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<span class="kw">let </span><font color="Maroon" title="c1">X1</font>, <font color="Maroon" title="c2">X2</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="trees_3.html#V3" title="TREES_3:attr.3">constituted-DTrees</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">t</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font> holds  <font color="Olive" title="b1">t</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  ) &amp; (  for <font color="Olive" title="b1">t</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X2</font> holds  <font color="Olive" title="b1">t</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  ) implies  for <font color="Olive" title="b1">C</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds  <font color="Olive" title="b1">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c1">X1</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:17"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
 for <font color="Olive" title="b1">t</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font> holds  <font color="Olive" title="b1">t</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 <span class="kw">and </span><br/><a NAME="E2:17"/><span class="lab"><font color="Green" title="E10">A2</font></span>: 
 for <font color="Olive" title="b1">t</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X2</font> holds  <font color="Olive" title="b1">t</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">C</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds  <font color="Olive" title="b1">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c1">X1</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span></span><br/>

<div><span class="lab"><font color="Green" title="E11">A3</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="17_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">t</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font> holds  <font color="Olive" title="b1">t</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">t</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">t</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> </span><br/><a NAME="E1:17_1"/>
( <font color="Maroon" title="c3">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X1</font> or <font color="Maroon" title="c3">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">X2</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" onmouseover="rs('xboole_0/D3')" onmouseout="rh()">XBOOLE_0:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E2:17_1"/>
<font color="Maroon" title="c3">t</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E10">A2</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">let </span><font color="Maroon" title="c3">C</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c1">X1</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c4">X</font> = <font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">f</font> = <font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">f1</font> = <font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c1">X1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">f2</font> = <font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font>;<br/>
<a NAME="E4:17"/><span class="lab"><font color="Green" title="E12">A4</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">C</font> <a href="trees_9.html#K12" title="TREES_9:func.12">-Subtrees</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E5:17"/><span class="lab"><font color="Green" title="E13">A5</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c1">X1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">C</font> <a href="trees_9.html#K12" title="TREES_9:func.12">-Subtrees</a> <font color="Maroon" title="c1">X1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E6:17"/><span class="lab"><font color="Green" title="E14">A6</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">C</font> <a href="trees_9.html#K12" title="TREES_9:func.12">-Subtrees</a> <font color="Maroon" title="c2">X2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E7:17"/><span class="lab"><font color="Green" title="E15">A7</font></span>: 
<font color="Maroon" title="c3">C</font> <a href="trees_9.html#K12" title="TREES_9:func.12">-Subtrees</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K12" title="TREES_9:func.12">-Subtrees</a> <font color="Maroon" title="c1">X1</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K12" title="TREES_9:func.12">-Subtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circtrm1.html#T8" target="_self" onmouseover="rs('circtrm1/T8')" onmouseout="rh()">Th8</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="17_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c1">X1</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span></span>)</span> holds <br/>( ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> ) &amp; (  not <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c1">X1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> ) )</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c1">X1</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span></span>)</span> implies ( ( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> ) &amp; (  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c1">X1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> ) ) )</span><br/><span class="kw">assume </span><a NAME="E1:17_2"/><span class="lab"><font color="Green" title="E16">A8</font></span>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c1">X1</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( ( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> ) &amp; (  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c1">X1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> ) )</span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">t</font> = <font color="Maroon" title="c8">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E15">A7</font></span></a></span>;<br/><a NAME="E3:17_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="txt" href="#E1:17_2"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="ref" href="funct_2.html#T5" onmouseover="rs('funct_2/T5')" onmouseout="rh()">FUNCT_2:5</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">p</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D11" onmouseover="rs('finseq_1/D11')" onmouseout="rh()">FINSEQ_1:def 11</a></span>;<br/><div><span class="kw">hereby </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c1">X1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:17_2_1"/><span class="lab"><font color="Green" title="E17">A9</font></span>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span><br/><a NAME="E2:17_2_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="ref" href="funct_2.html#T5" onmouseover="rs('funct_2/T5')" onmouseout="rh()">FUNCT_2:5</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">p2</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Maroon" title="c2">X2</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D11" onmouseover="rs('finseq_1/D11')" onmouseout="rh()">FINSEQ_1:def 11</a></span>;<br/><a NAME="E4:17_2_1"/><span class="lab"><font color="Green" title="E18">A10</font></span>: 
<font color="Maroon" title="c9">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <font color="Maroon" title="c10">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="txt" href="#E1:17_2"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="ref" href="trees_9.html#D13" onmouseover="rs('trees_9/D13')" onmouseout="rh()">TREES_9:def 13</a></span>;<br/><a NAME="E5:17_2_1"/>
<font color="Maroon" title="c9">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <font color="Maroon" title="c11">p2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="txt" href="#E1:17_2_1"><span class="lab"><font color="Green" title="E17">A9</font></span></a>, <a class="ref" href="trees_9.html#D13" onmouseover="rs('trees_9/D13')" onmouseout="rh()">TREES_9:def 13</a></span>;<br/><span class="kw">hence </span><a NAME="E6:17_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:17_2_1"><span class="lab"><font color="Green" title="E18">A10</font></span></a>, <a class="ref" href="trees_4.html#T15" onmouseover="rs('trees_4/T15')" onmouseout="rh()">TREES_4:15</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E6:17_2"/>
 not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c1">X1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span><br/><a NAME="E7:17_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A11</font></span>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c1">X1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17_2"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="ref" href="xboole_0.html#D3" onmouseover="rs('xboole_0/D3')" onmouseout="rh()">XBOOLE_0:def 3</a></span>;<br/><a NAME="E8:17_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c1">X1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Maroon" title="c1">X1</font></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="ref" href="funct_2.html#T5" onmouseover="rs('funct_2/T5')" onmouseout="rh()">FUNCT_2:5</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">p1</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c1">X1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Maroon" title="c1">X1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D11" onmouseover="rs('finseq_1/D11')" onmouseout="rh()">FINSEQ_1:def 11</a></span>;<br/><a NAME="E10:17_2"/><span class="lab"><font color="Green" title="E18">A12</font></span>: 
<font color="Maroon" title="c9">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <font color="Maroon" title="c10">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="txt" href="#E1:17_2"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="ref" href="trees_9.html#D13" onmouseover="rs('trees_9/D13')" onmouseout="rh()">TREES_9:def 13</a></span>;<br/><a NAME="E11:17_2"/>
<font color="Maroon" title="c9">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <font color="Maroon" title="c11">p1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="txt" href="#E7:17_2"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="ref" href="trees_9.html#D13" onmouseover="rs('trees_9/D13')" onmouseout="rh()">TREES_9:def 13</a></span>;<br/><span class="kw">hence </span><a NAME="E12:17_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c1">X1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:17_2"><span class="lab"><font color="Green" title="E18">A12</font></span></a>, <a class="ref" href="trees_4.html#T15" onmouseover="rs('trees_4/T15')" onmouseout="rh()">TREES_4:15</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E9:17"/>
<font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">X2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c1">X1</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="trees_9.html#K13" title="TREES_9:func.13">-ImmediateSubtrees</a> <font color="Maroon" title="c2">X2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="ref" href="funct_4.html#D1" onmouseover="rs('funct_4/D1')" onmouseout="rh()">FUNCT_4:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
