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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">E</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#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c1">G2</font>,<font color="Olive" title="b1">E</font><br/>  for <font color="Olive" title="b3">v1</font>, <font color="Olive" title="b4">e</font>, <font color="Olive" title="b5">v2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> &amp; <font color="Olive" title="b4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">E</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="b3">v1</font>,<font color="Olive" title="b5">v2</font>,<font color="Maroon" title="c1">G2</font> iff <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">v2</font>,<font color="Olive" title="b3">v1</font>,<font color="Olive" title="b2">G1</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">E</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#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">E</font><br/>  for <font color="Olive" title="b2">v1</font>, <font color="Olive" title="b3">e</font>, <font color="Olive" title="b4">v2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Maroon" title="c2">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> &amp; <font color="Olive" title="b3">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">E</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="b2">v1</font>,<font color="Olive" title="b4">v2</font>,<font color="Maroon" title="c1">G2</font> iff <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">v2</font>,<font color="Olive" title="b2">v1</font>,<font color="Olive" title="b1">G1</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">G1</font> be    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">E</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">v1</font>, <font color="Olive" title="b2">e</font>, <font color="Olive" title="b3">v2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Maroon" title="c2">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> &amp; <font color="Olive" title="b2">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">E</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="b1">v1</font>,<font color="Olive" title="b3">v2</font>,<font color="Maroon" title="c1">G2</font> iff <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">v2</font>,<font color="Olive" title="b1">v1</font>,<font color="Maroon" title="c3">G1</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">v1</font>, <font color="Maroon" title="c5">e</font>, <font color="Maroon" title="c6">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="c2">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> &amp; <font color="Maroon" title="c5">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">E</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="c4">v1</font>,<font color="Maroon" title="c6">v2</font>,<font color="Maroon" title="c1">G2</font> iff <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">v2</font>,<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c3">G1</font> ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:10"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
( <font color="Maroon" title="c2">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> &amp; <font color="Maroon" title="c5">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">E</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="c4">v1</font>,<font color="Maroon" title="c6">v2</font>,<font color="Maroon" title="c1">G2</font> iff <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">v2</font>,<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c3">G1</font> )</span><br/>

<span class="kw">hence </span><a NAME="E2:10"/>
( <font color="Maroon" title="c5">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c6">v2</font>,<font color="Maroon" title="c1">G2</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">v2</font>,<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c3">G1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="glib_007.html#E8"><span class="lab"><font color="Green" title="E7">Lm1</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="c5">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c6">v2</font>,<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c3">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="c4">v1</font>,<font color="Maroon" title="c6">v2</font>,<font color="Maroon" title="c1">G2</font> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">G3</font> = <font color="Maroon" title="c1">G2</font> as    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c3">G1</font>,<font color="Maroon" title="c2">E</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_007.html#T3" target="_self" onmouseover="rs('glib_007/T3')" onmouseout="rh()">Th3</a></span>;<br/>
<a NAME="E4:10"/>
<font color="Maroon" title="c2">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c3">G1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_007.html#T4" target="_self" onmouseover="rs('glib_007/T4')" onmouseout="rh()">Th4</a>, <a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E9">A1</font></span></a></span>;<br/>
<a NAME="E5:10"/><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">v2</font>,<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c3">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="c4">v1</font>,<font color="Maroon" title="c6">v2</font>,<font color="Maroon" title="c7">G3</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="glib_007.html#E8"><span class="lab"><font color="Green" title="E7">Lm1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:10"/>
( <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">v2</font>,<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c3">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="c4">v1</font>,<font color="Maroon" title="c6">v2</font>,<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"> verum</span><br/>


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