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<span class="kw">let </span><font color="Maroon" title="c1">T</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" 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">a</font>, <font color="Olive" title="b2">b</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font><br/>  for <font color="Olive" title="b3">P</font>, <font color="Olive" title="b4">Q</font>, <font color="Olive" title="b5">R</font> being    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>  st <font color="Olive" title="b3">P</font>,<font color="Olive" title="b4">Q</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a>  &amp; <font color="Olive" title="b4">Q</font>,<font color="Olive" title="b5">R</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a>  holds <br/><font color="Olive" title="b3">P</font>,<font color="Olive" title="b5">R</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</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">P</font>, <font color="Olive" title="b2">Q</font>, <font color="Olive" title="b3">R</font> being    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>  st <font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">Q</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a>  &amp; <font color="Olive" title="b2">Q</font>,<font color="Olive" title="b3">R</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a>  holds <br/><font color="Olive" title="b1">P</font>,<font color="Olive" title="b3">R</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> </span><br/>





<a NAME="E1:100"/>
1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/>
<a NAME="E2:100"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A1</font></span>: 
1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topmetr.html#T18" onmouseover="rs('topmetr/T18')" onmouseout="rh()">TOPMETR:18</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">B02</font> = <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T40" onmouseover="rs('borsuk_1/T40')" onmouseout="rh()">BORSUK_1:40</a>, <a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a>, <a class="ref" href="xxreal_1.html#T34" onmouseover="rs('xxreal_1/T34')" onmouseout="rh()">XXREAL_1:34</a></span>;<br/>
<a NAME="E4:100"/><span class="lab"><font color="Green" title="E81">A2</font></span>: 
1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/>
<a NAME="E5:100"/><span class="lab"><font color="Green" title="E82">A3</font></span>: 
1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/>
<a NAME="E6:100"/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">A4</font></span>: 
1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topmetr.html#T18" onmouseover="rs('topmetr/T18')" onmouseout="rh()">TOPMETR:18</a></span>;<br/>
<a NAME="E7:100"/>
<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T40" onmouseover="rs('borsuk_1/T40')" onmouseout="rh()">BORSUK_1:40</a>, <a class="ref" href="xxreal_1.html#T34" onmouseover="rs('xxreal_1/T34')" onmouseout="rh()">XXREAL_1:34</a></span>;<br/>
<a NAME="E8:100"/><span class="kw">then </span><span class="lab"><font color="Green" title="E84">A5</font></span>: 
<span class="p1"><a href="mcart_1.html#K8" title="MCART_1:func.8">[:</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span><a href="mcart_1.html#K8" title="MCART_1:func.8">:]</a></span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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 <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></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="borsuk_1.html#T40" onmouseover="rs('borsuk_1/T40')" onmouseout="rh()">BORSUK_1:40</a>, <a class="ref" href="zfmisc_1.html#T96" onmouseover="rs('zfmisc_1/T96')" onmouseout="rh()">ZFMISC_1:96</a></span>;<br/>
<a NAME="E9:100"/><span class="lab"><font color="Green" title="E85">A6</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topmetr.html#T18" onmouseover="rs('topmetr/T18')" onmouseout="rh()">TOPMETR:18</a></span>;<br/>
<a NAME="E10:100"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">Ewa</font> = <span class="p1"><a href="mcart_1.html#K8" title="MCART_1:func.8">[:</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span><a href="mcart_1.html#K8" title="MCART_1:func.8">:]</a></span> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></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="#E8:100"><span class="lab"><font color="Green" title="E84">A5</font></span></a>, <a class="txt" href="#E4:100"><span class="lab"><font color="Green" title="E81">A2</font></span></a>, <a class="ref" href="borsuk_1.html#D2" onmouseover="rs('borsuk_1/D2')" onmouseout="rh()">BORSUK_1:def 2</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">T1</font> = <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c5">Ewa</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">P2</font> =  <a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1,<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>,<span class="p1">(<span class="default">(<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>) as   <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1)</span>)</span>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="topmetr.html#T20" onmouseover="rs('topmetr/T20')" onmouseout="rh()">TOPMETR:20</a>, <a class="ref" href="treal_1.html#T12" onmouseover="rs('treal_1/T12')" onmouseout="rh()">TREAL_1:12</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">P1</font> =  <a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>,<span class="p1">(<span class="default">(<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>) as   <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>)</span>)</span>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="topmetr.html#T20" onmouseover="rs('topmetr/T20')" onmouseout="rh()">TOPMETR:20</a>, <a class="ref" href="treal_1.html#T12" onmouseover="rs('treal_1/T12')" onmouseout="rh()">TREAL_1:12</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c9">P</font>, <font color="Maroon" title="c10">Q</font>, <font color="Maroon" title="c11">R</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</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="c9">P</font>,<font color="Maroon" title="c10">Q</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a>  &amp; <font color="Maroon" title="c10">Q</font>,<font color="Maroon" title="c11">R</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a>  implies <font color="Maroon" title="c9">P</font>,<font color="Maroon" title="c11">R</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a>  )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E14:100"/><span class="lab"><font color="Green" title="E86">A7</font></span>: 
<font color="Maroon" title="c9">P</font>,<font color="Maroon" title="c10">Q</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 <span class="kw">and </span><br/><a NAME="E15:100"/><span class="lab"><font color="Green" title="E87">A8</font></span>: 
<font color="Maroon" title="c10">Q</font>,<font color="Maroon" title="c11">R</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</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="c9">P</font>,<font color="Maroon" title="c11">R</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> </span><br/>

<span class="kw">consider </span><font color="Maroon" title="c12">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span>,<font color="Maroon" title="c1">T</font><span class="kw"> such that </span><br/><a NAME="E17:100"/><span class="lab"><font color="Green" title="E88">A9</font></span>: 
<font color="Maroon" title="c12">f</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> 
 <span class="kw">and </span><br/><a NAME="E18:100"/><span class="lab"><font color="Green" title="E89">A10</font></span>: 
 for <font color="Olive" title="b1">s</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> holds <br/> ( <font color="Maroon" title="c12">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">s</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font> &amp; <font color="Maroon" title="c12">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">s</font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Q</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font> &amp; (  for <font color="Olive" title="b2">t</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> holds <br/> ( <font color="Maroon" title="c12">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Olive" title="b2">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c12">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Olive" title="b2">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> ) ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:100"><span class="lab"><font color="Green" title="E86">A7</font></span></a></span>;<br/>
<a NAME="E19:100"/><span class="lab"><font color="Green" title="E90">A11</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topmetr.html#T18" onmouseover="rs('topmetr/T18')" onmouseout="rh()">TOPMETR:18</a></span>;<br/>
<a NAME="E20:100"/>
<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T40" onmouseover="rs('borsuk_1/T40')" onmouseout="rh()">BORSUK_1:40</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c13">A01</font> = <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c14">B01</font> = <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T40" onmouseover="rs('borsuk_1/T40')" onmouseout="rh()">BORSUK_1:40</a>, <a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a>, <a class="ref" href="xxreal_1.html#T34" onmouseover="rs('xxreal_1/T34')" onmouseout="rh()">XXREAL_1:34</a></span>;<br/>
<a NAME="E23:100"/><span class="lab"><font color="Green" title="E91">A12</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topmetr.html#T18" onmouseover="rs('topmetr/T18')" onmouseout="rh()">TOPMETR:18</a></span>;<br/>
