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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>



<a NAME="E1:57"/><i><font color="Green">E29</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T44">FINSEQ_1:44</a></i>;<br/>
<b>thus </b><a NAME="E2:57"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="trees_3.html#V6" target="_self">DTree-yielding</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="trees_3.html#V6" target="_self">DTree-yielding</a> implies <font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>2</sub></font> is <a href="trees_3.html#V6" target="_self">DTree-yielding</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:57_1"/>
(  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>1</sub></font> is <a href="trees_3.html#V3" target="_self">constituted-DTrees</a> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>2</sub></font> is <a href="trees_3.html#V3" target="_self">constituted-DTrees</a> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D11" target="_self">TREES_3:def 11</a><br/>

<b>hence </b><a NAME="E2:57_1"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="trees_3.html#V3" target="_self">constituted-DTrees</a>
 <b>by </b><i><a class="txt" href="trees_3.html#E1:57"><i><font color="Green">E29</font></i></a>, <a class="ref" href="trees_3.html#T9" target="_self">Th9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D11" target="_self">TREES_3:def 11</a><br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E3:57"/><i><font color="Green">E30</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="trees_3.html#V3" target="_self">constituted-DTrees</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D11" target="_self">TREES_3:def 11</a><br/>

<b>hence </b><a NAME="E4:57"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>1</sub></font> is <a href="trees_3.html#V3" target="_self">constituted-DTrees</a>
 <b>by </b><i><a class="txt" href="trees_3.html#E1:57"><i><font color="Green">E29</font></i></a>, <a class="ref" href="trees_3.html#T9" target="_self">Th9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D11" target="_self">TREES_3:def 11</a><br/>

<b>thus </b><a NAME="E5:57"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>2</sub></font> is <a href="trees_3.html#V3" target="_self">constituted-DTrees</a>
 <b>by </b><i><a class="txt" href="trees_3.html#E1:57"><i><font color="Green">E29</font></i></a>, <a class="txt" href="trees_3.html#E3:57"><i><font color="Green">E30</font></i></a>, <a class="ref" href="trees_3.html#T9" target="_self">Th9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D11" target="_self">TREES_3:def 11</a><br/>


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