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<b>set </b><font color="Maroon">t1t2</font> = <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">T1</font>,<font color="Maroon">T2</font></span><a href="finseq_1.html#K10">*&gt;</a></span>;<br/>
<a NAME="E1:15_1_1"/>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">T1</font> is <a href="finset_1.html#V1">finite</a> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">T2</font> is <a href="finset_1.html#V1">finite</a> )
 
;<br/>
<a NAME="E2:15_1_1"/><b>then </b><i><font color="Green">E29</font></i>: 
( <font color="Maroon">T1</font> <a href="hidden.html#R2">in</a>  <a href="trees_3.html#K5">FinTrees</a> <font color="Maroon">D</font> &amp; <font color="Maroon">T2</font> <a href="hidden.html#R2">in</a>  <a href="trees_3.html#K5">FinTrees</a> <font color="Maroon">D</font> )
 
<b>by </b><i><a class="ref" href="trees_3.html#D8">TREES_3:def 8</a></i>;<br/>
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">T1</font>,<font color="Maroon">T2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> = 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">T1</font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">T2</font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D9">FINSEQ_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">T1</font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">T2</font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T44">FINSEQ_1:44</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">T1</font></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">T2</font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">T1</font></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">T2</font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">T1</font>,<font color="Maroon">T2</font></span><a href="tarski.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>
;<br/>
<a NAME="E4:15_1_1"/><b>then </b>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">T1</font>,<font color="Maroon">T2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="trees_3.html#K5">FinTrees</a> <font color="Maroon">D</font>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E5:15_1_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">T1</font>,<font color="Maroon">T2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="tarski.html#R1">c=</a>  <a href="trees_3.html#K5">FinTrees</a> <font color="Maroon">D</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">T1T2</font> = <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">T1</font>,<font color="Maroon">T2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="trees_3.html#K5">FinTrees</a> <font color="Maroon">D</font> <b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E7:15_1_1"/>
<font color="Maroon">x</font> <a href="trees_4.html#K10">-tree</a> <font color="Maroon">T1</font>,<font color="Maroon">T2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="trees_4.html#K12">-tree</a> <font color="Maroon">T1T2</font>
 
<b>by </b><i><a class="ref" href="trees_4.html#D6">TREES_4:def 6</a></i>;<br/>
<a NAME="E8:15_1_1"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="trees_4.html#K10">-tree</a> <font color="Maroon">T1</font>,<font color="Maroon">T2</font></span>)</span> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="ref" href="trees_3.html#D8">TREES_3:def 8</a></i>;<br/>
<b>hence </b><a NAME="E9:15_1_1"/>
<font color="Maroon">x</font> <a href="trees_4.html#K10">-tree</a> <font color="Maroon">T1</font>,<font color="Maroon">T2</font> is  <a href="finset_1.html#V1">finite</a> <a href="bintree1.html#V2" target="_self">binary</a> <a href="trees_2.html#NM6">DecoratedTree</a> of <font color="Maroon">D</font>
 <b>by </b><i>, <a class="ref" href="finset_1.html#T29">FINSET_1:29</a></i>;<br/>


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