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<b>let </b><font color="Maroon" title="c1">t</font> be   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</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">t</font> is <a href="trees_2.html#V1" title="TREES_2:attr.1">finite-order</a> implies <font color="Maroon" title="c1">t</font> is <a href="trees_9.html#V2" title="TREES_9:attr.2">finite-branching</a> )</span><br/>

<b>assume </b><a NAME="E1:18_1_1"/>
<font color="Maroon" title="c1">t</font> is <a href="trees_2.html#V1" title="TREES_2:attr.1">finite-order</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">t</font> is <a href="trees_9.html#V2" title="TREES_9:attr.2">finite-branching</a></span><br/>

<b>then reconsider </b><font color="Maroon" title="c2">a</font> = <font color="Maroon" title="c1">t</font> as  <a href="trees_2.html#V1" title="TREES_2:attr.1">finite-order</a> <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a> ;<br/>
<b>let </b><font color="Maroon" title="c3">x</font> be    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of <font color="Maroon" title="c1">t</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_9.html#D2" target="_self" title="TREES_9:def.2">TREES_9:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="trees_2.html#K1" title="TREES_2:func.1">succ</a> <font color="Maroon" title="c3">x</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a></span><br/>

<b>reconsider </b><font color="Maroon" title="c4">x</font> = <font color="Maroon" title="c3">x</font> as    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of <font color="Maroon" title="c2">a</font> ;<br/>
<a NAME="E4:18_1_1"/>
 <a href="trees_2.html#K1" title="TREES_2:func.1">succ</a> <font color="Maroon" title="c4">x</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
;<br/>
<b>hence </b><a NAME="E5:18_1_1"/>
 <a href="trees_2.html#K1" title="TREES_2:func.1">succ</a> <font color="Maroon" title="c3">x</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</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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