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<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c1">p</font> is <a href="trees_3.html#V4" title="TREES_3:attr.4">Tree-yielding</a> &amp; <font color="Maroon" title="c2">q</font> is <a href="trees_3.html#V4" title="TREES_3:attr.4">Tree-yielding</a> ) iff <font color="Maroon" title="c1">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c2">q</font> is <a href="trees_3.html#V4" title="TREES_3:attr.4">Tree-yielding</a> )</span><br/>



<a NAME="E1:55"/><i><font color="Green" title="E25">A1</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">q</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></i>;<br/>
<b>thus </b><a NAME="E2:55"/>
( <font color="Maroon" title="c1">p</font> is <a href="trees_3.html#V4" title="TREES_3:attr.4">Tree-yielding</a> &amp; <font color="Maroon" title="c2">q</font> is <a href="trees_3.html#V4" title="TREES_3:attr.4">Tree-yielding</a> implies <font color="Maroon" title="c1">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c2">q</font> is <a href="trees_3.html#V4" title="TREES_3:attr.4">Tree-yielding</a> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c2">q</font> is <a href="trees_3.html#V4" title="TREES_3:attr.4">Tree-yielding</a> implies ( <font color="Maroon" title="c1">p</font> is <a href="trees_3.html#V4" title="TREES_3:attr.4">Tree-yielding</a> &amp; <font color="Maroon" title="c2">q</font> is <a href="trees_3.html#V4" title="TREES_3:attr.4">Tree-yielding</a> ) )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:55_1"/>
(  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">p</font> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">q</font> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D9" target="_self" title="TREES_3:def.9">TREES_3:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c2">q</font> is <a href="trees_3.html#V4" title="TREES_3:attr.4">Tree-yielding</a></span><br/>

<b>hence </b><a NAME="E2:55_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c2">q</font></span>)</span> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a>
 <b>by </b><i><a class="txt" href="#E1:55"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="trees_3.html#T3" target="_self" title="TREES_3:th.3">Th3</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D9" target="_self" title="TREES_3:def.9">TREES_3:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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

<b>assume </b><a NAME="E3:55"/><i><font color="Green" title="E26">A2</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c2">q</font></span>)</span> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D9" target="_self" title="TREES_3:def.9">TREES_3:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> is <a href="trees_3.html#V4" title="TREES_3:attr.4">Tree-yielding</a> &amp; <font color="Maroon" title="c2">q</font> is <a href="trees_3.html#V4" title="TREES_3:attr.4">Tree-yielding</a> )</span><br/>

<b>hence </b><a NAME="E4:55"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">p</font> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a>
 <b>by </b><i><a class="txt" href="#E1:55"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="trees_3.html#T3" target="_self" title="TREES_3:th.3">Th3</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D9" target="_self" title="TREES_3:def.9">TREES_3:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">q</font> is <a href="trees_3.html#V4" title="TREES_3:attr.4">Tree-yielding</a></span><br/>

<b>thus </b><a NAME="E5:55"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">q</font> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a>
 <b>by </b><i><a class="txt" href="#E1:55"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="#E3:55"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="trees_3.html#T3" target="_self" title="TREES_3:th.3">Th3</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D9" target="_self" title="TREES_3:def.9">TREES_3:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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