<a NAME="E24:100"/>
<font color="Maroon" title="c13">A01</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T40" onmouseover="rs('borsuk_1/T40')" onmouseout="rh()">BORSUK_1:40</a></span>;<br/>
<a NAME="E25:100"/><span class="kw">then </span><span class="lab"><font color="Green" title="E92">A13</font></span>: 
 <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c13">A01</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T93" onmouseover="rs('tsep_1/T93')" onmouseout="rh()">TSEP_1:93</a></span>;<br/>
<a NAME="E26:100"/>
<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T40" onmouseover="rs('borsuk_1/T40')" onmouseout="rh()">BORSUK_1:40</a>, <a class="ref" href="xxreal_1.html#T34" onmouseover="rs('xxreal_1/T34')" onmouseout="rh()">XXREAL_1:34</a></span>;<br/>
<a NAME="E27:100"/><span class="kw">then </span><span class="lab"><font color="Green" title="E93">A14</font></span>: 
<span class="p1"><a href="mcart_1.html#K8" title="MCART_1:func.8">[:</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span><a href="mcart_1.html#K8" title="MCART_1:func.8">:]</a></span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</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 <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></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="borsuk_1.html#T40" onmouseover="rs('borsuk_1/T40')" onmouseout="rh()">BORSUK_1:40</a>, <a class="ref" href="zfmisc_1.html#T96" onmouseover="rs('zfmisc_1/T96')" onmouseout="rh()">ZFMISC_1:96</a></span>;<br/>
<a NAME="E28:100"/><span class="lab"><font color="Green" title="E94">A15</font></span>: 
1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T43" onmouseover="rs('borsuk_1/T43')" onmouseout="rh()">BORSUK_1:43</a></span>;<br/>
<a NAME="E29:100"/>
1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">Ewa1</font> = <span class="p1"><a href="mcart_1.html#K8" title="MCART_1:func.8">[:</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span><a href="mcart_1.html#K8" title="MCART_1:func.8">:]</a></span> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></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="#E4:100"><span class="lab"><font color="Green" title="E81">A2</font></span></a>, <a class="txt" href="#E27:100"><span class="lab"><font color="Green" title="E93">A14</font></span></a>, <a class="ref" href="borsuk_1.html#D2" onmouseover="rs('borsuk_1/D2')" onmouseout="rh()">BORSUK_1:def 2</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">T2</font> = <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c15">Ewa1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c17">e1</font> = <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c8">P1</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c18">e2</font> = <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c7">P2</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span>;<br/>
<a NAME="E31:100"/><span class="lab"><font color="Green" title="E95">A16</font></span>: 
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1,<span class="p2">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>,<span class="p2">(<span class="default">(<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1)</span>)</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="E32:100"/><span class="lab"><font color="Green" title="E96">A17</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c7">P2</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span> <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"><span class="p2">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p3">(<span class="default"><a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1,<span class="p4">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>,<span class="p4">(<span class="default">(<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>)</span>)</span></span>)</span></span><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#T67" onmouseover="rs('funct_3/T67')" onmouseout="rh()">FUNCT_3:67</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c19">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span>,<font color="Maroon" title="c1">T</font><span class="kw"> such that </span><br/><a NAME="E34:100"/><span class="lab"><font color="Green" title="E97">A18</font></span>: 
<font color="Maroon" title="c19">g</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> 
 <span class="kw">and </span><br/><a NAME="E35:100"/><span class="lab"><font color="Green" title="E98">A19</font></span>: 
 for <font color="Olive" title="b1">s</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> holds <br/> ( <font color="Maroon" title="c19">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">s</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Q</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font> &amp; <font color="Maroon" title="c19">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">s</font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">R</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font> &amp; (  for <font color="Olive" title="b2">t</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> holds <br/> ( <font color="Maroon" title="c19">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Olive" title="b2">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c19">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Olive" title="b2">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> ) ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:100"><span class="lab"><font color="Green" title="E87">A8</font></span></a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c20">f1</font> = <font color="Maroon" title="c12">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c8">P1</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c21">g1</font> = <font color="Maroon" title="c19">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c7">P2</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span>;<br/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c19">g</font> = 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_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/>.= 
<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 <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></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="borsuk_1.html#D2" onmouseover="rs('borsuk_1/D2')" onmouseout="rh()">BORSUK_1:def 2</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E99">A20</font></span>:  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c7">P2</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span></span>)</span> = 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c7">P2</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:100"><span class="lab"><font color="Green" title="E96">A17</font></span></a>, <a class="ref" href="relat_1.html#T27" onmouseover="rs('relat_1/T27')" onmouseout="rh()">RELAT_1:27</a>, <a class="ref" href="topmetr.html#T20" onmouseover="rs('topmetr/T20')" onmouseout="rh()">TOPMETR:20</a>, <a class="ref" href="zfmisc_1.html#T96" onmouseover="rs('zfmisc_1/T96')" onmouseout="rh()">ZFMISC_1:96</a></span>
<br/>.= 
<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 <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1)</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="txt" href="#E31:100"><span class="lab"><font color="Green" title="E95">A16</font></span></a>, <a class="ref" href="funct_3.html#D8" onmouseover="rs('funct_3/D8')" onmouseout="rh()">FUNCT_3:def 8</a></span>
;<br/>
<a NAME="E38:100"/>
 <a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">B02</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topmetr.html#T24" onmouseover="rs('topmetr/T24')" onmouseout="rh()">TOPMETR:24</a></span>;<br/>
<a NAME="E39:100"/><span class="kw">then </span>
( <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c7">P2</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span> is   <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<span class="p2">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1)</span>)</span></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span>,<span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> &amp; <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c15">Ewa1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<span class="p2">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1)</span>)</span></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="#E25:100"><span class="lab"><font color="Green" title="E92">A13</font></span></a>, <a class="ref" href="borsuk_3.html#T22" onmouseover="rs('borsuk_3/T22')" onmouseout="rh()">BORSUK_3:22</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c22">g1</font> = <font color="Maroon" title="c19">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c7">P2</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span> as   <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c15">Ewa1</font></span>)</span>,<font color="Maroon" title="c1">T</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:100"><span class="lab"><font color="Green" title="E97">A18</font></span></a></span>;<br/>
<a NAME="E41:100"/>
 <a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c14">B01</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topmetr.html#T24" onmouseover="rs('topmetr/T24')" onmouseout="rh()">TOPMETR:24</a></span>;<br/>
<a NAME="E42:100"/><span class="kw">then </span>
