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<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">H</font> being  <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span><br/> for <font color="Olive" title="b2">X1</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b3">Y1</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">Y</font>  st <font color="Olive" title="b1">H</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><font color="Olive" title="b2">X1</font>,<font color="Olive" title="b3">Y1</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span> holds <br/>( ( <font color="Olive" title="b3">Y1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <span class="p1">(<span class="default"><a href="borsuk_1.html#K10" title="BORSUK_1:func.10">Pr1</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b1">H</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of <font color="Olive" title="b2">X1</font> ) &amp; ( <font color="Olive" title="b2">X1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <span class="p1">(<span class="default"><a href="borsuk_1.html#K11" title="BORSUK_1:func.11">Pr2</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b1">H</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of <font color="Olive" title="b3">Y1</font> ) )</span><br/><b>let </b><font color="Maroon" title="c3">H</font> be   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">X1</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">Y1</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">Y</font>  st <font color="Maroon" title="c3">H</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><font color="Olive" title="b1">X1</font>,<font color="Olive" title="b2">Y1</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span> holds <br/>( ( <font color="Olive" title="b2">Y1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <span class="p1">(<span class="default"><a href="borsuk_1.html#K10" title="BORSUK_1:func.10">Pr1</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of <font color="Olive" title="b1">X1</font> ) &amp; ( <font color="Olive" title="b1">X1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <span class="p1">(<span class="default"><a href="borsuk_1.html#K11" title="BORSUK_1:func.11">Pr2</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of <font color="Olive" title="b2">Y1</font> ) )</span><br/><b>let </b><font color="Maroon" title="c4">X1</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">Y1</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">Y</font>  st <font color="Maroon" title="c3">H</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><font color="Maroon" title="c4">X1</font>,<font color="Olive" title="b1">Y1</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span> holds <br/>( ( <font color="Olive" title="b1">Y1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <span class="p1">(<span class="default"><a href="borsuk_1.html#K10" title="BORSUK_1:func.10">Pr1</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of <font color="Maroon" title="c4">X1</font> ) &amp; ( <font color="Maroon" title="c4">X1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <span class="p1">(<span class="default"><a href="borsuk_1.html#K11" title="BORSUK_1:func.11">Pr2</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of <font color="Olive" title="b1">Y1</font> ) )</span><br/><b>let </b><font color="Maroon" title="c5">Y1</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">H</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><font color="Maroon" title="c4">X1</font>,<font color="Maroon" title="c5">Y1</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span> implies ( ( <font color="Maroon" title="c5">Y1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <span class="p1">(<span class="default"><a href="borsuk_1.html#K10" title="BORSUK_1:func.10">Pr1</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of <font color="Maroon" title="c4">X1</font> ) &amp; ( <font color="Maroon" title="c4">X1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <span class="p1">(<span class="default"><a href="borsuk_1.html#K11" title="BORSUK_1:func.11">Pr2</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of <font color="Maroon" title="c5">Y1</font> ) ) )</span><br/>









<a NAME="E1:64"/><i><font color="Green" title="E50">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <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">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#D5" target="_self" title="BORSUK_1:def.5">Def5</a></i>;<br/>
<b>assume </b><a NAME="E2:64"/><i><font color="Green" title="E51">A2</font></i>: 
<span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><font color="Maroon" title="c4">X1</font>,<font color="Maroon" title="c5">Y1</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c3">H</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="setfam_1.html#D12" title="SETFAM_1:def.12">SETFAM_1:def 12</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c5">Y1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <span class="p1">(<span class="default"><a href="borsuk_1.html#K10" title="BORSUK_1:func.10">Pr1</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of <font color="Maroon" title="c4">X1</font> ) &amp; ( <font color="Maroon" title="c4">X1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <span class="p1">(<span class="default"><a href="borsuk_1.html#K11" title="BORSUK_1:func.11">Pr2</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of <font color="Maroon" title="c5">Y1</font> ) )</span><br/>

