3.html#K2" title="FUNCT_3:func.2">.:</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Maroon" title="c4">F</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#T29" title="FUNCT_3:th.29">FUNCT_3:29</a>, <a class="ref" href="relat_1.html#T123" title="RELAT_1:th.123">RELAT_1:123</a></span>;<br/>
<a NAME="E13:19"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A9</font></span>: 
<span class="p1">(<span class="default"><a href="funct_3.html#K2" title="FUNCT_3:func.2">.:</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c6">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:19"><span class="lab"><font color="Green" title="E18">A8</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E14:19"/>
<font color="Maroon" title="c6">G</font> is  <a href="tops_2.html#V1" title="TOPS_2:attr.1">open</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:19"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="txt" href="#E7:19"><span class="lab"><font color="Green" title="E16">A6</font></span></a>, <a class="ref" href="tops_2.html#T47" title="TOPS_2:th.47">TOPS_2:47</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">G9</font> being   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font><span class="kw"> such that </span><br/><a NAME="E16:19"/><span class="lab"><font color="Green" title="E20">A10</font></span>: 
<font color="Maroon" title="c7">G9</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">G</font>
 <span class="kw">and </span><br/><a NAME="E17:19"/><span class="lab"><font color="Green" title="E21">A11</font></span>: 
<font color="Maroon" title="c7">G9</font> is   <a href="struct_0.html#NM13" title="STRUCT_0:NM.13">Cover</a> of <font color="Maroon" title="c1">T</font>
 <span class="kw">and </span><br/><a NAME="E18:19"/><span class="lab"><font color="Green" title="E22">A12</font></span>: 
<font color="Maroon" title="c7">G9</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E10:19"><span class="lab"><font color="Green" title="E17">A7</font></span></a>, <a class="ref" href="compts_1.html#D1" target="_self" title="COMPTS_1:def.1">Def3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">F9</font> = <span class="p1">(<span class="default"><a href="funct_3.html#K2" title="FUNCT_3:func.2">.:</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c7">G9</font> as   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c2">S</font> ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c8">F9</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">F9</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">F</font> &amp; <font color="Maroon" title="c8">F9</font> is   <a href="struct_0.html#NM13" title="STRUCT_0:NM.13">Cover</a> of <font color="Maroon" title="c2">S</font> &amp; <font color="Maroon" title="c8">F9</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  )</span><br/>

<a NAME="E20:19"/>
<span class="p1">(<span class="default"><a href="funct_3.html#K2" title="FUNCT_3:func.2">.:</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c7">G9</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_3.html#K2" title="FUNCT_3:func.2">.:</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c6">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:19"><span class="lab"><font color="Green" title="E20">A10</font></span></a>, <a class="ref" href="relat_1.html#T123" title="RELAT_1:th.123">RELAT_1:123</a></span>;<br/>
<span class="kw">hence </span><a NAME="E21:19"/>
<font color="Maroon" title="c8">F9</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:19"><span class="lab"><font color="Green" title="E19">A9</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">F9</font> is   <a href="struct_0.html#NM13" title="STRUCT_0:NM.13">Cover</a> of <font color="Maroon" title="c2">S</font> &amp; <font color="Maroon" title="c8">F9</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  )</span><br/>

<a NAME="E22:19"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">then </span> <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c8">F9</font> = 
<font color="Maroon" title="c3">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c7">G9</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#T14" title="FUNCT_3:th.14">FUNCT_3:14</a></span>
<br/>.= 
<font color="Maroon" title="c3">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:19"><span class="lab"><font color="Green" title="E21">A11</font></span></a>, <a class="ref" href="setfam_1.html#T45" title="SETFAM_1:th.45">SETFAM_1:45</a></span>
<br/>.= 
<font color="Maroon" title="c3">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>
<br/>.= 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">S</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="ref" href="relat_1.html#T113" title="RELAT_1:th.113">RELAT_1:113</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E24:19"/>
<font color="Maroon" title="c8">F9</font> is   <a href="struct_0.html#NM13" title="STRUCT_0:NM.13">Cover</a> of <font color="Maroon" title="c2">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="setfam_1.html#D11" title="SETFAM_1:def.11">SETFAM_1:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c8">F9</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> </span><br/>

<span class="kw">thus </span><a NAME="E25:19"/>
<font color="Maroon" title="c8">F9</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:19"><span class="lab"><font color="Green" title="E22">A12</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
