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<span class="kw">let </span><font color="Maroon" title="c5">h</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="valued_2.html#K43" title="VALUED_2:func.43">[#]</a> <font color="Maroon" title="c3">r</font> implies <font color="Maroon" title="c5">h</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:112_3_1"/><span class="lab"><font color="Green" title="E42">A2</font></span>: 
<font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="valued_2.html#K43" title="VALUED_2:func.43">[#]</a> <font color="Maroon" title="c3">r</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">h</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> </span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c6">r</font> = <font color="Maroon" title="c3">r</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></span>;<br/>
<a NAME="E3:112_3_1"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">f</font> <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 <font color="Maroon" title="c2">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E4:112_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="valued_2.html#K64" title="VALUED_2:func.64">&lt;#&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">T</font> <a href="struct_0.html#K6" title="STRUCT_0:func.6">--&gt;</a> <font color="Maroon" title="c6">r</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112_3_1"><span class="lab"><font color="Green" title="E42">A2</font></span></a>, <a class="ref" href="toprealc.html#T31" target="_self" title="TOPREALC:th.31">Th31</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:112_3_1"/>
<font color="Maroon" title="c5">h</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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