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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">  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><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_010.html#V8" title="GLIB_010:attr.8">onto</a>  &amp; <font color="Olive" title="b1">F</font> is  <a href="glib_010.html#V13" title="GLIB_010:attr.13">semi-Dcontinuous</a>  &amp; <font color="Olive" title="b2">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="glib_010.html#K5" title="GLIB_010:func.5">_V</a></span>)</span> holds <br/>( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">F</font> <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="Olive" title="b2">v</font></span>)</span> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b2">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">F</font> <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="Olive" title="b2">v</font></span>)</span> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b2">v</font> <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_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">  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_010.html#V8" title="GLIB_010:attr.8">onto</a>  &amp; <font color="Maroon" title="c3">F</font> is  <a href="glib_010.html#V13" title="GLIB_010:attr.13">semi-Dcontinuous</a>  &amp; <font color="Olive" title="b1">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</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> holds <br/>( <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#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>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b1">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  &amp; <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#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>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b1">v</font> <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_010.html#V8" title="GLIB_010:attr.8">onto</a>  &amp; <font color="Maroon" title="c3">F</font> is  <a href="glib_010.html#V13" title="GLIB_010:attr.13">semi-Dcontinuous</a>  &amp; <font color="Maroon" title="c4">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</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> implies ( <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#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 href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c4">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  &amp; <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#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 href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c4">v</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:115"/>
( <font color="Maroon" title="c3">F</font> is  <a href="glib_010.html#V8" title="GLIB_010:attr.8">onto</a>  &amp; <font color="Maroon" title="c3">F</font> is  <a href="glib_010.html#V13" title="GLIB_010:attr.13">semi-Dcontinuous</a>  &amp; <font color="Maroon" title="c4">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</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> )
 ; <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"><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#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 href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c4">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  &amp; <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#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 href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c4">v</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  )</span><br/>

<a NAME="E2:115"/><span class="kw">then </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"><font color="Maroon" title="c4">v</font> <a href="glib_000.html#K26" title="GLIB_000:func.26">.edgesIn()</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="glib_000.html#K26" title="GLIB_000:func.26">.edgesIn()</a>  &amp; <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"><font color="Maroon" title="c4">v</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesOut()</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesOut()</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glibpre0.html#T83" target="_self" onmouseover="rs('glibpre0/T83')" onmouseout="rh()">Th89</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:115"/>
( <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#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 href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c4">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  &amp; <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#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 href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c4">v</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T67" onmouseover="rs('card_1/T67')" onmouseout="rh()">CARD_1:67</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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