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<span class="kw">let </span><font color="Maroon" title="c1">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">v</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <br/>  for <font color="Olive" title="b2">V</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">G1</font> being    <a href="glib_007.html#M2" title="GLIB_007:mode.2">addAdjVertexToAll</a> of <font color="Maroon" title="c1">G2</font>,<font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">V</font>  st <font color="Olive" title="b2">V</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">G2</font> &amp;  not <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G2</font> holds <br/>( (  for <font color="Olive" title="b4">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> (  not <font color="Olive" title="b4">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">v</font>,<font color="Olive" title="b1">v</font>,<font color="Olive" title="b3">G1</font> &amp; (  for <font color="Olive" title="b5">v1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( (  not <font color="Olive" title="b5">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">V</font> implies  not <font color="Olive" title="b4">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b5">v1</font>,<font color="Olive" title="b1">v</font>,<font color="Olive" title="b3">G1</font> ) &amp; (  for <font color="Olive" title="b6">v2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b5">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">v</font> &amp; <font color="Olive" title="b6">v2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">v</font> &amp; <font color="Olive" title="b4">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b5">v1</font>,<font color="Olive" title="b6">v2</font>,<font color="Olive" title="b3">G1</font> holds <br/><font color="Olive" title="b4">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b5">v1</font>,<font color="Olive" title="b6">v2</font>,<font color="Maroon" title="c1">G2</font> ) ) ) ) ) &amp;  ex <font color="Olive" title="b4">E</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  st <br/>(  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b2">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b4">E</font> &amp; <font color="Olive" title="b4">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Olive" title="b3">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b4">E</font> &amp; (  for <font color="Olive" title="b5">v1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b5">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">V</font> holds <br/> ex <font color="Olive" title="b6">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b6">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b4">E</font> &amp; <font color="Olive" title="b6">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b5">v1</font>,<font color="Olive" title="b1">v</font>,<font color="Olive" title="b3">G1</font> &amp; (  for <font color="Olive" title="b7">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b7">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b5">v1</font>,<font color="Olive" title="b1">v</font>,<font color="Olive" title="b3">G1</font> holds <br/><font color="Olive" title="b6">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">e2</font> ) ) ) ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">v</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">  for <font color="Olive" title="b1">V</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">G1</font> being    <a href="glib_007.html#M2" title="GLIB_007:mode.2">addAdjVertexToAll</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">v</font>,<font color="Olive" title="b1">V</font>  st <font color="Olive" title="b1">V</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">G2</font> &amp;  not <font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G2</font> holds <br/>( (  for <font color="Olive" title="b3">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> (  not <font color="Olive" title="b3">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c2">v</font>,<font color="Olive" title="b2">G1</font> &amp; (  for <font color="Olive" title="b4">v1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( (  not <font color="Olive" title="b4">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">V</font> implies  not <font color="Olive" title="b3">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b4">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Olive" title="b2">G1</font> ) &amp; (  for <font color="Olive" title="b5">v2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b4">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Olive" title="b5">v2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Olive" title="b3">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b4">v1</font>,<font color="Olive" title="b5">v2</font>,<font color="Olive" title="b2">G1</font> holds <br/><font color="Olive" title="b3">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b4">v1</font>,<font color="Olive" title="b5">v2</font>,<font color="Maroon" title="c1">G2</font> ) ) ) ) ) &amp;  ex <font color="Olive" title="b3">E</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  st <br/>(  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b3">E</font> &amp; <font color="Olive" title="b3">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Olive" title="b2">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b3">E</font> &amp; (  for <font color="Olive" title="b4">v1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b4">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">V</font> holds <br/> ex <font color="Olive" title="b5">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b5">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">E</font> &amp; <font color="Olive" title="b5">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b4">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Olive" title="b2">G1</font> &amp; (  for <font color="Olive" title="b6">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b6">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b4">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Olive" title="b2">G1</font> holds <br/><font color="Olive" title="b5">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">e2</font> ) ) ) ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">V</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">G1</font> being    <a href="glib_007.html#M2" title="GLIB_007:mode.2">addAdjVertexToAll</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">V</font>  st <font color="Maroon" title="c3">V</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">G2</font> &amp;  not <font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G2</font> holds <br/>( (  for <font color="Olive" title="b2">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> (  not <font color="Olive" title="b2">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c2">v</font>,<font color="Olive" title="b1">G1</font> &amp; (  for <font color="Olive" title="b3">v1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( (  not <font color="Olive" title="b3">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> implies  not <font color="Olive" title="b2">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b3">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Olive" title="b1">G1</font> ) &amp; (  for <font color="Olive" title="b4">v2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b3">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Olive" title="b4">v2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Olive" title="b2">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b3">v1</font>,<font color="Olive" title="b4">v2</font>,<font color="Olive" title="b1">G1</font> holds <br/><font color="Olive" title="b2">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b3">v1</font>,<font color="Olive" title="b4">v2</font>,<font color="Maroon" title="c1">G2</font> ) ) ) ) ) &amp;  ex <font color="Olive" title="b2">E</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  st <br/>(  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b2">E</font> &amp; <font color="Olive" title="b2">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Olive" title="b1">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b2">E</font> &amp; (  for <font color="Olive" title="b3">v1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b3">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> holds <br/> ex <font color="Olive" title="b4">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b4">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">E</font> &amp; <font color="Olive" title="b4">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b3">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Olive" title="b1">G1</font> &amp; (  for <font color="Olive" title="b5">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b5">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b3">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Olive" title="b1">G1</font> holds <br/><font color="Olive" title="b4">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">e2</font> ) ) ) ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">G1</font> be    <a href="glib_007.html#M2" title="GLIB_007:mode.2">addAdjVertexToAll</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">V</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">V</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">G2</font> &amp;  not <font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G2</font> implies ( (  for <font color="Olive" title="b1">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> (  not <font color="Olive" title="b1">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> &amp; (  for <font color="Olive" title="b2">v1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( (  not <font color="Olive" title="b2">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> implies  not <font color="Olive" title="b1">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b2">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> ) &amp; (  for <font color="Olive" title="b3">v2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b2">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Olive" title="b3">v2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Olive" title="b1">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b2">v1</font>,<font color="Olive" title="b3">v2</font>,<font color="Maroon" title="c4">G1</font> holds <br/><font color="Olive" title="b1">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b2">v1</font>,<font color="Olive" title="b3">v2</font>,<font color="Maroon" title="c1">G2</font> ) ) ) ) ) &amp;  ex <font color="Olive" title="b1">E</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  st <br/>(  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b1">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b1">E</font> &amp; (  for <font color="Olive" title="b2">v1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b2">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> holds <br/> ex <font color="Olive" title="b3">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b3">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b3">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b2">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> &amp; (  for <font color="Olive" title="b4">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b4">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b2">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> holds <br/><font color="Olive" title="b3">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">e2</font> ) ) ) ) ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:73"/><span class="lab"><font color="Green" title="E45">A1</font></span>: 
( <font color="Maroon" title="c3">V</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">G2</font> &amp;  not <font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">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">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> (  not <font color="Olive" title="b1">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> &amp; (  for <font color="Olive" title="b2">v1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( (  not <font color="Olive" title="b2">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> implies  not <font color="Olive" title="b1">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b2">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> ) &amp; (  for <font color="Olive" title="b3">v2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b2">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Olive" title="b3">v2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Olive" title="b1">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b2">v1</font>,<font color="Olive" title="b3">v2</font>,<font color="Maroon" title="c4">G1</font> holds <br/><font color="Olive" title="b1">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b2">v1</font>,<font color="Olive" title="b3">v2</font>,<font color="Maroon" title="c1">G2</font> ) ) ) ) ) &amp;  ex <font color="Olive" title="b1">E</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  st <br/>(  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b1">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b1">E</font> &amp; (  for <font color="Olive" title="b2">v1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b2">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> holds <br/> ex <font color="Olive" title="b3">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b3">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b3">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b2">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> &amp; (  for <font color="Olive" title="b4">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b4">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b2">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> holds <br/><font color="Olive" title="b3">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">e2</font> ) ) ) ) )</span><br/>