<b>thus </b><a NAME="E3:64"/>
( <font color="Maroon" title="c5">Y1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <span class="p1">(<span class="default"><a href="borsuk_1.html#K10" title="BORSUK_1:func.10">Pr1</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of <font color="Maroon" title="c4">X1</font> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">X1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <span class="p1">(<span class="default"><a href="borsuk_1.html#K11" title="BORSUK_1:func.11">Pr2</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of <font color="Maroon" title="c5">Y1</font> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:64_1"/>
<font color="Maroon" title="c5">Y1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="borsuk_1.html#K10" title="BORSUK_1:func.10">Pr1</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of <font color="Maroon" title="c4">X1</font></span><br/>

<b>then consider </b><font color="Maroon" title="c6">y</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">Y</font><b> such that </b><br/><a NAME="E3:64_1"/><i><font color="Green" title="E52">A3</font></i>: 
<font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Y1</font>
 <b>by </b><i><a class="ref" href="subset_1.html#T10" title="SUBSET_1:th.10">SUBSET_1:10</a></i>;<br/>
<b>let </b><font color="Maroon" title="c7">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="setfam_1.html#D12" title="SETFAM_1:def.12">SETFAM_1:def 12</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c7">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X1</font> or <font color="Maroon" title="c7">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K10" title="BORSUK_1:func.10">Pr1</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E4:64_1"/><i><font color="Green" title="E53">A4</font></i>: 
<font color="Maroon" title="c7">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K10" title="BORSUK_1:func.10">Pr1</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font></span>)</span></span><br/>

<b>then reconsider </b><font color="Maroon" title="c8">x</font> = <font color="Maroon" title="c7">e</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font> ;<br/>
<a NAME="E6:64_1"/>
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c6">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><font color="Maroon" title="c4">X1</font>,<font color="Maroon" title="c5">Y1</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>
 
<b>by </b><i><a class="txt" href="borsuk_1.html#E3:64_1"><i><font color="Green" title="E52">A3</font></i></a>, <a class="txt" href="borsuk_1.html#E4:64_1"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c9">A</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E8:64_1"/><i><font color="Green" title="E54">A5</font></i>: 
( <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c6">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A</font> &amp; <font color="Maroon" title="c9">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">H</font> )
 <b>by </b><i><a class="txt" href="borsuk_1.html#E2:64"><i><font color="Green" title="E51">A2</font></i></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/>
<i><font color="Green" title="E55">A6</font></i>:  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="funct_3.html#K2" title="FUNCT_3:func.2">.:</a> <span class="p2">(<span class="default"><a href="funct_3.html#K9" title="FUNCT_3:func.9">pr1</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span> = 
 <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="funct_3.html#K9" title="FUNCT_3:func.9">pr1</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_3.html#D1" title="FUNCT_3:def.1">FUNCT_3:def 1</a></i>
<br/>.= 
 <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
<b>by </b><i><a class="ref" href="funct_3.html#D5" title="FUNCT_3:def.5">FUNCT_3:def 5</a></i>
;<br/>
<a NAME="E10:64_1"/>
<span class="p1">(<span class="default"><a href="funct_3.html#K2" title="FUNCT_3:func.2">.:</a> <span class="p2">(<span class="default"><a href="funct_3.html#K9" title="FUNCT_3:func.9">pr1</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="funct_3.html#K9" title="FUNCT_3:func.9">pr1</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c9">A</font>
 
<b>by </b><i><a class="txt" href="borsuk_1.html#E1:64"><i><font color="Green" title="E50">A1</font></i></a>, <a class="txt" href="borsuk_1.html#E8:64_1"><i><font color="Green" title="E54">A5</font></i></a>, <a class="ref" href="borsuk_1.html#T9" target="_self" title="BORSUK_1:th.9">Th9</a></i>;<br/>
<a NAME="E11:64_1"/><b>then </b><i><font color="Green" title="E56">A7</font></i>: 
<span class="p1">(<span class="default"><a href="funct_3.html#K9" title="FUNCT_3:func.9">pr1</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c9">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K10" title="BORSUK_1:func.10">Pr1</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font>
 