( <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c8">P1</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span> is   <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<span class="p2">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>)</span>)</span></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span>,<span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> &amp; <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c5">Ewa</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<span class="p2">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>)</span>)</span></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="#E25:100"><span class="lab"><font color="Green" title="E92">A13</font></span></a>, <a class="ref" href="borsuk_3.html#T22" onmouseover="rs('borsuk_3/T22')" onmouseout="rh()">BORSUK_3:22</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c23">f1</font> = <font color="Maroon" title="c12">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c8">P1</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span> as   <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c5">Ewa</font></span>)</span>,<font color="Maroon" title="c1">T</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:100"><span class="lab"><font color="Green" title="E88">A9</font></span></a></span>;<br/>
<a NAME="E44:100"/><span class="lab"><font color="Green" title="E100">A21</font></span>: 
1 is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T43" onmouseover="rs('borsuk_1/T43')" onmouseout="rh()">BORSUK_1:43</a></span>;<br/>
<a NAME="E45:100"/><span class="lab"><font color="Green" title="E101">A22</font></span>: 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T43" onmouseover="rs('borsuk_1/T43')" onmouseout="rh()">BORSUK_1:43</a></span>;<br/>
<a NAME="E46:100"/><span class="kw">then </span><span class="lab"><font color="Green" title="E102">A23</font></span>: 
<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> is   <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:100"><span class="lab"><font color="Green" title="E100">A21</font></span></a>, <a class="ref" href="borsuk_4.html#T24" onmouseover="rs('borsuk_4/T24')" onmouseout="rh()">BORSUK_4:24</a></span>;<br/>
<a NAME="E47:100"/><span class="lab"><font color="Green" title="E103">A24</font></span>: 
1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T43" onmouseover="rs('borsuk_1/T43')" onmouseout="rh()">BORSUK_1:43</a></span>;<br/>
<a NAME="E48:100"/><span class="kw">then </span>
<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> is   <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E45:100"><span class="lab"><font color="Green" title="E101">A22</font></span></a>, <a class="ref" href="borsuk_4.html#T24" onmouseover="rs('borsuk_4/T24')" onmouseout="rh()">BORSUK_4:24</a></span>;<br/>
<a NAME="E49:100"/><span class="kw">then </span><span class="lab"><font color="Green" title="E104">A25</font></span>: 
<font color="Maroon" title="c5">Ewa</font> is   <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></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="#E46:100"><span class="lab"><font color="Green" title="E102">A23</font></span></a>, <a class="ref" href="borsuk_3.html#T23" onmouseover="rs('borsuk_3/T23')" onmouseout="rh()">BORSUK_3:23</a></span>;<br/>
<a NAME="E50:100"/>
<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> is   <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:100"><span class="lab"><font color="Green" title="E100">A21</font></span></a>, <a class="txt" href="#E47:100"><span class="lab"><font color="Green" title="E103">A24</font></span></a>, <a class="ref" href="borsuk_4.html#T24" onmouseover="rs('borsuk_4/T24')" onmouseout="rh()">BORSUK_4:24</a></span>;<br/>
<a NAME="E51:100"/><span class="kw">then </span><span class="lab"><font color="Green" title="E105">A26</font></span>: 
<font color="Maroon" title="c15">Ewa1</font> is   <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></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="#E46:100"><span class="lab"><font color="Green" title="E102">A23</font></span></a>, <a class="ref" href="borsuk_3.html#T23" onmouseover="rs('borsuk_3/T23')" onmouseout="rh()">BORSUK_3:23</a></span>;<br/>
<span class="lab"><font color="Green" title="E106">A27</font></span>:  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c8">P1</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span> = 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<span class="p2">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>)</span>)</span></span><a href="borsuk_1.html#K2" title="BORSUK_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/>.= 
<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 <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>)</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="borsuk_1.html#D2" onmouseover="rs('borsuk_1/D2')" onmouseout="rh()">BORSUK_1:def 2</a></span>
;<br/>
<a NAME="E53:100"/><span class="lab"><font color="Green" title="E107">A28</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c7">P2</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span> <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"><span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c7">P2</font></span>)</span></span><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D8" onmouseover="rs('funct_3/D8')" onmouseout="rh()">FUNCT_3:def 8</a></span>;<br/>
<a NAME="E54:100"/><span class="lab"><font color="Green" title="E108">A29</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c8">P1</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span> <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"><span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c8">P1</font></span>)</span></span><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D8" onmouseover="rs('funct_3/D8')" onmouseout="rh()">FUNCT_3:def 8</a></span>;<br/>
<span class="lab"><font color="Green" title="E109">A30</font></span>:  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c7">P2</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span> = 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<span class="p2">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1)</span>)</span></span><a href="borsuk_1.html#K2" title="BORSUK_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/>.= 
<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 <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1)</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="borsuk_1.html#D2" onmouseover="rs('borsuk_1/D2')" onmouseout="rh()">BORSUK_1:def 2</a></span>
;<br/>
<a NAME="E56:100"/><span class="lab"><font color="Green" title="E110">A31</font></span>: 
(  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c5">Ewa</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Ewa</font> &amp;  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c15">Ewa1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">Ewa1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_topc.html#D5" onmouseover="rs('pre_topc/D5')" onmouseout="rh()">PRE_TOPC:def 5</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E111">A32</font></span>: <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c5">Ewa</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c15">Ewa1</font></span>)</span></span>)</span> = 
<span class="p1"><a href="mcart_1.html#K8" title="MCART_1:func.8">[:</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<span class="p2">(<span class="default"><span class="p3"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p3"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span></span><a href="mcart_1.html#K8" title="MCART_1:func.8">:]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T99" onmouseover="rs('zfmisc_1/T99')" onmouseout="rh()">ZFMISC_1:99</a></span>
<br/>.= 
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></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="xxreal_1.html#T418" onmouseover="rs('xxreal_1/T418')" onmouseout="rh()">XXREAL_1:418</a></span>
;<br/>
<a NAME="E58:100"/><span class="lab"><font color="Green" title="E112">A33</font></span>: 
 for <font color="Olive" title="b1">p</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c5">Ewa</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c15">Ewa1</font></span>)</span></span>)</span> holds <br/><font color="Maroon" title="c23">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">g1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">p</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="100_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c24">p</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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="c24">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c5">Ewa</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c15">Ewa1</font></span>)</span></span>)</span> implies <font color="Maroon" title="c23">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">g1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">p</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:100_6"/>
<font color="Maroon" title="c24">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c5">Ewa</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c15">Ewa1</font></span>)</span></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"> <font color="Maroon" title="c23">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">g1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">p</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c25">x</font>, <font color="Maroon" title="c26">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:100_6"/><span class="lab"><font color="Green" title="E113">A34</font></span>: 
<font color="Maroon" title="c25">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 <span class="kw">and </span><br/><a NAME="E4:100_6"/><span class="lab"><font color="Green" title="E114">A35</font></span>: 
<font color="Maroon" title="c26">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">and </span><br/><a NAME="E5:100_6"/><span class="lab"><font color="Green" title="E115">A36</font></span>: 
