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<span class="kw">let </span><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of  <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</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">f</font> being   <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 <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>  st  ex <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/>( <font color="Olive" title="b2">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">b</font> &amp; <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font></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 <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b1">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font></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> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> ) holds <br/> ex <font color="Olive" title="b2">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font> st <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be   <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 <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</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"> (  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/>( <font color="Olive" title="b1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">b</font> &amp; <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></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 <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c3">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></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> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> ) implies  ex <font color="Olive" title="b1">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font> st <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> )</span><br/>



<span class="kw">given </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><span class="kw"> such that </span><a NAME="E2:27"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">b</font>
 <span class="kw">and </span><br/><a NAME="E3:27"/><span class="lab"><font color="Green" title="E21">A2</font></span>: 
<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></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 <font color="Maroon" title="c1">X</font>
 <span class="kw">and </span><br/><a NAME="E4:27"/><span class="lab"><font color="Green" title="E22">A3</font></span>: 
<font color="Maroon" title="c3">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></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> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</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">  ex <font color="Olive" title="b1">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font> st <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">g</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">Y</font> <a href="tmap_1.html#NK6" title="TMAP_1:NK.6">incl</a> <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font>;<br/>
<a NAME="E5:27"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font> <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#K3" title="TOPMETR:func.3">R^1</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T1" onmouseover="rs('borsuk_1/T1')" onmouseout="rh()">BORSUK_1:1</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">B</font> = <font color="Maroon" title="c3">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T1" onmouseover="rs('xboole_1/T1')" onmouseout="rh()">XBOOLE_1:1</a></span>;<br/>
<a NAME="E7:27"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">Y</font> <a href="tmap_1.html#NK6" title="TMAP_1:NK.6">incl</a> <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">Y</font> <a href="tmap_1.html#NK6" title="TMAP_1:NK.6">incl</a> <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T126" onmouseover="rs('relat_1/T126')" onmouseout="rh()">RELAT_1:126</a></span>;<br/>
<a NAME="E8:27"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">Y</font> <a href="tmap_1.html#NK6" title="TMAP_1:NK.6">incl</a> <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.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#K3" title="TOPMETR:func.3">R^1</a></span>)</span> <a href="tmap_1.html#K2" title="TMAP_1:func.2">|</a> <font color="Maroon" title="c2">Y</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c7">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tmap_1.html#D6" onmouseover="rs('tmap_1/D6')" onmouseout="rh()">TMAP_1:def 6</a></span>;<br/>
<a NAME="E9:27"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">Y</font> <a href="tmap_1.html#NK6" title="TMAP_1:NK.6">incl</a> <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c7">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tmap_1.html#T55" onmouseover="rs('tmap_1/T55')" onmouseout="rh()">TMAP_1:55</a></span>;<br/>
<a NAME="E10:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A4</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">Y</font> <a href="tmap_1.html#NK6" title="TMAP_1:NK.6">incl</a> <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></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> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="ref" href="funct_1.html#T92" onmouseover="rs('funct_1/T92')" onmouseout="rh()">FUNCT_1:92</a></span>;<br/>
<a NAME="E11:27"/><span class="lab"><font color="Green" title="E24">A5</font></span>: 
( <font color="Maroon" title="c2">Y</font> <a href="tmap_1.html#NK6" title="TMAP_1:NK.6">incl</a> <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a> 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 <font color="Maroon" title="c2">Y</font>,<a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a> &amp;  <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>  is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of  <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tmap_1.html#T87" onmouseover="rs('tmap_1/T87')" onmouseout="rh()">TMAP_1:87</a>, <a class="ref" href="tsep_1.html#T2" onmouseover="rs('tsep_1/T2')" onmouseout="rh()">TSEP_1:2</a></span>;<br/>
<a NAME="E12:27"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <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#K3" title="TOPMETR:func.3">R^1</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T1" onmouseover="rs('borsuk_1/T1')" onmouseout="rh()">BORSUK_1:1</a></span>;<br/>
<a NAME="E13:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A6</font></span>: 
<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></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#K3" title="TOPMETR:func.3">R^1</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E21">A2</font></span></a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="27_1"><span class="kw">now </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">  ex <font color="Olive" title="b1">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font> st <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font></span></a><div class="add"><span class="kw">consider </span><font color="Maroon" title="c8">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:27_1"/><span class="lab"><font color="Green" title="E26">A7</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">Y</font> <a href="tmap_1.html#NK6" title="TMAP_1:NK.6">incl</a> <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="txt" href="#E11:27"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E13:27"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="txt" href="#E10:27"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="ref" href="treal_1.html#T23" target="_self" onmouseover="rs('treal_1/T23')" onmouseout="rh()">Th23</a></span>;<br/><a NAME="E3:27_1"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font> <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#K3" title="TOPMETR:func.3">R^1</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T1" onmouseover="rs('borsuk_1/T1')" onmouseout="rh()">BORSUK_1:1</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">y</font> = <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">x</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a> ;<br/><span class="kw">take </span><font color="Maroon" title="c10">x</font> = <font color="Maroon" title="c8">x</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">x</font></span><br/><span class="kw">thus </span><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">Y</font> <a href="tmap_1.html#NK6" title="TMAP_1:NK.6">incl</a> <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">y</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="tmap_1.html#T84" onmouseover="rs('tmap_1/T84')" onmouseout="rh()">TMAP_1:84</a></span>
<br/>.= 
<font color="Maroon" title="c10">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27_1"><span class="lab"><font color="Green" title="E26">A7</font></span></a>, <a class="ref" href="funct_2.html#T15" onmouseover="rs('funct_2/T15')" onmouseout="rh()">FUNCT_2:15</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="E15:27"/>
 ex <font color="Olive" title="b1">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font> st <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</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/>


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