<?xml version="1.0"?>
<div class="add">

<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">  for <font color="Olive" title="b1">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>  st <font color="Olive" title="b1">F</font> is  <a href="glib_010.html#V15" title="GLIB_010:attr.15">weak_SG-embedding</a>  holds <br/> <a href="glenum00.html#K5" title="GLENUM00:func.5">SG2SGFunc</a> <font color="Olive" title="b1">F</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">F</font> be    <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>; <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">F</font> is  <a href="glib_010.html#V15" title="GLIB_010:attr.15">weak_SG-embedding</a>  implies  <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><br/>





<span class="kw">assume </span><a NAME="E1:40"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
<font color="Maroon" title="c3">F</font> is  <a href="glib_010.html#V15" title="GLIB_010:attr.15">weak_SG-embedding</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="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> </span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="40_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">x1</font>, <font color="Olive" title="b2">x2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x1</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> &amp; <font color="Olive" title="b2">x2</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> &amp; <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">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x2</font> holds <br/><font color="Olive" title="b1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x2</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">x1</font>, <font color="Maroon" title="c5">x2</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">x1</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> &amp; <font color="Maroon" title="c5">x2</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> &amp; <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">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x2</font> implies <font color="Maroon" title="c4">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x2</font> )</span><br/><span class="kw">set </span><font color="Maroon" title="c6">f</font> =  <a href="glenum00.html#K5" title="GLENUM00:func.5">SG2SGFunc</a> <font color="Maroon" title="c3">F</font>;<br/><span class="kw">assume </span><a NAME="E1:40_1"/><span class="lab"><font color="Green" title="E30">A2</font></span>: 
( <font color="Maroon" title="c4">x1</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> &amp; <font color="Maroon" title="c5">x2</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> &amp; <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">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">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="c4">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x2</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">H1</font> = <font color="Maroon" title="c4">x1</font>, <font color="Maroon" title="c8">H2</font> = <font color="Maroon" title="c5">x2</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="lab"><font color="Green" title="E31">A3</font></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> <font color="Maroon" title="c7">H1</font></span>)</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">x1</font>
<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 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="c8">H2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:40_1"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="ref" href="glenum00.html#D5" target="_self" onmouseover="rs('glenum00/D5')" onmouseout="rh()">Def5</a></span>
;<br/><a NAME="E4:40_1"/><span class="lab"><font color="Green" title="E32">A4</font></span>: 
( <font color="Maroon" title="c3">F</font> <a href="glib_010.html#K10" title="GLIB_010:func.10">|</a> <font color="Maroon" title="c7">H1</font> is  <a href="glib_010.html#V7" title="GLIB_010:attr.7">total</a>  &amp; <font color="Maroon" title="c3">F</font> <a href="glib_010.html#K10" title="GLIB_010:func.10">|</a> <font color="Maroon" title="c8">H2</font> is  <a href="glib_010.html#V7" title="GLIB_010:attr.7">total</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:40"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="glib_010.html#T57" onmouseover="rs('glib_010/T57')" onmouseout="rh()">GLIB_010:57</a></span>;<br/><span class="lab"><font color="Green" title="E33">A5</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="glib_010.html#K5" title="GLIB_010:func.5">_V</a></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c7">H1</font></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#K5" title="GLIB_010:func.5">_V</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c7">H1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T115" onmouseover="rs('relat_1/T115')" onmouseout="rh()">RELAT_1:115</a></span>
<br/>.= 
 <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <span class="p1">(<span class="default"><a href="glib_010.html#K9" title="GLIB_010:func.9">rng</a> <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> <font color="Maroon" title="c7">H1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:40_1"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="ref" href="glib_010.html#T54" onmouseover="rs('glib_010/T54')" onmouseout="rh()">GLIB_010:54</a></span>
<br/>.= 
 <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> <font color="Maroon" title="c8">H2</font></span>)</span> <a href="glib_010.html#K5" title="GLIB_010:func.5">_V</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:40_1"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="txt" href="#E4:40_1"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="ref" href="glib_010.html#T54" onmouseover="rs('glib_010/T54')" onmouseout="rh()">GLIB_010:54</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="glib_010.html#K5" title="GLIB_010:func.5">_V</a></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c8">H2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T115" onmouseover="rs('relat_1/T115')" onmouseout="rh()">RELAT_1:115</a></span>