<font color="Maroon" title="c24">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c25">x</font>,<font color="Maroon" title="c26">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E57:100"><span class="lab"><font color="Green" title="E111">A32</font></span></a>, <a class="ref" href="zfmisc_1.html#D2" onmouseover="rs('zfmisc_1/D2')" onmouseout="rh()">ZFMISC_1:def 2</a></span>;<br/>
<a NAME="E6:100_6"/>
<font color="Maroon" title="c25">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">r</font> where <font color="Olive" title="b1">r</font> is   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> : (  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">r</font> &amp; <font color="Olive" title="b1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 ) </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:100_6"><span class="lab"><font color="Green" title="E113">A34</font></span></a>, <a class="ref" href="rcomp_1.html#D1" onmouseover="rs('rcomp_1/D1')" onmouseout="rh()">RCOMP_1:def 1</a></span>;<br/>
<a NAME="E7:100_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E116">A37</font></span>: 
 ex <font color="Olive" title="b1">r1</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/>( <font color="Olive" title="b1">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">x</font> &amp;  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">r1</font> &amp; <font color="Olive" title="b1">r1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 )
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c27">x9</font> = <font color="Maroon" title="c25">x</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T43" onmouseover="rs('borsuk_1/T43')" onmouseout="rh()">BORSUK_1:43</a></span>;<br/>
<a NAME="E9:100_6"/><span class="lab"><font color="Green" title="E117">A38</font></span>: 
<font color="Maroon" title="c26">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:100_6"><span class="lab"><font color="Green" title="E114">A35</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<a NAME="E10:100_6"/>
<font color="Maroon" title="c23">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">g1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">p</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="100_6_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:100_6_1"/>
1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c28">y9</font> = 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>)</span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="topmetr.html#T18" onmouseover="rs('topmetr/T18')" onmouseout="rh()">TOPMETR:18</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c29">t9</font> = 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c30">r1</font> =  <a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1), <font color="Maroon" title="c31">r2</font> = (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a>  as   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> ;<br/>
<span class="lab"><font color="Green" title="E118">A39</font></span>: <font color="Maroon" title="c8">P1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c28">y9</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c31">r2</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c30">r1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c30">r1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c31">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#T11" onmouseover="rs('treal_1/T11')" onmouseout="rh()">TREAL_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c30">r1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c30">r1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c31">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#D2" onmouseover="rs('treal_1/D2')" onmouseout="rh()">TREAL_1:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c30">r1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c31">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#D1" onmouseover="rs('treal_1/D1')" onmouseout="rh()">TREAL_1:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#D1" onmouseover="rs('treal_1/D1')" onmouseout="rh()">TREAL_1:def 1</a></span>
<br/>.= 
1

;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c32">y9</font> = 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1)</span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:100"><span class="lab"><font color="Green" title="E82">A3</font></span></a>, <a class="ref" href="topmetr.html#T18" onmouseover="rs('topmetr/T18')" onmouseout="rh()">TOPMETR:18</a></span>;<br/>
<span class="lab"><font color="Green" title="E119">A40</font></span>: <font color="Maroon" title="c7">P2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c32">y9</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c31">r2</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c30">r1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c30">r1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c31">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#T11" onmouseover="rs('treal_1/T11')" onmouseout="rh()">TREAL_1:11</a></span>
<br/>.= 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#D14" onmouseover="rs('borsuk_1/D14')" onmouseout="rh()">BORSUK_1:def 14</a>, <a class="ref" href="treal_1.html#T5" onmouseover="rs('treal_1/T5')" onmouseout="rh()">TREAL_1:5</a></span>
;<br/>
<a NAME="E7:100_6_1"/><span class="lab"><font color="Green" title="E120">A41</font></span>: 
<font color="Maroon" title="c25">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:100_6"><span class="lab"><font color="Green" title="E116">A37</font></span></a>, <a class="ref" href="borsuk_1.html#T43" onmouseover="rs('borsuk_1/T43')" onmouseout="rh()">BORSUK_1:43</a></span>;<br/>
<a NAME="E8:100_6_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E121">A42</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c25">x</font>,<font color="Maroon" title="c26">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c7">P2</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:100"><span class="lab"><font color="Green" title="E109">A30</font></span></a>, <a class="txt" href="#E6:100"><span class="lab"><font color="Green" title="E83">A4</font></span></a>, <a class="txt" href="#E9:100_6"><span class="lab"><font color="Green" title="E117">A38</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="E9:100_6_1"/><span class="lab"><font color="Green" title="E122">A43</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c25">x</font>,<font color="Maroon" title="c26">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c8">P1</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:100"><span class="lab"><font color="Green" title="E80">A1</font></span></a>, <a class="txt" href="#E52:100"><span class="lab"><font color="Green" title="E106">A27</font></span></a>, <a class="txt" href="#E9:100_6"><span class="lab"><font color="Green" title="E117">A38</font></span></a>, <a class="txt" href="#E7:100_6_1"><span class="lab"><font color="Green" title="E120">A41</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" onmouseover="rs('zfmisc_1/T87')" onmouseout="rh()">ZFMISC_1:87</a></span>;<br/>
<span class="kw">then </span><font color="Maroon" title="c23">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">p</font> = 
<font color="Maroon" title="c12">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c8">P1</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c25">x</font>,<font color="Maroon" title="c26">y</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:100_6"><span class="lab"><font color="Green" title="E115">A36</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>
<br/>.= 
<font color="Maroon" title="c12">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">x</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">P1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c26">y</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E54:100"><span class="lab"><font color="Green" title="E108">A29</font></span></a>, <a class="txt" href="#E9:100_6_1"><span class="lab"><font color="Green" title="E122">A43</font></span></a>, <a class="ref" href="funct_3.html#T65" onmouseover="rs('funct_3/T65')" onmouseout="rh()">FUNCT_3:65</a></span>
<br/>.= 
<font color="Maroon" title="c12">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c27">x9</font>,1)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:100_6"><span class="lab"><font color="Green" title="E117">A38</font></span></a>, <a class="txt" href="#E4:100_6_1"><span class="lab"><font color="Green" title="E118">A39</font></span></a>, <a class="ref" href="funct_1.html#T18" onmouseover="rs('funct_1/T18')" onmouseout="rh()">FUNCT_1:18</a></span>
<br/>.= 
<font color="Maroon" title="c10">Q</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c27">x9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:100"><span class="lab"><font color="Green" title="E89">A10</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c19">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c27">x9</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:100"><span class="lab"><font color="Green" title="E98">A19</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c19">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c27">x9</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">P2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c26">y</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:100_6"><span class="lab"><font color="Green" title="E117">A38</font></span></a>, <a class="txt" href="#E6:100_6_1"><span class="lab"><font color="Green" title="E119">A40</font></span></a>, <a class="ref" href="funct_1.html#T18" onmouseover="rs('funct_1/T18')" onmouseout="rh()">FUNCT_1:18</a></span>
<br/>.= 
