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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="analmetr.html#NM2">OrtAfPl</a>;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<div><i><font color="Green">E21</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:23_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="euclmetr.html#V6" target="_self">translation</a>
 ;<br/><a NAME="E2:23_1"/><b>then </b>
 <a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font> <a href="papdesaf.html#NR4" target="_self">satisfies_des'</a> 
 <b>by </b><i><a class="ref" href="euclmetr.html#D6" target="_self">Def6</a></i>;<br/><b>hence </b><a NAME="E3:23_1"/>
 <a href="conmetr.html#NR8" target="_self">des_holds_in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="euclmetr.html#E22"><i><font color="Green">Lemma20</font></i></a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:23_2"/>
 <a href="conmetr.html#NR8" target="_self">des_holds_in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:23_2"/><b>then </b>
 <a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font> is <a href="aff_2.html#V11">translational</a>
 <b>by </b><i><a class="txt" href="euclmetr.html#E22"><i><font color="Green">Lemma20</font></i></a></i>;<br/><b>hence </b><a NAME="E3:23_2"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="euclmetr.html#V6" target="_self">translation</a>
 <b>by </b><i><a class="ref" href="euclmetr.html#D6" target="_self">Def6</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:23"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="euclmetr.html#V6" target="_self">translation</a> iff  <a href="conmetr.html#NR8" target="_self">des_holds_in</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="euclmetr.html#E1:23"><i><font color="Green">E21</font></i></a></i>;<br/>


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