<div><span class="kw">hereby </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">  ex <font color="Olive" title="b1">E</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  st <br/>(  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b1">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b1">E</font> &amp; (  for <font color="Olive" title="b2">v1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b2">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> holds <br/> ex <font color="Olive" title="b3">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b3">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b3">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b2">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> &amp; (  for <font color="Olive" title="b4">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b4">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b2">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> holds <br/><font color="Olive" title="b3">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">e2</font> ) ) ) )</span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c5">e</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"> (  not <font color="Maroon" title="c5">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> &amp; (  for <font color="Olive" title="b1">v1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( (  not <font color="Olive" title="b1">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> implies  not <font color="Maroon" title="c5">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> ) &amp; (  for <font color="Olive" title="b2">v2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Olive" title="b2">v2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Maroon" title="c5">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c4">G1</font> holds <br/><font color="Maroon" title="c5">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c1">G2</font> ) ) ) )</span><br/><a NAME="E1:73_1"/>
 not <font color="Maroon" title="c5">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:73"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="ref" href="glib_007.html#T38" target="_self" onmouseover="rs('glib_007/T38')" onmouseout="rh()">Th38</a></span>;<br/><span class="kw">hence </span><a NAME="E2:73_1"/>
 not <font color="Maroon" title="c5">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T16" onmouseover="rs('glib_000/T16')" onmouseout="rh()">GLIB_000:16</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">  for <font color="Olive" title="b1">v1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( (  not <font color="Olive" title="b1">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> implies  not <font color="Maroon" title="c5">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> ) &amp; (  for <font color="Olive" title="b2">v2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Olive" title="b2">v2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Maroon" title="c5">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c4">G1</font> holds <br/><font color="Maroon" title="c5">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c1">G2</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">v1</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"> ( (  not <font color="Maroon" title="c6">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> implies  not <font color="Maroon" title="c5">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> ) &amp; (  for <font color="Olive" title="b1">v2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Maroon" title="c6">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Olive" title="b1">v2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Maroon" title="c5">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c6">v1</font>,<font color="Olive" title="b1">v2</font>,<font color="Maroon" title="c4">G1</font> holds <br/><font color="Maroon" title="c5">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c6">v1</font>,<font color="Olive" title="b1">v2</font>,<font color="Maroon" title="c1">G2</font> ) )</span><br/><span class="kw">thus </span><a NAME="E3:73_1"/>
(  not <font color="Maroon" title="c6">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> implies  not <font color="Maroon" title="c5">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">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">  for <font color="Olive" title="b1">v2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Maroon" title="c6">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Olive" title="b1">v2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Maroon" title="c5">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c6">v1</font>,<font color="Olive" title="b1">v2</font>,<font color="Maroon" title="c4">G1</font> holds <br/><font color="Maroon" title="c5">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c6">v1</font>,<font color="Olive" title="b1">v2</font>,<font color="Maroon" title="c1">G2</font></span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="73_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:73_1_1"/><span class="lab"><font color="Green" title="E46">A2</font></span>: 
 not <font color="Maroon" title="c6">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</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">  not <font color="Maroon" title="c5">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font></span><br/>

