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<span class="kw">consider </span><font color="Maroon" title="c2">d</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font>;<br/>
<span class="kw">take </span><font color="Maroon" title="c3">Z</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="trees_2.html#K9" title="TREES_2:func.9">--&gt;</a> <font color="Maroon" title="c2">d</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> holds <br/><font color="Olive" title="b1">x</font> is   <a href="trees_2.html#NM5" title="TREES_2:NM.5">DecoratedTree</a> of <font color="Maroon" title="c1">D</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> implies <font color="Maroon" title="c4">x</font> is   <a href="trees_2.html#NM5" title="TREES_2:NM.5">DecoratedTree</a> of <font color="Maroon" title="c1">D</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:36_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font>
 ; <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="c4">x</font> is   <a href="trees_2.html#NM5" title="TREES_2:NM.5">DecoratedTree</a> of <font color="Maroon" title="c1">D</font></span><br/>

<span class="kw">hence </span><a NAME="E3:36_1_1"/>
<font color="Maroon" title="c4">x</font> is   <a href="trees_2.html#NM5" title="TREES_2:NM.5">DecoratedTree</a> of <font color="Maroon" title="c1">D</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>; <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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