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<span class="kw">thus </span><a NAME="E1:38_1_1"/>
 not  <a href="glenum00.html#K5" title="GLENUM00:func.5">SG2SGFunc</a> <font color="Maroon" title="c3">F</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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">  <a href="glenum00.html#K5" title="GLENUM00:func.5">SG2SGFunc</a> <font color="Maroon" title="c3">F</font> is  <a href="glib_000.html#V12" title="GLIB_000:attr.12">Graph-yielding</a> </span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="38_1_1_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">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>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="glenum00.html#K5" title="GLENUM00:func.5">SG2SGFunc</a> <font color="Maroon" title="c3">F</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="glenum00.html#K5" title="GLENUM00:func.5">SG2SGFunc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> is   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">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="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="glenum00.html#K5" title="GLENUM00:func.5">SG2SGFunc</a> <font color="Maroon" title="c3">F</font></span>)</span> implies <span class="p1">(<span class="default"><a href="glenum00.html#K5" title="GLENUM00:func.5">SG2SGFunc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> is   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> )</span><br/><span class="kw">assume </span><a NAME="E1:38_1_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="glenum00.html#K5" title="GLENUM00:func.5">SG2SGFunc</a> <font color="Maroon" title="c3">F</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"><a href="glenum00.html#K5" title="GLENUM00:func.5">SG2SGFunc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> is   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">H</font> = <font color="Maroon" title="c4">x</font> as   <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> <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/><a NAME="E3:38_1_1_1"/>
<span class="p1">(<span class="default"><a href="glenum00.html#K5" title="GLENUM00:func.5">SG2SGFunc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">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="c5">H</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glenum00.html#D5" target="_self" onmouseover="rs('glenum00/D5')" onmouseout="rh()">Def5</a></span>;<br/><span class="kw">hence </span><a NAME="E4:38_1_1_1"/>
<span class="p1">(<span class="default"><a href="glenum00.html#K5" title="GLENUM00:func.5">SG2SGFunc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> is   <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"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:38_1_1"/>
 <a href="glenum00.html#K5" title="GLENUM00:func.5">SG2SGFunc</a> <font color="Maroon" title="c3">F</font> is  <a href="glib_000.html#V12" title="GLIB_000:attr.12">Graph-yielding</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D53" onmouseover="rs('glib_000/D53')" onmouseout="rh()">GLIB_000:def 53</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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