<span class="kw">assume </span><a NAME="E2:73_1_1"/>
<font color="Maroon" title="c5">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">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"> contradiction</span><br/>

<a NAME="E3:73_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c5">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> or <font color="Maroon" title="c5">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c4">G1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T16" onmouseover="rs('glib_000/T16')" onmouseout="rh()">GLIB_000:16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:73_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:73"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="txt" href="#E1:73_1_1"><span class="lab"><font color="Green" title="E46">A2</font></span></a>, <a class="ref" href="glib_007.html#T38" target="_self" onmouseover="rs('glib_007/T38')" onmouseout="rh()">Th38</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">let </span><font color="Maroon" title="c7">v2</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="c6">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Maroon" title="c7">v2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Maroon" title="c5">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">G1</font> implies <font color="Maroon" title="c5">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c1">G2</font> )</span><br/><span class="kw">assume </span><a NAME="E4:73_1"/><span class="lab"><font color="Green" title="E46">A3</font></span>: 
( <font color="Maroon" title="c6">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Maroon" title="c7">v2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> &amp; <font color="Maroon" title="c5">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">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="c5">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c1">G2</font></span><br/><span class="kw">thus </span><a NAME="E5:73_1"/>
<font color="Maroon" title="c5">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c1">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:73"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="txt" href="#E4:73_1"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="glib_007.html#T40" target="_self" onmouseover="rs('glib_007/T40')" onmouseout="rh()">Th40</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">set </span><font color="Maroon" title="c5">E</font> = <font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</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"> (  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span>)</span> &amp; (  for <font color="Olive" title="b1">v1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> holds <br/> ex <font color="Olive" title="b2">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b2">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> &amp; <font color="Olive" title="b2">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> &amp; (  for <font color="Olive" title="b3">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b3">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> holds <br/><font color="Olive" title="b2">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">e2</font> ) ) ) )</span><br/>

<span class="kw">thus </span><a NAME="E3:73"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="glib_007.html#E56"><span class="lab"><font color="Green" title="E43">Lm8</font></span></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"> ( <font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span>)</span> &amp; (  for <font color="Olive" title="b1">v1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> holds <br/> ex <font color="Olive" title="b2">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b2">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> &amp; <font color="Olive" title="b2">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> &amp; (  for <font color="Olive" title="b3">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b3">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> holds <br/><font color="Olive" title="b2">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">e2</font> ) ) ) )</span><br/>