<font color="Maroon" title="c19">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c7">P2</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c25">x</font>,<font color="Maroon" title="c26">y</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E53:100"><span class="lab"><font color="Green" title="E107">A28</font></span></a>, <a class="txt" href="#E8:100_6_1"><span class="lab"><font color="Green" title="E121">A42</font></span></a>, <a class="ref" href="funct_3.html#T65" onmouseover="rs('funct_3/T65')" onmouseout="rh()">FUNCT_3:65</a></span>
<br/>.= 
<font color="Maroon" title="c22">g1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">p</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:100_6"><span class="lab"><font color="Green" title="E115">A36</font></span></a>, <a class="txt" href="#E8:100_6_1"><span class="lab"><font color="Green" title="E121">A42</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E11:100_6_1"/>
<font color="Maroon" title="c23">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">g1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">p</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">hence </span><a NAME="E11:100_6"/>
<font color="Maroon" title="c23">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">g1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">p</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="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c5">Ewa</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c15">Ewa1</font></span>)</span></span>)</span> = 
<span class="p1"><a href="mcart_1.html#K8" title="MCART_1:func.8">[:</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<span class="p2">(<span class="default"><span class="p3"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span></span><a href="mcart_1.html#K8" title="MCART_1:func.8">:]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E56:100"><span class="lab"><font color="Green" title="E110">A31</font></span></a>, <a class="ref" href="zfmisc_1.html#T97" onmouseover="rs('zfmisc_1/T97')" onmouseout="rh()">ZFMISC_1:97</a></span>
<br/>.= 
<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 <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></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="borsuk_1.html#T40" onmouseover="rs('borsuk_1/T40')" onmouseout="rh()">BORSUK_1:40</a>, <a class="ref" href="xxreal_1.html#T174" onmouseover="rs('xxreal_1/T174')" onmouseout="rh()">XXREAL_1:174</a></span>
<br/>.= 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#D2" onmouseover="rs('borsuk_1/D2')" onmouseout="rh()">BORSUK_1:def 2</a></span>
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c24">h</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span>,<font color="Maroon" title="c1">T</font><span class="kw"> such that </span><br/><a NAME="E61:100"/><span class="lab"><font color="Green" title="E113">A44</font></span>: 
<font color="Maroon" title="c24">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c22">g1</font>
 <span class="kw">and </span><br/><a NAME="E62:100"/><span class="lab"><font color="Green" title="E114">A45</font></span>: 
<font color="Maroon" title="c24">h</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:100"><span class="lab"><font color="Green" title="E104">A25</font></span></a>, <a class="txt" href="#E51:100"><span class="lab"><font color="Green" title="E105">A26</font></span></a>, <a class="txt" href="#E58:100"><span class="lab"><font color="Green" title="E112">A33</font></span></a>, <a class="ref" href="borsuk_2.html#T1" onmouseover="rs('borsuk_2/T1')" onmouseout="rh()">BORSUK_2:1</a></span>;<br/>
<a NAME="E63:100"/><span class="lab"><font color="Green" title="E115">A46</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topmetr.html#T18" onmouseover="rs('topmetr/T18')" onmouseout="rh()">TOPMETR:18</a></span>;<br/>
<a NAME="E64:100"/><span class="lab"><font color="Green" title="E116">A47</font></span>: 
 for <font color="Olive" title="b1">t</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> holds <br/> ( <font color="Maroon" title="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Olive" title="b1">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Olive" title="b1">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="100_8"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c25">t</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</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="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c25">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Maroon" title="c25">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> )</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="100_8_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="E1:100_8_1"/>
( <font color="Maroon" title="c25">t</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 or <font color="Maroon" title="c25">t</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="100_8_1_1"><span class="kw">suppose </span></a><a NAME="E1:100_8_1_1"/><span class="lab"><font color="Green" title="E117">A48</font></span>: 
<font color="Maroon" title="c25">t</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 ; <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="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c25">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Maroon" title="c25">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> )</span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c26">r1</font> =  <a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1), <font color="Maroon" title="c27">r2</font> = (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a>  as   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> ;<br/><a NAME="E3:100_8_1_1"/><span class="lab"><font color="Green" title="E118">A49</font></span>: 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c25">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T43" onmouseover="rs('borsuk_1/T43')" onmouseout="rh()">BORSUK_1:43</a></span>;<br/><a NAME="E4:100_8_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E119">A50</font></span>: 
<font color="Maroon" title="c25">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:100"><span class="lab"><font color="Green" title="E85">A6</font></span></a>, <a class="txt" href="#E1:100_8_1_1"><span class="lab"><font color="Green" title="E117">A48</font></span></a>, <a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/><a NAME="E5:100_8_1_1"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T43" onmouseover="rs('borsuk_1/T43')" onmouseout="rh()">BORSUK_1:43</a></span>;<br/><a NAME="E6:100_8_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E120">A51</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c25">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c8">P1</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E52:100"><span class="lab"><font color="Green" title="E106">A27</font></span></a>, <a class="txt" href="#E4:100_8_1_1"><span class="lab"><font color="Green" title="E119">A50</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" onmouseover="rs('zfmisc_1/T87')" onmouseout="rh()">ZFMISC_1:87</a></span>;<br/><font color="Maroon" title="c8">P1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">t</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c27">r2</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c27">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:100_8_1_1"><span class="lab"><font color="Green" title="E119">A50</font></span></a>, <a class="ref" href="treal_1.html#T11" onmouseover="rs('treal_1/T11')" onmouseout="rh()">TREAL_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#D2" onmouseover="rs('treal_1/D2')" onmouseout="rh()">TREAL_1:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#D1" onmouseover="rs('treal_1/D1')" onmouseout="rh()">TREAL_1:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#D1" onmouseover="rs('treal_1/D1')" onmouseout="rh()">TREAL_1:def 1</a></span>
<br/>.= 
2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font>

;<br/><a NAME="E8:100_8_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E121">A52</font></span>: 
<font color="Maroon" title="c8">P1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">t</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:100_8_1_1"><span class="lab"><font color="Green" title="E117">A48</font></span></a>, <a class="ref" href="borsuk_6.html#T3" target="_self" onmouseover="rs('borsuk_6/T3')" onmouseout="rh()">Th3</a></span>;<br/><a NAME="E9:100_8_1_1"/>
 not <font color="Maroon" title="c25">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:100"><span class="lab"><font color="Green" title="E90">A11</font></span></a>, <a class="txt" href="#E1:100_8_1_1"><span class="lab"><font color="Green" title="E117">A48</font></span></a>, <a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/><a NAME="E10:100_8_1_1"/><span class="kw">then </span>
 not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c25">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <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="c22">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:100"><span class="lab"><font color="Green" title="E99">A20</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" onmouseover="rs('zfmisc_1/T87')" onmouseout="rh()">ZFMISC_1:87</a></span>;<br/><span class="kw">hence </span><font color="Maroon" title="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c25">t</font>) = 
<font color="Maroon" title="c23">f1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c25">t</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E61:100"><span class="lab"><font color="Green" title="E113">A44</font></span></a>, <a class="ref" href="funct_4.html#T11" onmouseover="rs('funct_4/T11')" onmouseout="rh()">FUNCT_4:11</a></span>
<br/>.= 
