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<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <a href="glenum00.html#M1" title="GLENUM00:mode.1">Element</a> of  <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a></span>)</span>) <span class="kw">-&gt; </span>   <a href="glib_000.html#M2" title="GLIB_000:mode.2">inducedSubgraph</a> of <font color="Maroon" title="c2">G2</font>, <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="glib_010.html#K10" title="GLIB_010:func.10">|</a> $1</span>)</span> <a href="glib_010.html#K5" title="GLIB_010:func.5">_V</a></span>)</span>, <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="glib_010.html#K10" title="GLIB_010:func.10">|</a> $1</span>)</span> <a href="glib_010.html#K6" title="GLIB_010:func.6">_E</a></span>)</span> =  <a href="glib_010.html#K9" title="GLIB_010:func.9">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="glib_010.html#K10" title="GLIB_010:func.10">|</a> $1</span>)</span>;<br/>
<a NAME="E1:37_1_1"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="glenum00.html#M1" title="GLENUM00:mode.1">Element</a> of  <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a></span>)</span> holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">G2</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/>
<span class="kw">consider </span><font color="Maroon" title="c4">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a></span>)</span><span class="kw"> such that </span><br/><a NAME="E3:37_1_1"/><span class="lab"><font color="Green" title="E28">A2</font></span>: 
 for <font color="Olive" title="b1">H</font> being    <a href="glenum00.html#M1" title="GLENUM00:mode.1">Element</a> of  <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a></span>)</span> holds  <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">H</font>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="glibpre1.html#S1" onmouseover="rs('glibpre1/S1')" onmouseout="rh()">GLIBPRE1:sch 1</a>(<a class="txt" href="#E1:37_1_1"><span class="lab"><font color="Green" title="E27">A1</font></span></a>);<br/></span>
<span class="kw">reconsider </span><font color="Maroon" title="c5">f</font> = <font color="Maroon" title="c4">f</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a></span>)</span> ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c5">f</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">  for <font color="Olive" title="b1">H</font> being   <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">G1</font> holds  <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_010.html#K9" title="GLIB_010:func.9">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="glib_010.html#K10" title="GLIB_010:func.10">|</a> <font color="Olive" title="b1">H</font></span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">H</font> be   <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">G1</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="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_010.html#K9" title="GLIB_010:func.9">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="glib_010.html#K10" title="GLIB_010:func.10">|</a> <font color="Maroon" title="c6">H</font></span>)</span></span><br/>

<a NAME="E5:37_1_1"/>
<font color="Maroon" title="c6">H</font> is    <a href="glenum00.html#M1" title="GLENUM00:mode.1">Element</a> of  <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a></span>)</span>
 
<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/>
<span class="kw">hence </span><a NAME="E6:37_1_1"/>
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_010.html#K9" title="GLIB_010:func.9">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="glib_010.html#K10" title="GLIB_010:func.10">|</a> <font color="Maroon" title="c6">H</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37_1_1"><span class="lab"><font color="Green" title="E28">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/>


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