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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:9_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="vectmetr.html#K1" target="_self">ISOM</a> <font color="Maroon">V</font>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">V</font>,<font color="Maroon">V</font><b> such that </b><br/><a NAME="E3:9_1_1_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>and </b><br/><a NAME="E4:9_1_1_1"/>
<font color="Maroon">f</font> is <a href="vectmetr.html#V3" target="_self">isometric</a>
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E5:9_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>
 <b>by </b><i>, <a class="ref" href="funct_2.html#T11">FUNCT_2:11</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:9_1_1"/>
 <a href="vectmetr.html#K1" target="_self">ISOM</a> <font color="Maroon">V</font> is   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="funct_2.html#K1">Funcs</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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