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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> is <a href="trees_3.html#V4" title="TREES_3:attr.4">Tree-yielding</a> iff ( <font color="Maroon" title="c1">x</font> is   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a> &amp; <font color="Maroon" title="c2">y</font> is   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a> ) )</span><br/>



<a NAME="E1:61"/>
( ( <font color="Maroon" title="c1">x</font> is   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a> &amp; <font color="Maroon" title="c2">y</font> is   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a> implies <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a> ) &amp; ( <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> is <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a> implies ( <font color="Maroon" title="c1">x</font> is   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a> &amp; <font color="Maroon" title="c2">y</font> is   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a> ) ) &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 
<b>by </b><i><a class="ref" href="trees_3.html#T16" target="_self" title="TREES_3:th.16">Th16</a>, <a class="ref" href="finseq_2.html#T147" title="FINSEQ_2:th.147">FINSEQ_2:147</a></i>;<br/>
<b>hence </b><a NAME="E2:61"/>
( <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> is <a href="trees_3.html#V4" title="TREES_3:attr.4">Tree-yielding</a> iff ( <font color="Maroon" title="c1">x</font> is   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a> &amp; <font color="Maroon" title="c2">y</font> is   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a> ) )
 <b>by </b><i><a class="ref" href="trees_3.html#D9" target="_self" title="TREES_3:def.9">Def9</a></i>; <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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