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<span class="kw">let </span><font color="Maroon" title="c3">tr1</font>, <font color="Maroon" title="c4">tr2</font> be   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="trees_2.html#NM5" title="TREES_2:NM.5">DecoratedTree</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">Tr</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="trees_2.html#NM5" title="TREES_2:NM.5">DecoratedTree</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font> holds <br/> ( <font color="Olive" title="b1">Tr</font> <a href="prelamb.html#R1" title="PRELAMB:pred.1">represents</a> <font color="Maroon" title="c2">x</font> iff <font color="Maroon" title="c3">tr1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">Tr</font> ) ) &amp; (  for <font color="Olive" title="b1">Tr</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="trees_2.html#NM5" title="TREES_2:NM.5">DecoratedTree</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font> holds <br/> ( <font color="Olive" title="b1">Tr</font> <a href="prelamb.html#R1" title="PRELAMB:pred.1">represents</a> <font color="Maroon" title="c2">x</font> iff <font color="Maroon" title="c4">tr2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">Tr</font> ) ) implies <font color="Maroon" title="c3">tr1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">tr2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:13_1_1"/><span class="lab"><font color="Green" title="E4">A2</font></span>: 
 for <font color="Olive" title="b1">Tr</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="trees_2.html#NM5" title="TREES_2:NM.5">DecoratedTree</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font> holds <br/> ( <font color="Olive" title="b1">Tr</font> <a href="prelamb.html#R1" title="PRELAMB:pred.1">represents</a> <font color="Maroon" title="c2">x</font> iff <font color="Maroon" title="c3">tr1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">Tr</font> )
 <span class="kw">and </span><br/><a NAME="E2:13_1_1"/><span class="lab"><font color="Green" title="E5">A3</font></span>: 
 for <font color="Olive" title="b1">Tr</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="trees_2.html#NM5" title="TREES_2:NM.5">DecoratedTree</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font> holds <br/> ( <font color="Olive" title="b1">Tr</font> <a href="prelamb.html#R1" title="PRELAMB:pred.1">represents</a> <font color="Maroon" title="c2">x</font> iff <font color="Maroon" title="c4">tr2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">Tr</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">tr1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">tr2</font></span><br/>

<a NAME="E3:13_1_1"/>
<font color="Maroon" title="c3">tr1</font> <a href="prelamb.html#R1" title="PRELAMB:pred.1">represents</a> <font color="Maroon" title="c2">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1_1"><span class="lab"><font color="Green" title="E4">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:13_1_1"/>
<font color="Maroon" title="c3">tr1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">tr2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1_1"><span class="lab"><font color="Green" title="E5">A3</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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