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<span class="kw">let </span><font color="Maroon" title="c1">F</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">F</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  implies ( <font color="Maroon" title="c1">F</font> is  <a href="trees_3.html#V4" title="TREES_3:attr.4">Tree-yielding</a>  &amp; <font color="Maroon" title="c1">F</font> is  <a href="trees_3.html#V5" title="TREES_3:attr.5">FinTree-yielding</a>  &amp; <font color="Maroon" title="c1">F</font> is  <a href="trees_3.html#V6" title="TREES_3:attr.6">DTree-yielding</a>  ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:52_1_1"/><span class="lab"><font color="Green" title="E22">A1</font></span>: 
<font color="Maroon" title="c1">F</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">F</font> is  <a href="trees_3.html#V4" title="TREES_3:attr.4">Tree-yielding</a>  &amp; <font color="Maroon" title="c1">F</font> is  <a href="trees_3.html#V5" title="TREES_3:attr.5">FinTree-yielding</a>  &amp; <font color="Maroon" title="c1">F</font> is  <a href="trees_3.html#V6" title="TREES_3:attr.6">DTree-yielding</a>  )</span><br/>

<span class="kw">hence </span><a NAME="E2:52_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">F</font> is  <a href="trees_3.html#V1" title="TREES_3:attr.1">constituted-Trees</a> 
 ; <span class="comment"><font color="Red">:: according to </font></span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">F</font> is  <a href="trees_3.html#V5" title="TREES_3:attr.5">FinTree-yielding</a>  &amp; <font color="Maroon" title="c1">F</font> is  <a href="trees_3.html#V6" title="TREES_3:attr.6">DTree-yielding</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E3:52_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">F</font> is  <a href="trees_3.html#V2" title="TREES_3:attr.2">constituted-FinTrees</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1"><span class="lab"><font color="Green" title="E22">A1</font></span></a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="trees_3.html#D10" target="_self" title="TREES_3:def.10">TREES_3:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">F</font> is  <a href="trees_3.html#V6" title="TREES_3:attr.6">DTree-yielding</a> </span><br/>

<span class="kw">thus </span><a NAME="E4:52_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">F</font> is  <a href="trees_3.html#V3" title="TREES_3:attr.3">constituted-DTrees</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1"><span class="lab"><font color="Green" title="E22">A1</font></span></a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="trees_3.html#D11" target="_self" title="TREES_3:def.11">TREES_3:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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