<a NAME="E4:73"/>
<span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="glib_007.html#E34"><span class="lab"><font color="Green" title="E29">Lm6</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:73"/>
<font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D7" onmouseover="rs('xboole_0/D7')" onmouseout="rh()">XBOOLE_0:def 7</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"> (  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span>)</span> &amp; (  for <font color="Olive" title="b1">v1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> holds <br/> ex <font color="Olive" title="b2">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b2">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> &amp; <font color="Olive" title="b2">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> &amp; (  for <font color="Olive" title="b3">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b3">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> holds <br/><font color="Olive" title="b2">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">e2</font> ) ) ) )</span><br/>

<span class="kw">thus </span><a NAME="E6:73"/>
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c4">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:73"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="ref" href="glib_007.html#D2" target="_self" onmouseover="rs('glib_007/D2')" onmouseout="rh()">Def2</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">  for <font color="Olive" title="b1">v1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> holds <br/> ex <font color="Olive" title="b2">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b2">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> &amp; <font color="Olive" title="b2">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> &amp; (  for <font color="Olive" title="b3">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b3">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> holds <br/><font color="Olive" title="b2">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">e2</font> ) )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">v1</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="c6">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> implies  ex <font color="Olive" title="b1">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> &amp; <font color="Olive" title="b1">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> &amp; (  for <font color="Olive" title="b2">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b2">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> holds <br/><font color="Olive" title="b1">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">e2</font> ) ) )</span><br/>

<span class="kw">assume </span><a NAME="E7:73"/><span class="lab"><font color="Green" title="E46">A4</font></span>: 
<font color="Maroon" title="c6">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</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">  ex <font color="Olive" title="b1">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> &amp; <font color="Olive" title="b1">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> &amp; (  for <font color="Olive" title="b2">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b2">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> holds <br/><font color="Olive" title="b1">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">e2</font> ) )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c7">e1</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">v1</font>,<span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<span class="kw">take </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">v1</font>,<span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.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"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">v1</font>,<span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">v1</font>,<span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> &amp; (  for <font color="Olive" title="b1">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">v1</font>,<span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">e2</font> ) )</span><br/>

<a NAME="E8:73"/>
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<a NAME="E9:73"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">v1</font>,<span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">V</font>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:73"><span class="lab"><font color="Green" title="E46">A4</font></span></a>, <a class="ref" href="zfmisc_1.html#D2" onmouseover="rs('zfmisc_1/D2')" onmouseout="rh()">ZFMISC_1:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:73"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">v1</font>,<span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#D2" onmouseover="rs('funcop_1/D2')" onmouseout="rh()">FUNCOP_1:def 2</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"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">v1</font>,<span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> &amp; (  for <font color="Olive" title="b1">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">v1</font>,<span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">e2</font> ) )</span><br/>

<a NAME="E11:73"/><span class="lab"><font color="Green" title="E47">A5</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">v1</font>,<span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c4">G1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:73"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="txt" href="#E7:73"><span class="lab"><font color="Green" title="E46">A4</font></span></a>, <a class="ref" href="glib_007.html#T42" target="_self" onmouseover="rs('glib_007/T42')" onmouseout="rh()">Th42</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:73"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">v1</font>,<span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T16" onmouseover="rs('glib_000/T16')" onmouseout="rh()">GLIB_000:16</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">  for <font color="Olive" title="b1">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">v1</font>,<span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">e2</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c8">e2</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="c8">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font> implies <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">v1</font>,<span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">e2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E13:73"/><span class="lab"><font color="Green" title="E48">A6</font></span>: 
<font color="Maroon" title="c8">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">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"> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">v1</font>,<span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">e2</font></span><br/>

<a NAME="E14:73"/>
 not <font color="Maroon" title="c8">e2</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c4">G1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:73"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="ref" href="glib_007.html#T38" target="_self" onmouseover="rs('glib_007/T38')" onmouseout="rh()">Th38</a></span>;<br/>
<a NAME="E15:73"/><span class="kw">then </span>
<font color="Maroon" title="c8">e2</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c4">G1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:73"><span class="lab"><font color="Green" title="E48">A6</font></span></a>, <a class="ref" href="glib_000.html#T16" onmouseover="rs('glib_000/T16')" onmouseout="rh()">GLIB_000:16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E16:73"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">v1</font>,<span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:73"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="txt" href="#E11:73"><span class="lab"><font color="Green" title="E47">A5</font></span></a>, <a class="ref" href="glib_007.html#T38" target="_self" onmouseover="rs('glib_007/T38')" onmouseout="rh()">Th38</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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