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<span class="kw">let </span><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</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"> ( <font color="Maroon" title="c2">G2</font> is <font color="Maroon" title="c1">G1</font> <a href="glib_010.html#V19" title="GLIB_010:attr.19">-isomorphic</a>  implies <font color="Maroon" title="c1">G1</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a> ,<font color="Maroon" title="c2">G2</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a>  <a href="glib_015.html#R2" title="GLIB_015:pred.2">are_isomorphic</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:44"/>
<font color="Maroon" title="c2">G2</font> is <font color="Maroon" title="c1">G1</font> <a href="glib_010.html#V19" title="GLIB_010:attr.19">-isomorphic</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="c1">G1</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a> ,<font color="Maroon" title="c2">G2</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a>  <a href="glib_015.html#R2" title="GLIB_015:pred.2">are_isomorphic</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">F</font> being    <a href="glib_010.html#M1" title="GLIB_010:mode.1">PGraphMapping</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font><span class="kw"> such that </span><br/><a NAME="E3:44"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
<font color="Maroon" title="c3">F</font> is  <a href="glib_010.html#V17" title="GLIB_010:attr.17">isomorphism</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_010.html#D23" onmouseover="rs('glib_010/D23')" onmouseout="rh()">GLIB_010:def 23</a></span>;<br/>
<a NAME="E4:44"/><span class="lab"><font color="Green" title="E31">A2</font></span>: 
 <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 href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G1</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a> 
 
<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="E5:44"/><span class="lab"><font color="Green" title="E32">A3</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</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 href="hidden.html#R1" title="HIDDEN:pred.1">=</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="txt" href="#E3:44"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="glenum00.html#T32" target="_self" onmouseover="rs('glenum00/T32')" onmouseout="rh()">Th32</a></span>;<br/>
<a NAME="E6:44"/><span class="lab"><font color="Green" title="E33">A4</font></span>: 
 <a href="glenum00.html#K5" title="GLENUM00:func.5">SG2SGFunc</a> <font color="Maroon" title="c3">F</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="glenum00.html#T31" target="_self" onmouseover="rs('glenum00/T31')" onmouseout="rh()">Th31</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="44_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">G</font> being   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>  st <font color="Olive" title="b1">G</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">G1</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a>  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">G</font> is  <font color="Olive">b<sub>1</sub></font> <a href="glib_010.html#V19" title="GLIB_010:attr.19">-isomorphic</a>  <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">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"> ( <font color="Maroon" title="c4">G</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">G1</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a>  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">G</font> is  <font color="Maroon" title="c4">G</font> <a href="glib_010.html#V19" title="GLIB_010:attr.19">-isomorphic</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> )</span><br/><span class="kw">assume </span><a NAME="E1:44_1"/>
<font color="Maroon" title="c4">G</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">G1</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</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"> <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">G</font> is  <font color="Maroon" title="c4">G</font> <a href="glib_010.html#V19" title="GLIB_010:attr.19">-isomorphic</a>  <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">G</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/><span class="kw">reconsider </span><font color="Maroon" title="c6">F9</font> = <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> as    <a href="glib_010.html#M1" title="GLIB_010:mode.1">PGraphMapping</a> of <font color="Maroon" title="c5">H</font>, <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="glibpre1.html#T88" onmouseover="rs('glibpre1/T88')" onmouseout="rh()">GLIBPRE1:88</a></span>;<br/><a NAME="E4:44_1"/><span class="lab"><font color="Green" title="E34">A5</font></span>: 
<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">G</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/><a NAME="E5:44_1"/>
<font color="Maroon" title="c6">F9</font> is  <a href="glib_010.html#V17" title="GLIB_010:attr.17">isomorphism</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="glibpre1.html#T110" onmouseover="rs('glibpre1/T110')" onmouseout="rh()">GLIBPRE1:110</a></span>;<br/><span class="kw">hence </span><a NAME="E6:44_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">G</font> is  <font color="Maroon" title="c4">G</font> <a href="glib_010.html#V19" title="GLIB_010:attr.19">-isomorphic</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:44_1"><span class="lab"><font color="Green" title="E34">A5</font></span></a>, <a class="ref" href="glib_010.html#D23" onmouseover="rs('glib_010/D23')" onmouseout="rh()">GLIB_010:def 23</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="E8:44"/>
<font color="Maroon" title="c1">G1</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a> ,<font color="Maroon" title="c2">G2</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a>  <a href="glib_015.html#R2" title="GLIB_015:pred.2">are_isomorphic</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:44"><span class="lab"><font color="Green" title="E31">A2</font></span></a>, <a class="txt" href="#E5:44"><span class="lab"><font color="Green" title="E32">A3</font></span></a>, <a class="txt" href="#E6:44"><span class="lab"><font color="Green" title="E33">A4</font></span></a>, <a class="ref" href="glib_015.html#D13" onmouseover="rs('glib_015/D13')" onmouseout="rh()">GLIB_015:def 13</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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