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<span class="kw">let </span><font color="Maroon" title="c1">iC</font> be   <a href="finset_1.html#NV2" title="FINSET_1:NV.2">infinite</a>  <a href="card_1.html#NM1" title="CARD_1:NM.1">Cardinal</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">TM</font> being   <a href="pcomps_1.html#V3" title="PCOMPS_1:attr.3">metrizable</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>  st (  for <font color="Olive" title="b2">Am</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">TM</font>  st <font color="Olive" title="b2">Am</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Olive" title="b2">Am</font> is  <a href="tex_2.html#V2" title="TEX_2:attr.2">discrete</a>  holds <br/> <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b2">Am</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">iC</font> ) holds <br/> for <font color="Olive" title="b2">Am</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">TM</font>  st <font color="Olive" title="b2">Am</font> is  <a href="tex_2.html#V2" title="TEX_2:attr.2">discrete</a>  holds <br/> <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b2">Am</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">iC</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">TM</font> be   <a href="pcomps_1.html#V3" title="PCOMPS_1:attr.3">metrizable</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">Am</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">TM</font>  st <font color="Olive" title="b1">Am</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Olive" title="b1">Am</font> is  <a href="tex_2.html#V2" title="TEX_2:attr.2">discrete</a>  holds <br/> <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">Am</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">iC</font> ) implies  for <font color="Olive" title="b1">Am</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">TM</font>  st <font color="Olive" title="b1">Am</font> is  <a href="tex_2.html#V2" title="TEX_2:attr.2">discrete</a>  holds <br/> <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">Am</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">iC</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:28"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
 for <font color="Olive" title="b1">Am</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">TM</font>  st <font color="Olive" title="b1">Am</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Olive" title="b1">Am</font> is  <a href="tex_2.html#V2" title="TEX_2:attr.2">discrete</a>  holds <br/> <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">Am</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">iC</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Am</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">TM</font>  st <font color="Olive" title="b1">Am</font> is  <a href="tex_2.html#V2" title="TEX_2:attr.2">discrete</a>  holds <br/> <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">Am</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">iC</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">Am</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">TM</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">Am</font> is  <a href="tex_2.html#V2" title="TEX_2:attr.2">discrete</a>  implies  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">Am</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">iC</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:28"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<font color="Maroon" title="c3">Am</font> is  <a href="tex_2.html#V2" title="TEX_2:attr.2">discrete</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">Am</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">iC</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:28_1"/>
( <font color="Maroon" title="c3">Am</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  or  not <font color="Maroon" title="c3">Am</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1"><span class="kw">suppose </span></a><a NAME="E1:28_1_1"/>
<font color="Maroon" title="c3">Am</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">Am</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">iC</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:28_1_1"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">Am</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">iC</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_2"><span class="kw">suppose </span></a><a NAME="E1:28_1_2"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
 not <font color="Maroon" title="c3">Am</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">Am</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">iC</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">Tm</font> = <font color="Maroon" title="c2">TM</font> as   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pcomps_1.html#V3" title="PCOMPS_1:attr.3">metrizable</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a> ;<br/><a NAME="E3:28_1_2"/>
<font color="Maroon" title="c3">Am</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c3">Am</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_topc.html#T18" onmouseover="rs('pre_topc/T18')" onmouseout="rh()">PRE_TOPC:18</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">ClA</font> =  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c3">Am</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c4">Tm</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28_1_2"><span class="lab"><font color="Green" title="E17">A3</font></span></a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c6">TA</font> = <font color="Maroon" title="c4">Tm</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c5">ClA</font>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c7">A9</font> = <font color="Maroon" title="c3">Am</font> as   <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">Tm</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c5">ClA</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="ref" href="metrizts.html#T12" target="_self" onmouseover="rs('metrizts/T12')" onmouseout="rh()">Th12</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c8">F</font> being   <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a>   <a href="tops_2.html#V2" title="TOPS_2:attr.2">closed</a>  <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">Tm</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c5">ClA</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E7:28_1_2"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