<b>by </b><i><a class="txt" href="borsuk_1.html#E1:64"><i><font color="Green" title="E50">A1</font></i></a>, <a class="txt" href="borsuk_1.html#E8:64_1"><i><font color="Green" title="E54">A5</font></i></a>, <a class="txt" href="borsuk_1.html#E9:64_1"><i><font color="Green" title="E55">A6</font></i></a>, <a class="ref" href="funct_1.html#D12" title="FUNCT_1:def.12">FUNCT_1:def 12</a></i>;<br/>
<a NAME="E12:64_1"/>
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c6">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E13:64_1"/><b>then </b><i><font color="Green" title="E57">A8</font></i>: 
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c6">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="funct_3.html#K9" title="FUNCT_3:func.9">pr1</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_3.html#D5" title="FUNCT_3:def.5">FUNCT_3:def 5</a></i>;<br/>
<a NAME="E14:64_1"/>
<font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="funct_3.html#K9" title="FUNCT_3:func.9">pr1</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c6">y</font>
 
<b>by </b><i><a class="ref" href="funct_3.html#D5" title="FUNCT_3:def.5">FUNCT_3:def 5</a></i>;<br/>
<a NAME="E15:64_1"/><b>then </b>
<font color="Maroon" title="c7">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_3.html#K9" title="FUNCT_3:func.9">pr1</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c9">A</font>
 
<b>by </b><i><a class="txt" href="borsuk_1.html#E8:64_1"><i><font color="Green" title="E54">A5</font></i></a>, <a class="txt" href="borsuk_1.html#E13:64_1"><i><font color="Green" title="E57">A8</font></i></a>, <a class="ref" href="funct_1.html#D12" title="FUNCT_1:def.12">FUNCT_1:def 12</a></i>;<br/>
<b>hence </b><a NAME="E16:64_1"/>
<font color="Maroon" title="c7">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K10" title="BORSUK_1:func.10">Pr1</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font></span>)</span>
 <b>by </b><i><a class="txt" href="borsuk_1.html#E11:64_1"><i><font color="Green" title="E56">A7</font></i></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E4:64"/>
<font color="Maroon" title="c4">X1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="borsuk_1.html#K11" title="BORSUK_1:func.11">Pr2</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font> is    <a href="setfam_1.html#M1" title="SETFAM_1:mode.1">Cover</a> of <font color="Maroon" title="c5">Y1</font></span><br/>

<b>then consider </b><font color="Maroon" title="c6">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E6:64"/><i><font color="Green" title="E52">A9</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X1</font>
 <b>by </b><i><a class="ref" href="subset_1.html#T10" title="SUBSET_1:th.10">SUBSET_1:10</a></i>;<br/>
<b>let </b><font color="Maroon" title="c7">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="setfam_1.html#D12" title="SETFAM_1:def.12">SETFAM_1:def 12</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c7">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Y1</font> or <font color="Maroon" title="c7">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K11" title="BORSUK_1:func.11">Pr2</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E7:64"/><i><font color="Green" title="E53">A10</font></i>: 
<font color="Maroon" title="c7">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Y1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K11" title="BORSUK_1:func.11">Pr2</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font></span>)</span></span><br/>

<b>then reconsider </b><font color="Maroon" title="c8">y</font> = <font color="Maroon" title="c7">e</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">Y</font> ;<br/>
<a NAME="E9:64"/>
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c8">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><font color="Maroon" title="c4">X1</font>,<font color="Maroon" title="c5">Y1</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>
 
