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<span class="kw">let </span><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c2">q</font> iff  <a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> (<font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> )</span><br/>

<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> (<font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> implies <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c2">q</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:3_1"/>
<font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> (<font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font></span><br/><a NAME="E2:3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E2">A1</font></span>: 
<font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> (<font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="helly.html#D1" target="_self" title="HELLY:def.1">Def1</a></span>;<br/><a NAME="E3:3_1"/>
 <a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> (<font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="helly.html#D1" target="_self" title="HELLY:def.1">Def1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:3_1"/>
 <a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> (<font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:3_1"><span class="lab"><font color="Green" title="E2">A1</font></span></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></span>; <a class="txt" 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">assume </span><a NAME="E2:3"/>
 <a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> (<font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c2">q</font></span><br/>

<span class="kw">hence </span><a NAME="E3:3"/>
<font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c2">q</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="helly.html#D1" target="_self" title="HELLY:def.1">Def1</a></span>; <a class="txt" 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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