<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">T1</font>, <font color="Maroon" title="c2">T2</font> be   <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">  <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <span class="p1">(<span class="default"><a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c1">T1</font></span>)</span> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <span class="p1">(<span class="default"><a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c2">T2</font></span>)</span></span><br/>



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_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="E1:13_1"/>
( <font color="Maroon" title="c1">T1</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  or <font color="Maroon" title="c2">T2</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  or (  not <font color="Maroon" title="c1">T1</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp;  not <font color="Maroon" title="c2">T2</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_1"><span class="kw">suppose </span></a><a NAME="E1:13_1_1"/>
( <font color="Maroon" title="c1">T1</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  or <font color="Maroon" title="c2">T2</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">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="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <span class="p1">(<span class="default"><a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c1">T1</font></span>)</span> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <span class="p1">(<span class="default"><a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c2">T2</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:13_1_1"/>
 <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <span class="p1">(<span class="default"><a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c1">T1</font></span>)</span> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <span class="p1">(<span class="default"><a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c2">T2</font></span>)</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><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_2"><span class="kw">suppose </span></a><a NAME="E1:13_1_2"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
(  not <font color="Maroon" title="c1">T1</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp;  not <font color="Maroon" title="c2">T2</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">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="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <span class="p1">(<span class="default"><a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c1">T1</font></span>)</span> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <span class="p1">(<span class="default"><a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c2">T2</font></span>)</span></span><br/><div class="add"><span class="kw">consider </span><font color="Maroon" title="c3">B2</font> being   <a href="cantor_1.html#NM1" title="CANTOR_1:NM.1">Basis</a> of <font color="Maroon" title="c2">T2</font><span class="kw"> such that </span><br/><a NAME="E3:13_1_2"/><span class="lab"><font color="Green" title="E8">A2</font></span>: 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c2">T2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel23.html#T74" onmouseover="rs('waybel23/T74')" onmouseout="rh()">WAYBEL23:74</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c4">B1</font> being   <a href="cantor_1.html#NM1" title="CANTOR_1:NM.1">Basis</a> of <font color="Maroon" title="c1">T1</font><span class="kw"> such that </span><br/><a NAME="E5:13_1_2"/><span class="lab"><font color="Green" title="E9">A3</font></span>: 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c4">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c1">T1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel23.html#T74" onmouseover="rs('waybel23/T74')" onmouseout="rh()">WAYBEL23:74</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c5">B12</font> = <span class="p1"> { <span class="default"> <span class="p2"><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">[:</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">:]</a></span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T1</font>, <font color="Olive" title="b2">b</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">T2</font> : ( <font color="Olive" title="b1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">B1</font> &amp; <font color="Olive" title="b2">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">B2</font> ) </span> } </span>  as   <a href="cantor_1.html#NM1" title="CANTOR_1:NM.1">Basis</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1_2"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="yellow_9.html#T40" onmouseover="rs('yellow_9/T40')" onmouseout="rh()">YELLOW_9:40</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c6">B1</font> = <font color="Maroon" title="c4">B1</font>, <font color="Maroon" title="c7">B2</font> = <font color="Maroon" title="c3">B2</font>, <font color="Maroon" title="c8">B12</font> = <font color="Maroon" title="c5">B12</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1_2"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="yellow12.html#T34" onmouseover="rs('yellow12/T34')" onmouseout="rh()">YELLOW12:34</a></span>;<br/><span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c6">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>) <span class="kw">-&gt; </span>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  = <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default">$1 <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a></span>)</span>,<span class="p2">(<span class="default">$1 <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/><a NAME="E8:13_1_2"/><span class="lab"><font color="Green" title="E10">A4</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c6">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>) is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c8">B12</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c6">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</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"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c9">x</font>) is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c8">B12</font></span><br/>

<a NAME="E1:13_1_2_1"/>
( <font color="Maroon" title="c9">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">B1</font> &amp; <font color="Maroon" title="c9">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c7">B2</font> )
 
;<br/>
<a NAME="E2:13_1_2_1"/><span class="kw">then </span>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c9">x</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">B12</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E3:13_1_2_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c9">x</font>) is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c8">B12</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><span class="kw">consider </span><font color="Maroon" title="c9">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c6">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<font color="Maroon" title="c8">B12</font><span class="kw"> such that </span><br/><a NAME="E10:13_1_2"/><span class="lab"><font color="Green" title="E11">A5</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c6">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> holds  <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="funct_2.html#S9" onmouseover="rs('funct_2/S9')" onmouseout="rh()">FUNCT_2:sch 9</a>(<a class="txt" href="#E8:13_1_2"><span class="lab"><font color="Green" title="E10">A4</font></span></a>);<br/></span><a NAME="E11:13_1_2"/><span class="lab"><font color="Green" title="E12">A6</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c6">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/><a NAME="E12:13_1_2"/>
<font color="Maroon" title="c8">B12</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c9">f</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_2_2"><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> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</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"> (  not <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">B12</font> or <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN: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><br/>

<span class="kw">assume </span><a NAME="E1:13_1_2_2"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">B12</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="c10">x</font> <a href="hidden.html#R2" title="HIDDEN: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><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">a</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T1</font>, <font color="Maroon" title="c12">b</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">T2</font><span class="kw"> such that </span><br/><a NAME="E3:13_1_2_2"/><span class="lab"><font color="Green" title="E13">A7</font></span>: 
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">[:</a><span class="default"><font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font></span><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">:]</a></span>
 <span class="kw">and </span><br/><a NAME="E4:13_1_2_2"/><span class="lab"><font color="Green" title="E14">A8</font></span>: 
( <font color="Maroon" title="c11">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">B1</font> &amp; <font color="Maroon" title="c12">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c7">B2</font> )
 ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">ab</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c6">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13_1_2_2"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" onmouseover="rs('zfmisc_1/T87')" onmouseout="rh()">ZFMISC_1:87</a></span>;<br/>
<a NAME="E6:13_1_2_2"/>
( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a</font> &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b</font> )
 
;<br/>
<a NAME="E7:13_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">ab</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1_2"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E3:13_1_2_2"><span class="lab"><font color="Green" title="E13">A7</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:13_1_2_2"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN: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="txt" href="#E11:13_1_2"><span class="lab"><font color="Green" title="E12">A6</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</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="E13:13_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A9</font></span>: 
(  <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c8">B12</font> &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c8">B12</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c6">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:13_1_2"><span class="lab"><font color="Green" title="E12">A6</font></span></a>, <a class="ref" href="card_1.html#T12" onmouseover="rs('card_1/T12')" onmouseout="rh()">CARD_1:12</a>, <a class="ref" href="waybel23.html#T73" onmouseover="rs('waybel23/T73')" onmouseout="rh()">WAYBEL23:73</a></span>;<br/> <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c6">B1</font>,<font color="Maroon" title="c7">B2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> = 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c6">B1</font></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c7">B2</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_2.html#T7" onmouseover="rs('card_2/T7')" onmouseout="rh()">CARD_2:7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c6">B1</font></span>)</span> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c7">B2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_2.html#D2" onmouseover="rs('card_2/D2')" onmouseout="rh()">CARD_2:def 2</a></span>
;<br/><span class="kw">hence </span><a NAME="E15:13_1_2"/>
 <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <span class="p1">(<span class="default"><a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c1">T1</font></span>)</span> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <span class="p1">(<span class="default"><a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c2">T2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1_2"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E3:13_1_2"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="txt" href="#E13:13_1_2"><span class="lab"><font color="Green" title="E13">A9</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>

</div>
