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<b>let </b><font color="Maroon">T</font> be   <a href="trees_2.html#NM4">DecoratedTree</a>, <font color="Maroon">T'</font> be   <a href="trees_2.html#NM4">DecoratedTree</a>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="trees_1.html#M1">Element</a> of  <a href="relat_1.html#K1">dom</a> <font color="Maroon">T</font>, <font color="Maroon">q</font> be    <a href="trees_1.html#M1">Element</a> of  <a href="relat_1.html#K1">dom</a> <font color="Maroon">T</font>;<br/>



<b>assume </b><a NAME="E1:107"/>
not <font color="Maroon">p</font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Maroon">q</font>
 ;<br/>

<a NAME="E2:107"/><b>then </b>
( <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T</font></span>)</span> <a href="trees_1.html#K5">with-replacement</a> <font color="Maroon">p</font>,<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T'</font></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="trees_2.html#K8">with-replacement</a> <font color="Maroon">p</font>,<font color="Maroon">T'</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T</font></span>)</span> <a href="trees_1.html#K5">with-replacement</a> <font color="Maroon">p</font>,<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T'</font></span>)</span> &amp; ( for <font color="Olive">r</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a>   holds <br/>(  not <font color="Olive">r</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">T'</font> or  not <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">r</font> or  not <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="trees_2.html#K8">with-replacement</a> <font color="Maroon">p</font>,<font color="Maroon">T'</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T'</font> <a href="funct_1.html#K1">.</a> <font color="Olive">r</font> ) ) )
 
<b>by </b><i><a class="ref" href="trees_1.html#T8">TREES_1:8</a>, <a class="ref" href="trees_2.html#T9">TREES_2:9</a>, <a class="ref" href="trees_2.html#D12">TREES_2:def 12</a></i>;<br/>
<b>hence </b><a NAME="E3:107"/>
<span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="trees_2.html#K8">with-replacement</a> <font color="Maroon">p</font>,<font color="Maroon">T'</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">q</font>
 <b>by </b><i><a class="ref" href="trees_2.html#D12">TREES_2:def 12</a></i>;<br/>


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