<font color="Maroon" title="c7">A9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c8">F</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topgen_4.html#D6" onmouseover="rs('topgen_4/D6')" onmouseout="rh()">TOPGEN_4:def 6</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c9">f</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <font color="Maroon" title="c8">F</font><span class="kw"> such that </span><br/><a NAME="E9:28_1_2"/><span class="lab"><font color="Green" title="E19">A5</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28_1_2"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E7:28_1_2"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="card_3.html#T96" onmouseover="rs('card_3/T96')" onmouseout="rh()">CARD_3:96</a>, <a class="ref" href="zfmisc_1.html#T2" onmouseover="rs('zfmisc_1/T2')" onmouseout="rh()">ZFMISC_1:2</a></span>;<br/><a NAME="E10:28_1_2"/><span class="lab"><font color="Green" title="E20">A6</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c9">f</font> holds <br/> <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">iC</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="28_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c10">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c9">f</font> implies  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font></span>)</span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">iC</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:28_1_2_1"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c9">f</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font></span>)</span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">iC</font></span><br/>

<a NAME="E2:28_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A7</font></span>: 
<font color="Maroon" title="c9">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c9">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">fx</font> = <font color="Maroon" title="c9">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">Tm</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c5">ClA</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:28_1_2"><span class="lab"><font color="Green" title="E19">A5</font></span></a></span>;<br/>
<a NAME="E4:28_1_2_1"/><span class="lab"><font color="Green" title="E22">A8</font></span>: 
<font color="Maroon" title="c9">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">Am</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:28_1_2"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E2:28_1_2_1"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="ref" href="zfmisc_1.html#T74" onmouseover="rs('zfmisc_1/T74')" onmouseout="rh()">ZFMISC_1:74</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c12">Fx</font> = <font color="Maroon" title="c9">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">TM</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T1" onmouseover="rs('xboole_1/T1')" onmouseout="rh()">XBOOLE_1:1</a></span>;<br/>
<a NAME="E6:28_1_2_1"/>
(  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Tm</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c5">ClA</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">ClA</font> &amp; <font color="Maroon" title="c11">fx</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28_1_2_1"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="ref" href="pre_topc.html#D5" onmouseover="rs('pre_topc/D5')" onmouseout="rh()">PRE_TOPC:def 5</a>, <a class="ref" href="tops_2.html#D2" onmouseover="rs('tops_2/D2')" onmouseout="rh()">TOPS_2:def 2</a></span>;<br/>
<a NAME="E7:28_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">Fx</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T8" onmouseover="rs('tsep_1/T8')" onmouseout="rh()">TSEP_1:8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:28_1_2_1"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font></span>)</span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">iC</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E4:28_1_2_1"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="ref" href="tex_2.html#T22" onmouseover="rs('tex_2/T22')" onmouseout="rh()">TEX_2:22</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E11:28_1_2"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c9">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28_1_2"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E7:28_1_2"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="card_1.html#T47" onmouseover="rs('card_1/T47')" onmouseout="rh()">CARD_1:47</a>, <a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a>, <a class="ref" href="zfmisc_1.html#T2" onmouseover="rs('zfmisc_1/T2')" onmouseout="rh()">ZFMISC_1:2</a></span>;<br/><a NAME="E12:28_1_2"/><span class="kw">then </span>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Maroon" title="c9">f</font></span>)</span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c1">iC</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:28_1_2"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="ref" href="card_2.html#T86" onmouseover="rs('card_2/T86')" onmouseout="rh()">CARD_2:86</a></span>;<br/><span class="kw">hence </span><a NAME="E13:28_1_2"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">Am</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">iC</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:28_1_2"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E9:28_1_2"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="metrizts.html#E18"><span class="lab"><font color="Green" title="E12">Lm5</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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