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<span class="kw">let </span><font color="Maroon" title="c1">R</font>, <font color="Maroon" title="c2">S</font>, <font color="Maroon" title="c3">T</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <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="c1">R</font> <a href="necklace.html#R3" title="NECKLACE:pred.3">is_equimorphic_to</a> <font color="Maroon" title="c2">S</font> &amp; <font color="Maroon" title="c2">S</font> <a href="necklace.html#R3" title="NECKLACE:pred.3">is_equimorphic_to</a> <font color="Maroon" title="c3">T</font> implies <font color="Maroon" title="c1">R</font> <a href="necklace.html#R3" title="NECKLACE:pred.3">is_equimorphic_to</a> <font color="Maroon" title="c3">T</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:18"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
( <font color="Maroon" title="c1">R</font> <a href="necklace.html#R3" title="NECKLACE:pred.3">is_equimorphic_to</a> <font color="Maroon" title="c2">S</font> &amp; <font color="Maroon" title="c2">S</font> <a href="necklace.html#R3" title="NECKLACE:pred.3">is_equimorphic_to</a> <font color="Maroon" title="c3">T</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="c1">R</font> <a href="necklace.html#R3" title="NECKLACE:pred.3">is_equimorphic_to</a> <font color="Maroon" title="c3">T</font></span><br/>

<a NAME="E2:18"/><span class="kw">then </span>
( <font color="Maroon" title="c2">S</font> <a href="necklace.html#R2" title="NECKLACE:pred.2">embeds</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c3">T</font> <a href="necklace.html#R2" title="NECKLACE:pred.2">embeds</a> <font color="Maroon" title="c2">S</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="necklace.html#D3" target="_self" title="NECKLACE:def.3">Def3</a></span>;<br/>
<a NAME="E3:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A2</font></span>: 
<font color="Maroon" title="c3">T</font> <a href="necklace.html#R2" title="NECKLACE:pred.2">embeds</a> <font color="Maroon" title="c1">R</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="necklace.html#T13" target="_self" title="NECKLACE:th.13">Th13</a></span>;<br/>
<a NAME="E4:18"/>
( <font color="Maroon" title="c1">R</font> <a href="necklace.html#R2" title="NECKLACE:pred.2">embeds</a> <font color="Maroon" title="c2">S</font> &amp; <font color="Maroon" title="c2">S</font> <a href="necklace.html#R2" title="NECKLACE:pred.2">embeds</a> <font color="Maroon" title="c3">T</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="necklace.html#D3" target="_self" title="NECKLACE:def.3">Def3</a></span>;<br/>
<a NAME="E5:18"/><span class="kw">then </span>
<font color="Maroon" title="c1">R</font> <a href="necklace.html#R2" title="NECKLACE:pred.2">embeds</a> <font color="Maroon" title="c3">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="necklace.html#T13" target="_self" title="NECKLACE:th.13">Th13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:18"/>
<font color="Maroon" title="c1">R</font> <a href="necklace.html#R3" title="NECKLACE:pred.3">is_equimorphic_to</a> <font color="Maroon" title="c3">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="ref" href="necklace.html#D3" target="_self" title="NECKLACE:def.3">Def3</a></span>; <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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