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<span class="kw">let </span><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">F</font> being    <a href="glib_010.html#M1" title="GLIB_010:mode.1">PGraphMapping</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font>  st <font color="Olive" title="b1">F</font> is  <a href="glib_010.html#V17" title="GLIB_010:attr.17">isomorphism</a>  holds <br/>( <font color="Maroon" title="c1">G1</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  iff <font color="Maroon" title="c2">G2</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">F</font> be    <a href="glib_010.html#M1" title="GLIB_010:mode.1">PGraphMapping</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">F</font> is  <a href="glib_010.html#V17" title="GLIB_010:attr.17">isomorphism</a>  implies ( <font color="Maroon" title="c1">G1</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  iff <font color="Maroon" title="c2">G2</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:51"/><span class="lab"><font color="Green" title="E31">A1</font></span>: 
<font color="Maroon" title="c3">F</font> is  <a href="glib_010.html#V17" title="GLIB_010:attr.17">isomorphism</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="c1">G1</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  iff <font color="Maroon" title="c2">G2</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  )</span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">F0</font> = <font color="Maroon" title="c3">F</font> as   <a href="glib_010.html#V9" title="GLIB_010:attr.9">one-to-one</a>   <a href="glib_010.html#M1" title="GLIB_010:mode.1">PGraphMapping</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font> ;<br/>
<a NAME="E3:51"/>
<font color="Maroon" title="c4">F0</font> <a href="glib_010.html#K12" title="GLIB_010:func.12">"</a>  is  <a href="glib_010.html#V17" title="GLIB_010:attr.17">isomorphism</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:51"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="glib_010.html#T75" onmouseover="rs('glib_010/T75')" onmouseout="rh()">GLIB_010:75</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:51"/>
( <font color="Maroon" title="c1">G1</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  implies <font color="Maroon" title="c2">G2</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="glpacy00.html#E32"><span class="lab"><font color="Green" title="E29">Lm5</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="c2">G2</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  implies <font color="Maroon" title="c1">G1</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E5:51"/>
( <font color="Maroon" title="c2">G2</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  implies <font color="Maroon" title="c1">G1</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:51"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="txt" href="glpacy00.html#E32"><span class="lab"><font color="Green" title="E29">Lm5</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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