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<span class="kw">let </span><font color="Maroon" title="c1">G</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">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">E</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <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">G</font></span>)</span><br/>  for <font color="Olive" title="b3">H</font> being    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c1">G</font>,<font color="Olive" title="b1">X</font> holds <br/> ( <font color="Olive" title="b2">E</font> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Maroon" title="c1">G</font> iff <font color="Olive" title="b2">E</font> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Olive" title="b3">H</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">X</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">E</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <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">G</font></span>)</span><br/>  for <font color="Olive" title="b2">H</font> being    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">X</font> holds <br/> ( <font color="Olive" title="b1">E</font> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Maroon" title="c1">G</font> iff <font color="Olive" title="b1">E</font> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Olive" title="b2">H</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">E</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <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">G</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">  for <font color="Olive" title="b1">H</font> being    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">X</font> holds <br/> ( <font color="Maroon" title="c3">E</font> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Maroon" title="c1">G</font> iff <font color="Maroon" title="c3">E</font> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Olive" title="b1">H</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">H</font> be    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">X</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">E</font> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Maroon" title="c1">G</font> iff <font color="Maroon" title="c3">E</font> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Maroon" title="c4">H</font> )</span><br/>







<span class="kw">thus </span><a NAME="E1:80"/>
( <font color="Maroon" title="c3">E</font> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Maroon" title="c1">G</font> implies <font color="Maroon" title="c3">E</font> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Maroon" title="c4">H</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="glibpre0.html#E73"><span class="lab"><font color="Green" title="E17">Lm3</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">E</font> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Maroon" title="c4">H</font> implies <font color="Maroon" title="c3">E</font> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Maroon" title="c1">G</font> )</span><br/>

<a NAME="E2:80"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
<font color="Maroon" title="c1">G</font> is    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c2">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_007.html#T3" onmouseover="rs('glib_007/T3')" onmouseout="rh()">GLIB_007:3</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:80"/>
<font color="Maroon" title="c3">E</font> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Maroon" title="c4">H</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">E</font> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Maroon" title="c1">G</font></span><br/>

<span class="kw">hence </span><a NAME="E4:80"/>
<font color="Maroon" title="c3">E</font> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:80"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="glibpre0.html#E73"><span class="lab"><font color="Green" title="E17">Lm3</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"> verum</span><br/>


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