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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#V6" title="GLIB_000:attr.6">non-Dmulti</a>  <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_011.html#V1" title="GLIB_011:attr.1">directed</a>   <a href="glib_011.html#M1" title="GLIB_011:mode.1">PVertexMapping</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font><br/>  for <font color="Olive" title="b2">v</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font>  st <font color="Olive" title="b1">f</font> is  <a href="glib_011.html#V5" title="GLIB_011:attr.5">Disomorphism</a>  holds <br/>( <font color="Olive" title="b2">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  &amp; <font color="Olive" title="b2">v</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be   <a href="glib_011.html#V1" title="GLIB_011:attr.1">directed</a>   <a href="glib_011.html#M1" title="GLIB_011:mode.1">PVertexMapping</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">  for <font color="Olive" title="b1">v</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font>  st <font color="Maroon" title="c3">f</font> is  <a href="glib_011.html#V5" title="GLIB_011:attr.5">Disomorphism</a>  holds <br/>( <font color="Olive" title="b1">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">v</font></span>)</span> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  &amp; <font color="Olive" title="b1">v</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">v</font></span>)</span> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">v</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</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="c3">f</font> is  <a href="glib_011.html#V5" title="GLIB_011:attr.5">Disomorphism</a>  implies ( <font color="Maroon" title="c4">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  &amp; <font color="Maroon" title="c4">v</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:133"/>
<font color="Maroon" title="c3">f</font> is  <a href="glib_011.html#V5" title="GLIB_011:attr.5">Disomorphism</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">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  &amp; <font color="Maroon" title="c4">v</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  )</span><br/>

<a NAME="E2:133"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A1</font></span>: 
 <a href="glib_011.html#K4" title="GLIB_011:func.4">DPVM2PGM</a> <font color="Maroon" title="c3">f</font> is  <a href="glib_010.html#V18" title="GLIB_010:attr.18">Disomorphism</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_011.html#T48" onmouseover="rs('glib_011/T48')" onmouseout="rh()">GLIB_011:48</a></span>;<br/>
<span class="kw">thus </span><font color="Maroon" title="c4">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_011.html#K4" title="GLIB_011:func.4">DPVM2PGM</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="glib_010.html#K5" title="GLIB_010:func.5">_V</a></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:133"><span class="lab"><font color="Green" title="E40">A1</font></span></a>, <a class="ref" href="glibpre0.html#T92" target="_self" onmouseover="rs('glibpre0/T92')" onmouseout="rh()">Th98</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</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">v</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a> </span><br/>

<span class="kw">thus </span><font color="Maroon" title="c4">v</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_011.html#K4" title="GLIB_011:func.4">DPVM2PGM</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="glib_010.html#K5" title="GLIB_010:func.5">_V</a></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:133"><span class="lab"><font color="Green" title="E40">A1</font></span></a>, <a class="ref" href="glibpre0.html#T92" target="_self" onmouseover="rs('glibpre0/T92')" onmouseout="rh()">Th98</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</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/>


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