;<br/><a NAME="E6:40_1"/>
(  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c7">H1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G1</font> &amp;  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c8">H2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G1</font> )
 ;<br/><a NAME="E7:40_1"/><span class="kw">then </span>
(  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c7">H1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="glib_010.html#K5" title="GLIB_010:func.5">_V</a></span>)</span> &amp;  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c8">H2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="glib_010.html#K5" title="GLIB_010:func.5">_V</a></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:40"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="glib_010.html#D11" onmouseover="rs('glib_010/D11')" onmouseout="rh()">GLIB_010:def 11</a></span>;<br/><a NAME="E8:40_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A6</font></span>: 
(  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c7">H1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c8">H2</font> &amp;  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c8">H2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c7">H1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:40"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E5:40_1"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="ref" href="funct_1.html#T87" onmouseover="rs('funct_1/T87')" onmouseout="rh()">FUNCT_1:87</a></span>;<br/><span class="lab"><font color="Green" title="E35">A7</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="glib_010.html#K6" title="GLIB_010:func.6">_E</a></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c7">H1</font></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#K6" title="GLIB_010:func.6">_E</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c7">H1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T115" onmouseover="rs('relat_1/T115')" onmouseout="rh()">RELAT_1:115</a></span>
<br/>.= 
 <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <span class="p1">(<span class="default"><a href="glib_010.html#K9" title="GLIB_010:func.9">rng</a> <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> <font color="Maroon" title="c7">H1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:40_1"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="ref" href="glib_010.html#T54" onmouseover="rs('glib_010/T54')" onmouseout="rh()">GLIB_010:54</a></span>
<br/>.= 
 <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> <font color="Maroon" title="c8">H2</font></span>)</span> <a href="glib_010.html#K6" title="GLIB_010:func.6">_E</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:40_1"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="txt" href="#E4:40_1"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="ref" href="glib_010.html#T54" onmouseover="rs('glib_010/T54')" onmouseout="rh()">GLIB_010:54</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="glib_010.html#K6" title="GLIB_010:func.6">_E</a></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c8">H2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T115" onmouseover="rs('relat_1/T115')" onmouseout="rh()">RELAT_1:115</a></span>
;<br/><a NAME="E10:40_1"/>
(  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c7">H1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G1</font> &amp;  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c8">H2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G1</font> )
 ;<br/><a NAME="E11:40_1"/><span class="kw">then </span>
(  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c7">H1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="glib_010.html#K6" title="GLIB_010:func.6">_E</a></span>)</span> &amp;  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c8">H2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="glib_010.html#K6" title="GLIB_010:func.6">_E</a></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:40"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="glib_010.html#D11" onmouseover="rs('glib_010/D11')" onmouseout="rh()">GLIB_010:def 11</a></span>;<br/><a NAME="E12:40_1"/><span class="kw">then </span>
(  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c7">H1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c8">H2</font> &amp;  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c8">H2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c7">H1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:40"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E9:40_1"><span class="lab"><font color="Green" title="E35">A7</font></span></a>, <a class="ref" href="funct_1.html#T87" onmouseover="rs('funct_1/T87')" onmouseout="rh()">FUNCT_1:87</a></span>;<br/><a NAME="E13:40_1"/><span class="kw">then </span>
( <font color="Maroon" title="c7">H1</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c8">H2</font> &amp; <font color="Maroon" title="c8">H2</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c7">H1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:40_1"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="ref" href="glib_000.html#T44" onmouseover="rs('glib_000/T44')" onmouseout="rh()">GLIB_000:44</a></span>;<br/><span class="kw">hence </span><a NAME="E14:40_1"/>
<font color="Maroon" title="c4">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T87" onmouseover="rs('glib_000/T87')" onmouseout="rh()">GLIB_000:87</a>, <a class="ref" href="glib_009.html#T44" onmouseover="rs('glib_009/T44')" onmouseout="rh()">GLIB_009:44</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="E3:40"/>
 <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="ref" href="funct_1.html#D4" onmouseover="rs('funct_1/D4')" onmouseout="rh()">FUNCT_1:def 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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