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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</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="struct_0.html#NM12" title="STRUCT_0:NM.12">PartFunc</a> of <a href="topalg_2.html#K2" title="TOPALG_2:func.2">R^1</a>,<font color="Maroon" title="c1">T</font>  st <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/><font color="Olive" title="b1">f</font> is  <a href="topalg_6.html#V4" title="TOPALG_6:attr.4">parametrized-curve</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font> be   <a href="struct_0.html#NM12" title="STRUCT_0:NM.12">PartFunc</a> of <a href="topalg_2.html#K2" title="TOPALG_2:func.2">R^1</a>,<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"> ( <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <font color="Maroon" title="c2">f</font> is  <a href="topalg_6.html#V4" title="TOPALG_6:attr.4">parametrized-curve</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:34"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.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"> <font color="Maroon" title="c2">f</font> is  <a href="topalg_6.html#V4" title="TOPALG_6:attr.4">parametrized-curve</a> </span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c3">f</font> = <font color="Maroon" title="c2">f</font> as   <a href="struct_0.html#NM12" title="STRUCT_0:NM.12">PartFunc</a> of <a href="topalg_2.html#K2" title="TOPALG_2:func.2">R^1</a>,<font color="Maroon" title="c1">T</font> ;<br/>
<a NAME="E3:34"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34"><span class="lab"><font color="Green" title="E21">A1</font></span></a></span>;<br/>
<a NAME="E4:34"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A2</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 
;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">A</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topalg_2.html#K2" title="TOPALG_2:func.2">R^1</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T2" onmouseover="rs('xboole_1/T2')" onmouseout="rh()">XBOOLE_1:2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">S</font> = <a href="topalg_2.html#K2" title="TOPALG_2:func.2">R^1</a> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">A</font> as    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of  <a href="topalg_2.html#K2" title="TOPALG_2:func.2">R^1</a>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">g</font> = <font color="Maroon" title="c3">f</font> as   <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c5">S</font></span>)</span>,<span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34"><span class="lab"><font color="Green" title="E21">A1</font></span></a></span>;<br/>
<a NAME="E8:34"/><span class="lab"><font color="Green" title="E23">A3</font></span>: 
<font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c6">g</font>
 
;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">g</font> = <font color="Maroon" title="c6">g</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c1">T</font> ;<br/>
<a NAME="E10:34"/>
 for <font color="Olive" title="b1">P1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>  st <font color="Olive" title="b1">P1</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  holds <br/><font color="Maroon" title="c7">g</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Olive" title="b1">P1</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> 
 
;<br/>
<a NAME="E11:34"/><span class="kw">then </span>
<font color="Maroon" title="c7">g</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="ref" href="pre_topc.html#D6" onmouseover="rs('pre_topc/D6')" onmouseout="rh()">PRE_TOPC:def 6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:34"/>
<font color="Maroon" title="c2">f</font> is  <a href="topalg_6.html#V4" title="TOPALG_6:attr.4">parametrized-curve</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:34"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="txt" href="#E4:34"><span class="lab"><font color="Green" title="E22">A2</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/>


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