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<b>let </b><font color="Maroon">X</font> be   <a href="rltopsp1.html#NM1">LinearTopSpace</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">x2</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><b>that </b><br/><a NAME="E1:67_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>
 <b>and </b><br/><a NAME="E2:67_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">x2</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>
 <b>and </b><br/><a NAME="E3:67_1"/><i><font color="Green">E38</font></i>: 
<span class="p1">(<span class="default"><a href="rltopsp1.html#K3" target="_self">transl</a> <font color="Maroon">a</font>,<font color="Maroon">X</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" target="_self">transl</a> <font color="Maroon">a</font>,<font color="Maroon">X</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font>
 ;<br/><b>reconsider </b><font color="Maroon">x1'</font> = <font color="Maroon">x1</font>, <font color="Maroon">x2'</font> = <font color="Maroon">x2</font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font> <b>by </b><i>, <a class="txt" href="rltopsp1.html#E4"><i><font color="Green">Lemma44</font></i></a></i>;<br/><a NAME="E5:67_1"/>
( <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" target="_self">transl</a> <font color="Maroon">a</font>,<font color="Maroon">X</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">x1'</font> &amp; <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" target="_self">transl</a> <font color="Maroon">a</font>,<font color="Maroon">X</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">x2'</font> )
 <b>by </b><i><a class="ref" href="rltopsp1.html#T3" target="_self">Th3</a></i>;<br/><b>hence </b><a NAME="E6:67_1"/>
<font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font>
 <b>by </b><i><a class="txt" href="rltopsp1.html#E5"><i><font color="Green">Lemma45</font></i></a>, <a class="ref" href="rlvect_1.html#T21">RLVECT_1:21</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:67"/>
 <a href="rltopsp1.html#K3" target="_self">transl</a> <font color="Maroon">a</font>,<font color="Maroon">X</font> is <a href="funct_1.html#V2">one-to-one</a>
 <b>by </b><i><a class="ref" href="funct_2.html#T25">FUNCT_2:25</a></i>;<br/>


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