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<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</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">H1</font>, <font color="Olive" title="b2">H2</font> being   <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a>   <a href="glib_009.html#V1" title="GLIB_009:attr.1">plain</a>   <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c1">G</font> holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">H1</font>,<font color="Olive" title="b2">H2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glenum00.html#K13" title="GLENUM00:func.13">SubtreeRel</a> <font color="Maroon" title="c1">G</font> iff <font color="Olive" title="b1">H1</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Olive" title="b2">H2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">H1</font>, <font color="Maroon" title="c3">H2</font> be   <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a>   <a href="glib_009.html#V1" title="GLIB_009:attr.1">plain</a>   <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c1">G</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"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">H1</font>,<font color="Maroon" title="c3">H2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glenum00.html#K13" title="GLENUM00:func.13">SubtreeRel</a> <font color="Maroon" title="c1">G</font> iff <font color="Maroon" title="c2">H1</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c3">H2</font> )</span><br/>



<a NAME="E1:203"/><span class="lab"><font color="Green" title="E121">A1</font></span>: 
( <font color="Maroon" title="c2">H1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a>  &amp; <font color="Maroon" title="c3">H2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glenum00.html#T1" target="_self" onmouseover="rs('glenum00/T1')" onmouseout="rh()">Th1</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"> ( <font color="Maroon" title="c2">H1</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c3">H2</font> implies <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">H1</font>,<font color="Maroon" title="c3">H2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glenum00.html#K13" title="GLENUM00:func.13">SubtreeRel</a> <font color="Maroon" title="c1">G</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:203_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">H1</font>,<font color="Maroon" title="c3">H2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glenum00.html#K13" title="GLENUM00:func.13">SubtreeRel</a> <font color="Maroon" title="c1">G</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="c2">H1</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c3">H2</font></span><br/><a NAME="E2:203_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">H1</font>,<font color="Maroon" title="c3">H2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glenum00.html#K6" title="GLENUM00:func.6">SubgraphRel</a> <font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mmlquer2.html#T4" onmouseover="rs('mmlquer2/T4')" onmouseout="rh()">MMLQUER2:4</a></span>;<br/><span class="kw">hence </span><a NAME="E3:203_1"/>
<font color="Maroon" title="c2">H1</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c3">H2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:203"><span class="lab"><font color="Green" title="E121">A1</font></span></a>, <a class="ref" href="glenum00.html#D6" target="_self" onmouseover="rs('glenum00/D6')" onmouseout="rh()">Def6</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>

<a NAME="E3:203"/><span class="lab"><font color="Green" title="E122">A2</font></span>: 
( <font color="Maroon" title="c2">H1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K12" title="GLENUM00:func.12">.allTrees()</a>  &amp; <font color="Maroon" title="c3">H2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K12" title="GLENUM00:func.12">.allTrees()</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glenum00.html#T138" target="_self" onmouseover="rs('glenum00/T138')" onmouseout="rh()">Th138</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:203"/>
<font color="Maroon" title="c2">H1</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c3">H2</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"> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">H1</font>,<font color="Maroon" title="c3">H2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glenum00.html#K13" title="GLENUM00:func.13">SubtreeRel</a> <font color="Maroon" title="c1">G</font></span><br/>

<a NAME="E5:203"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">H1</font>,<font color="Maroon" title="c3">H2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glenum00.html#K6" title="GLENUM00:func.6">SubgraphRel</a> <font color="Maroon" title="c1">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:203"><span class="lab"><font color="Green" title="E121">A1</font></span></a>, <a class="ref" href="glenum00.html#D6" target="_self" onmouseover="rs('glenum00/D6')" onmouseout="rh()">Def6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:203"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">H1</font>,<font color="Maroon" title="c3">H2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glenum00.html#K13" title="GLENUM00:func.13">SubtreeRel</a> <font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:203"><span class="lab"><font color="Green" title="E122">A2</font></span></a>, <a class="ref" href="mmlquer2.html#T4" onmouseover="rs('mmlquer2/T4')" onmouseout="rh()">MMLQUER2:4</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/>


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