<b>by </b><i><a class="txt" href="borsuk_1.html#E6:64"><i><font color="Green" title="E52">A9</font></i></a>, <a class="txt" href="borsuk_1.html#E7:64"><i><font color="Green" title="E53">A10</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c9">A</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E11:64"/><i><font color="Green" title="E54">A11</font></i>: 
( <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c8">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A</font> &amp; <font color="Maroon" title="c9">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">H</font> )
 <b>by </b><i><a class="txt" href="borsuk_1.html#E2:64"><i><font color="Green" title="E51">A2</font></i></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/>
<i><font color="Green" title="E55">A12</font></i>:  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="funct_3.html#K2" title="FUNCT_3:func.2">.:</a> <span class="p2">(<span class="default"><a href="funct_3.html#K10" title="FUNCT_3:func.10">pr2</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span> = 
 <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="funct_3.html#K10" title="FUNCT_3:func.10">pr2</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_3.html#D1" title="FUNCT_3:def.1">FUNCT_3:def 1</a></i>
<br/>.= 
 <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
<b>by </b><i><a class="ref" href="funct_3.html#D6" title="FUNCT_3:def.6">FUNCT_3:def 6</a></i>
;<br/>
<a NAME="E13:64"/>
<span class="p1">(<span class="default"><a href="funct_3.html#K2" title="FUNCT_3:func.2">.:</a> <span class="p2">(<span class="default"><a href="funct_3.html#K10" title="FUNCT_3:func.10">pr2</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="funct_3.html#K10" title="FUNCT_3:func.10">pr2</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c9">A</font>
 
<b>by </b><i><a class="txt" href="borsuk_1.html#E1:64"><i><font color="Green" title="E50">A1</font></i></a>, <a class="txt" href="borsuk_1.html#E11:64"><i><font color="Green" title="E54">A11</font></i></a>, <a class="ref" href="borsuk_1.html#T10" target="_self" title="BORSUK_1:th.10">Th10</a></i>;<br/>
<a NAME="E14:64"/><b>then </b><i><font color="Green" title="E56">A13</font></i>: 
<span class="p1">(<span class="default"><a href="funct_3.html#K10" title="FUNCT_3:func.10">pr2</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c9">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K11" title="BORSUK_1:func.11">Pr2</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font>
 
<b>by </b><i><a class="txt" href="borsuk_1.html#E1:64"><i><font color="Green" title="E50">A1</font></i></a>, <a class="txt" href="borsuk_1.html#E11:64"><i><font color="Green" title="E54">A11</font></i></a>, <a class="txt" href="borsuk_1.html#E12:64"><i><font color="Green" title="E55">A12</font></i></a>, <a class="ref" href="funct_1.html#D12" title="FUNCT_1:def.12">FUNCT_1:def 12</a></i>;<br/>
<a NAME="E15:64"/>
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c8">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E16:64"/><b>then </b><i><font color="Green" title="E57">A14</font></i>: 
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c8">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="funct_3.html#K10" title="FUNCT_3:func.10">pr2</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_3.html#D6" title="FUNCT_3:def.6">FUNCT_3:def 6</a></i>;<br/>
<a NAME="E17:64"/>
<font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="funct_3.html#K10" title="FUNCT_3:func.10">pr2</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c8">y</font>
 
<b>by </b><i><a class="ref" href="funct_3.html#D6" title="FUNCT_3:def.6">FUNCT_3:def 6</a></i>;<br/>
<a NAME="E18:64"/><b>then </b>
<font color="Maroon" title="c7">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_3.html#K10" title="FUNCT_3:func.10">pr2</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c9">A</font>
 
<b>by </b><i><a class="txt" href="borsuk_1.html#E11:64"><i><font color="Green" title="E54">A11</font></i></a>, <a class="txt" href="borsuk_1.html#E16:64"><i><font color="Green" title="E57">A14</font></i></a>, <a class="ref" href="funct_1.html#D12" title="FUNCT_1:def.12">FUNCT_1:def 12</a></i>;<br/>
<b>hence </b><a NAME="E19:64"/>
<font color="Maroon" title="c7">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_1.html#K11" title="BORSUK_1:func.11">Pr2</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">H</font></span>)</span>
 <b>by </b><i><a class="txt" href="borsuk_1.html#E14:64"><i><font color="Green" title="E56">A13</font></i></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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