<font color="Maroon" title="c12">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c8">P1</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c25">t</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:100_8_1_1"><span class="lab"><font color="Green" title="E120">A51</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>
<br/>.= 
<font color="Maroon" title="c12">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">P1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">t</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E54:100"><span class="lab"><font color="Green" title="E108">A29</font></span></a>, <a class="txt" href="#E6:100_8_1_1"><span class="lab"><font color="Green" title="E120">A51</font></span></a>, <a class="ref" href="funct_3.html#T65" onmouseover="rs('funct_3/T65')" onmouseout="rh()">FUNCT_3:65</a></span>
<br/>.= 
<font color="Maroon" title="c12">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">P1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">t</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E45:100"><span class="lab"><font color="Green" title="E101">A22</font></span></a>, <a class="ref" href="funct_1.html#T18" onmouseover="rs('funct_1/T18')" onmouseout="rh()">FUNCT_1:18</a></span>
<br/>.= 
<font color="Maroon" title="c2">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:100"><span class="lab"><font color="Green" title="E89">A10</font></span></a>, <a class="txt" href="#E8:100_8_1_1"><span class="lab"><font color="Green" title="E121">A52</font></span></a></span>
;<br/> <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="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Maroon" title="c25">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font></span><br/><a NAME="E12:100_8_1_1"/>
<font color="Maroon" title="c25">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E63:100"><span class="lab"><font color="Green" title="E115">A46</font></span></a>, <a class="txt" href="#E1:100_8_1_1"><span class="lab"><font color="Green" title="E117">A48</font></span></a>, <a class="txt" href="#E3:100_8_1_1"><span class="lab"><font color="Green" title="E118">A49</font></span></a>, <a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/><a NAME="E13:100_8_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E122">A53</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,<font color="Maroon" title="c25">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c8">P1</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E52:100"><span class="lab"><font color="Green" title="E106">A27</font></span></a>, <a class="txt" href="#E28:100"><span class="lab"><font color="Green" title="E94">A15</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" onmouseover="rs('zfmisc_1/T87')" onmouseout="rh()">ZFMISC_1:87</a></span>;<br/><font color="Maroon" title="c8">P1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">t</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c27">r2</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c27">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:100_8_1_1"><span class="lab"><font color="Green" title="E119">A50</font></span></a>, <a class="ref" href="treal_1.html#T11" onmouseover="rs('treal_1/T11')" onmouseout="rh()">TREAL_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#D2" onmouseover="rs('treal_1/D2')" onmouseout="rh()">TREAL_1:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#D1" onmouseover="rs('treal_1/D1')" onmouseout="rh()">TREAL_1:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#D1" onmouseover="rs('treal_1/D1')" onmouseout="rh()">TREAL_1:def 1</a></span>
<br/>.= 
2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font>

;<br/><a NAME="E15:100_8_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E123">A54</font></span>: 
<font color="Maroon" title="c8">P1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">t</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:100_8_1_1"><span class="lab"><font color="Green" title="E117">A48</font></span></a>, <a class="ref" href="borsuk_6.html#T3" target="_self" onmouseover="rs('borsuk_6/T3')" onmouseout="rh()">Th3</a></span>;<br/><a NAME="E16:100_8_1_1"/>
 not <font color="Maroon" title="c25">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:100"><span class="lab"><font color="Green" title="E91">A12</font></span></a>, <a class="txt" href="#E1:100_8_1_1"><span class="lab"><font color="Green" title="E117">A48</font></span></a>, <a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/><a NAME="E17:100_8_1_1"/><span class="kw">then </span>
 not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,<font color="Maroon" title="c25">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <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="c22">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:100"><span class="lab"><font color="Green" title="E99">A20</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" onmouseover="rs('zfmisc_1/T87')" onmouseout="rh()">ZFMISC_1:87</a></span>;<br/><span class="kw">hence </span><font color="Maroon" title="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Maroon" title="c25">t</font>) = 
<font color="Maroon" title="c23">f1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Maroon" title="c25">t</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E61:100"><span class="lab"><font color="Green" title="E113">A44</font></span></a>, <a class="ref" href="funct_4.html#T11" onmouseover="rs('funct_4/T11')" onmouseout="rh()">FUNCT_4:11</a></span>
<br/>.= 
<font color="Maroon" title="c12">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c8">P1</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Maroon" title="c25">t</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:100_8_1_1"><span class="lab"><font color="Green" title="E122">A53</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>
<br/>.= 
<font color="Maroon" title="c12">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">P1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">t</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E54:100"><span class="lab"><font color="Green" title="E108">A29</font></span></a>, <a class="txt" href="#E13:100_8_1_1"><span class="lab"><font color="Green" title="E122">A53</font></span></a>, <a class="ref" href="funct_3.html#T65" onmouseover="rs('funct_3/T65')" onmouseout="rh()">FUNCT_3:65</a></span>
<br/>.= 
<font color="Maroon" title="c12">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<span class="p1">(<span class="default"><font color="Maroon" title="c8">P1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">t</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:100"><span class="lab"><font color="Green" title="E100">A21</font></span></a>, <a class="ref" href="funct_1.html#T18" onmouseover="rs('funct_1/T18')" onmouseout="rh()">FUNCT_1:18</a></span>
<br/>.= 
<font color="Maroon" title="c3">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:100"><span class="lab"><font color="Green" title="E89">A10</font></span></a>, <a class="txt" href="#E15:100_8_1_1"><span class="lab"><font color="Green" title="E123">A54</font></span></a></span>
;<br/> <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="100_8_1_2"><span class="kw">suppose </span></a><a NAME="E1:100_8_1_2"/><span class="lab"><font color="Green" title="E117">A55</font></span>: 
<font color="Maroon" title="c25">t</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 ; <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="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c25">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Maroon" title="c25">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> )</span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c26">r1</font> =  <a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1), <font color="Maroon" title="c27">r2</font> = (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a>  as   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> ;<br/><a NAME="E3:100_8_1_2"/>
<font color="Maroon" title="c25">t</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T43" onmouseover="rs('borsuk_1/T43')" onmouseout="rh()">BORSUK_1:43</a></span>;<br/><a NAME="E4:100_8_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E118">A56</font></span>: 
<font color="Maroon" title="c25">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:100"><span class="lab"><font color="Green" title="E90">A11</font></span></a>, <a class="txt" href="#E1:100_8_1_2"><span class="lab"><font color="Green" title="E117">A55</font></span></a>, <a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/><a NAME="E5:100_8_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E119">A57</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,<font color="Maroon" title="c25">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c7">P2</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:100"><span class="lab"><font color="Green" title="E109">A30</font></span></a>, <a class="txt" href="#E28:100"><span class="lab"><font color="Green" title="E94">A15</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" onmouseover="rs('zfmisc_1/T87')" onmouseout="rh()">ZFMISC_1:87</a></span>;<br/><font color="Maroon" title="c7">P2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">t</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c27">r2</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c27">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:100_8_1_2"><span class="lab"><font color="Green" title="E118">A56</font></span></a>, <a class="ref" href="treal_1.html#T11" onmouseover="rs('treal_1/T11')" onmouseout="rh()">TREAL_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c27">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#D2" onmouseover="rs('treal_1/D2')" onmouseout="rh()">TREAL_1:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c27">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#D1" onmouseover="rs('treal_1/D1')" onmouseout="rh()">TREAL_1:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c27">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#D1" onmouseover="rs('treal_1/D1')" onmouseout="rh()">TREAL_1:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c27">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#D2" onmouseover="rs('treal_1/D2')" onmouseout="rh()">TREAL_1:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1

