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<b>let </b><font color="Maroon" title="c3">it1</font>, <font color="Maroon" title="c4">it2</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">it1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c1">p</font> &amp; <font color="Maroon" title="c3">it1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c2">q</font> &amp; ( for <font color="Olive" title="b1">r</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b1">r</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c1">p</font> &amp; <font color="Olive" title="b1">r</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c2">q</font> holds <br/><font color="Olive" title="b1">r</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c3">it1</font> ) &amp; <font color="Maroon" title="c4">it2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c1">p</font> &amp; <font color="Maroon" title="c4">it2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c2">q</font> &amp; ( for <font color="Olive" title="b1">r</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b1">r</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c1">p</font> &amp; <font color="Olive" title="b1">r</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c2">q</font> holds <br/><font color="Olive" title="b1">r</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c4">it2</font> ) implies <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">it2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:2_1_2"/><i><font color="Green" title="E1">A13</font></i>: 
<font color="Maroon" title="c3">it1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">p</font>
 <b>and </b><br/><a NAME="E2:2_1_2"/><i><font color="Green" title="E2">A14</font></i>: 
<font color="Maroon" title="c3">it1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">q</font>
 <b>and </b><br/><a NAME="E3:2_1_2"/><i><font color="Green" title="E3">A15</font></i>: 
for <font color="Olive" title="b1">r</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b1">r</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">p</font> &amp; <font color="Olive" title="b1">r</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">q</font> holds <br/><font color="Olive" title="b1">r</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">it1</font>
 <b>and </b><br/><a NAME="E4:2_1_2"/><i><font color="Green" title="E4">A16</font></i>: 
<font color="Maroon" title="c4">it2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">p</font>
 <b>and </b><br/><a NAME="E5:2_1_2"/><i><font color="Green" title="E5">A17</font></i>: 
<font color="Maroon" title="c4">it2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">q</font>
 <b>and </b><br/><a NAME="E6:2_1_2"/><i><font color="Green" title="E6">A18</font></i>: 
for <font color="Olive" title="b1">r</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b1">r</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">p</font> &amp; <font color="Olive" title="b1">r</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">q</font> holds <br/><font color="Olive" title="b1">r</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">it2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">it2</font></span><br/>

<a NAME="E7:2_1_2"/><i><font color="Green" title="E7">A19</font></i>: 
<font color="Maroon" title="c3">it1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">it2</font>
 
<b>by </b><i><a class="txt" href="#E1:2_1_2"><i><font color="Green" title="E1">A13</font></i></a>, <a class="txt" href="#E2:2_1_2"><i><font color="Green" title="E2">A14</font></i></a>, <a class="txt" href="#E6:2_1_2"><i><font color="Green" title="E6">A18</font></i></a></i>;<br/>
<a NAME="E8:2_1_2"/>
<font color="Maroon" title="c4">it2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">it1</font>
 
<b>by </b><i><a class="txt" href="#E3:2_1_2"><i><font color="Green" title="E3">A15</font></i></a>, <a class="txt" href="#E4:2_1_2"><i><font color="Green" title="E4">A16</font></i></a>, <a class="txt" href="#E5:2_1_2"><i><font color="Green" title="E5">A17</font></i></a></i>;<br/>
<b>hence </b><a NAME="E9:2_1_2"/>
<font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">it2</font>
 <b>by </b><i><a class="txt" href="#E7:2_1_2"><i><font color="Green" title="E7">A19</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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