;<br/><a NAME="E7:100_8_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E120">A58</font></span>: 
<font color="Maroon" title="c7">P2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">t</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:100_8_1_2"><span class="lab"><font color="Green" title="E117">A55</font></span></a>, <a class="ref" href="borsuk_6.html#T4" target="_self" onmouseover="rs('borsuk_6/T4')" onmouseout="rh()">Th4</a></span>;<br/><font color="Maroon" title="c7">P2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">t</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c27">r2</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c27">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:100_8_1_2"><span class="lab"><font color="Green" title="E118">A56</font></span></a>, <a class="ref" href="treal_1.html#T11" onmouseover="rs('treal_1/T11')" onmouseout="rh()">TREAL_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c27">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#D2" onmouseover="rs('treal_1/D2')" onmouseout="rh()">TREAL_1:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c26">r1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c27">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#D1" onmouseover="rs('treal_1/D1')" onmouseout="rh()">TREAL_1:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c27">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#D1" onmouseover="rs('treal_1/D1')" onmouseout="rh()">TREAL_1:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#D2" onmouseover="rs('treal_1/D2')" onmouseout="rh()">TREAL_1:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">t</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1

;<br/><a NAME="E9:100_8_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E121">A59</font></span>: 
<font color="Maroon" title="c7">P2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">t</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:100_8_1_2"><span class="lab"><font color="Green" title="E117">A55</font></span></a>, <a class="ref" href="borsuk_6.html#T4" target="_self" onmouseover="rs('borsuk_6/T4')" onmouseout="rh()">Th4</a></span>;<br/><a NAME="E10:100_8_1_2"/><span class="lab"><font color="Green" title="E122">A60</font></span>: 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T43" onmouseover="rs('borsuk_1/T43')" onmouseout="rh()">BORSUK_1:43</a></span>;<br/><a NAME="E11:100_8_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E123">A61</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c25">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c7">P2</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:100"><span class="lab"><font color="Green" title="E109">A30</font></span></a>, <a class="txt" href="#E4:100_8_1_2"><span class="lab"><font color="Green" title="E118">A56</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="E12:100_8_1_2"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c25">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <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="c22">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:100"><span class="lab"><font color="Green" title="E99">A20</font></span></a>, <a class="txt" href="#E10:100_8_1_2"><span class="lab"><font color="Green" title="E122">A60</font></span></a>, <a class="txt" href="#E4:100_8_1_2"><span class="lab"><font color="Green" title="E118">A56</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" onmouseover="rs('zfmisc_1/T87')" onmouseout="rh()">ZFMISC_1:87</a></span>;<br/><span class="kw">hence </span><font color="Maroon" title="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c25">t</font>) = 
<font color="Maroon" title="c22">g1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c25">t</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E61:100"><span class="lab"><font color="Green" title="E113">A44</font></span></a>, <a class="ref" href="funct_4.html#T13" onmouseover="rs('funct_4/T13')" onmouseout="rh()">FUNCT_4:13</a></span>
<br/>.= 
<font color="Maroon" title="c19">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c7">P2</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c25">t</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:100_8_1_2"><span class="lab"><font color="Green" title="E123">A61</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>
<br/>.= 
<font color="Maroon" title="c19">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">P2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">t</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E53:100"><span class="lab"><font color="Green" title="E107">A28</font></span></a>, <a class="txt" href="#E11:100_8_1_2"><span class="lab"><font color="Green" title="E123">A61</font></span></a>, <a class="ref" href="funct_3.html#T65" onmouseover="rs('funct_3/T65')" onmouseout="rh()">FUNCT_3:65</a></span>
<br/>.= 
<font color="Maroon" title="c19">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">P2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">t</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E45:100"><span class="lab"><font color="Green" title="E101">A22</font></span></a>, <a class="ref" href="funct_1.html#T18" onmouseover="rs('funct_1/T18')" onmouseout="rh()">FUNCT_1:18</a></span>
<br/>.= 
<font color="Maroon" title="c2">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:100"><span class="lab"><font color="Green" title="E98">A19</font></span></a>, <a class="txt" href="#E9:100_8_1_2"><span class="lab"><font color="Green" title="E121">A59</font></span></a></span>
;<br/> <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="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Maroon" title="c25">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font></span><br/><a NAME="E14:100_8_1_2"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,<font color="Maroon" title="c25">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <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="c22">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:100"><span class="lab"><font color="Green" title="E99">A20</font></span></a>, <a class="txt" href="#E28:100"><span class="lab"><font color="Green" title="E94">A15</font></span></a>, <a class="txt" href="#E4:100_8_1_2"><span class="lab"><font color="Green" title="E118">A56</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" onmouseover="rs('zfmisc_1/T87')" onmouseout="rh()">ZFMISC_1:87</a></span>;<br/><span class="kw">hence </span><font color="Maroon" title="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Maroon" title="c25">t</font>) = 
<font color="Maroon" title="c22">g1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Maroon" title="c25">t</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E61:100"><span class="lab"><font color="Green" title="E113">A44</font></span></a>, <a class="ref" href="funct_4.html#T13" onmouseover="rs('funct_4/T13')" onmouseout="rh()">FUNCT_4:13</a></span>
<br/>.= 
<font color="Maroon" title="c19">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c7">P2</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Maroon" title="c25">t</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:100_8_1_2"><span class="lab"><font color="Green" title="E119">A57</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>
<br/>.= 
<font color="Maroon" title="c19">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">P2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">t</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E53:100"><span class="lab"><font color="Green" title="E107">A28</font></span></a>, <a class="txt" href="#E5:100_8_1_2"><span class="lab"><font color="Green" title="E119">A57</font></span></a>, <a class="ref" href="funct_3.html#T65" onmouseover="rs('funct_3/T65')" onmouseout="rh()">FUNCT_3:65</a></span>
<br/>.= 
<font color="Maroon" title="c19">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<span class="p1">(<span class="default"><font color="Maroon" title="c7">P2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">t</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:100"><span class="lab"><font color="Green" title="E100">A21</font></span></a>, <a class="ref" href="funct_1.html#T18" onmouseover="rs('funct_1/T18')" onmouseout="rh()">FUNCT_1:18</a></span>
<br/>.= 
<font color="Maroon" title="c3">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:100"><span class="lab"><font color="Green" title="E98">A19</font></span></a>, <a class="txt" href="#E7:100_8_1_2"><span class="lab"><font color="Green" title="E120">A58</font></span></a></span>
;<br/> <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><span class="kw">end;</span></div>
<a NAME="E65:100"/>
 for <font color="Olive" title="b1">s</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> holds <br/> ( <font color="Maroon" title="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">s</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font> &amp; <font color="Maroon" title="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">s</font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">R</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font> )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="100_9"><span class="kw">proof </span></a><div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c25">r1</font> =  <a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1), <font color="Maroon" title="c26">r2</font> = (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a>  as   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> ;<br/>
<span class="kw">let </span><font color="Maroon" title="c27">s</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</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="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c27">s</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c27">s</font> &amp; <font color="Maroon" title="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c27">s</font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">R</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c27">s</font> )</span><br/>

<a NAME="E2:100_9"/>
( 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a>  &amp; 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#D2" onmouseover="rs('treal_1/D2')" onmouseout="rh()">TREAL_1:def 2</a></span>;<br/>
<a NAME="E3:100_9"/><span class="kw">then </span><span class="lab"><font color="Green" title="E117">A62</font></span>: 
<font color="Maroon" title="c7">P2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#T13" onmouseover="rs('treal_1/T13')" onmouseout="rh()">TREAL_1:13</a></span>;<br/>
<a NAME="E4:100_9"/><span class="lab"><font color="Green" title="E118">A63</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topmetr.html#T18" onmouseover="rs('topmetr/T18')" onmouseout="rh()">TOPMETR:18</a></span>;<br/>
<a NAME="E5:100_9"/><span class="kw">then </span><span class="lab"><font color="Green" title="E119">A64</font></span>: 
1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/>
<a NAME="E6:100_9"/><span class="kw">then </span><span class="lab"><font color="Green" title="E120">A65</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c27">s</font>,1</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c7">P2</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:100"><span class="lab"><font color="Green" title="E109">A30</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="E7:100_9"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c27">s</font>,1</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <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="c22">g1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:100"><span class="lab"><font color="Green" title="E99">A20</font></span></a>, <a class="txt" href="#E5:100_9"><span class="lab"><font color="Green" title="E119">A64</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" onmouseover="rs('zfmisc_1/T87')" onmouseout="rh()">ZFMISC_1:87</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E121">A66</font></span>: <font color="Maroon" title="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c27">s</font>,1) = 
<font color="Maroon" title="c22">g1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c27">s</font>,1)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E61:100"><span class="lab"><font color="Green" title="E113">A44</font></span></a>, <a class="ref" href="funct_4.html#T13" onmouseover="rs('funct_4/T13')" onmouseout="rh()">FUNCT_4:13</a></span>
<br/>.= 
<font color="Maroon" title="c19">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c7">P2</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c27">s</font>,1)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:100_9"><span class="lab"><font color="Green" title="E120">A65</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>
<br/>.= 
<font color="Maroon" title="c19">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c27">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">P2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E53:100"><span class="lab"><font color="Green" title="E107">A28</font></span></a>, <a class="txt" href="#E6:100_9"><span class="lab"><font color="Green" title="E120">A65</font></span></a>, <a class="ref" href="funct_3.html#T65" onmouseover="rs('funct_3/T65')" onmouseout="rh()">FUNCT_3:65</a></span>
<br/>.= 
<font color="Maroon" title="c19">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c27">s</font>,1)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:100_9"><span class="lab"><font color="Green" title="E117">A62</font></span></a>, <a class="ref" href="funct_1.html#T18" onmouseover="rs('funct_1/T18')" onmouseout="rh()">FUNCT_1:18</a></span>
<br/>.= 
<font color="Maroon" title="c11">R</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c27">s</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:100"><span class="lab"><font color="Green" title="E98">A19</font></span></a></span>
;<br/>
<a NAME="E9:100_9"/><span class="lab"><font color="Green" title="E122">A67</font></span>: 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:100"><span class="lab"><font color="Green" title="E85">A6</font></span></a>, <a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E123">A68</font></span>: <font color="Maroon" title="c8">P1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c26">r2</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c25">r1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c25">r1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c26">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#T11" onmouseover="rs('treal_1/T11')" onmouseout="rh()">TREAL_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c26">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#D1" onmouseover="rs('treal_1/D1')" onmouseout="rh()">TREAL_1:def 1</a></span>
;<br/>
<a NAME="E11:100_9"/><span class="lab"><font color="Green" title="E124">A69</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c27">s</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c8">P1</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E52:100"><span class="lab"><font color="Green" title="E106">A27</font></span></a>, <a class="txt" href="#E9:100_9"><span class="lab"><font color="Green" title="E122">A67</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="E12:100_9"/>
 not  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>,1)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:100_9"><span class="lab"><font color="Green" title="E118">A63</font></span></a>, <a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/>
<a NAME="E13:100_9"/><span class="kw">then </span>
 not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c27">s</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <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="c22">g1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:100"><span class="lab"><font color="Green" title="E99">A20</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" onmouseover="rs('zfmisc_1/T87')" onmouseout="rh()">ZFMISC_1:87</a></span>;<br/>
<span class="kw">then </span><font color="Maroon" title="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c27">s</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) = 
<font color="Maroon" title="c23">f1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c27">s</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E61:100"><span class="lab"><font color="Green" title="E113">A44</font></span></a>, <a class="ref" href="funct_4.html#T11" onmouseover="rs('funct_4/T11')" onmouseout="rh()">FUNCT_4:11</a></span>
<br/>.= 
<font color="Maroon" title="c12">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">[:</a><span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span>,<font color="Maroon" title="c8">P1</font></span><a href="borsuk_2.html#K3" title="BORSUK_2:func.3">:]</a></span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c27">s</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:100_9"><span class="lab"><font color="Green" title="E124">A69</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>
<br/>.= 
<font color="Maroon" title="c12">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c27">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">P1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E54:100"><span class="lab"><font color="Green" title="E108">A29</font></span></a>, <a class="txt" href="#E11:100_9"><span class="lab"><font color="Green" title="E124">A69</font></span></a>, <a class="ref" href="funct_3.html#T65" onmouseover="rs('funct_3/T65')" onmouseout="rh()">FUNCT_3:65</a></span>
<br/>.= 
<font color="Maroon" title="c12">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c27">s</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:100_9"><span class="lab"><font color="Green" title="E123">A68</font></span></a>, <a class="ref" href="funct_1.html#T18" onmouseover="rs('funct_1/T18')" onmouseout="rh()">FUNCT_1:18</a></span>
<br/>.= 
<font color="Maroon" title="c9">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c27">s</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:100"><span class="lab"><font color="Green" title="E89">A10</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E15:100_9"/>
( <font color="Maroon" title="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c27">s</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c27">s</font> &amp; <font color="Maroon" title="c24">h</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c27">s</font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">R</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c27">s</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:100_9"><span class="lab"><font color="Green" title="E121">A66</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>
<span class="kw">hence </span><a NAME="E66:100"/>
<font color="Maroon" title="c9">P</font>,<font color="Maroon" title="c11">R</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E62:100"><span class="lab"><font color="Green" title="E114">A45</font></span></a>, <a class="txt" href="#E64:100"><span class="lab"><font color="Green" title="E116">A47</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>
