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<span class="kw">let </span><font color="Maroon" title="c1">Omega</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <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">Sigma</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">Omega</font><br/>  for <font color="Olive" title="b2">P</font> being    <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of <font color="Olive" title="b1">Sigma</font><br/>  for <font color="Olive" title="b3">BSeq</font> being   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">Omega</font>  st (  for <font color="Olive" title="b4">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds  <font color="Olive" title="b3">BSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b4">n</font> is    <a href="prob_4.html#M1" title="PROB_4:mode.1">thin</a> of <font color="Olive" title="b2">P</font> ) holds <br/> ex <font color="Olive" title="b4">CSeq</font> being   <a href="prob_1.html#NM4" title="PROB_1:NM.4">SetSequence</a> of <font color="Olive" title="b1">Sigma</font> st <br/> for <font color="Olive" title="b5">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds <br/> ( <font color="Olive" title="b3">BSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b5">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">CSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b5">n</font> &amp; <font color="Olive" title="b2">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">CSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b5">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">Sigma</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">Omega</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">P</font> being    <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of <font color="Maroon" title="c2">Sigma</font><br/>  for <font color="Olive" title="b2">BSeq</font> being   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">Omega</font>  st (  for <font color="Olive" title="b3">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds  <font color="Olive" title="b2">BSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b3">n</font> is    <a href="prob_4.html#M1" title="PROB_4:mode.1">thin</a> of <font color="Olive" title="b1">P</font> ) holds <br/> ex <font color="Olive" title="b3">CSeq</font> being   <a href="prob_1.html#NM4" title="PROB_1:NM.4">SetSequence</a> of <font color="Maroon" title="c2">Sigma</font> st <br/> for <font color="Olive" title="b4">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds <br/> ( <font color="Olive" title="b2">BSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b4">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">CSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b4">n</font> &amp; <font color="Olive" title="b1">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">CSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b4">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">P</font> be    <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of <font color="Maroon" title="c2">Sigma</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">BSeq</font> being   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">Omega</font>  st (  for <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds  <font color="Olive" title="b1">BSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b2">n</font> is    <a href="prob_4.html#M1" title="PROB_4:mode.1">thin</a> of <font color="Maroon" title="c3">P</font> ) holds <br/> ex <font color="Olive" title="b2">CSeq</font> being   <a href="prob_1.html#NM4" title="PROB_1:NM.4">SetSequence</a> of <font color="Maroon" title="c2">Sigma</font> st <br/> for <font color="Olive" title="b3">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds <br/> ( <font color="Olive" title="b1">BSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b3">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">CSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b3">n</font> &amp; <font color="Maroon" title="c3">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">CSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b3">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">BSeq</font> be   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">Omega</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">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds  <font color="Maroon" title="c4">BSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b1">n</font> is    <a href="prob_4.html#M1" title="PROB_4:mode.1">thin</a> of <font color="Maroon" title="c3">P</font> ) implies  ex <font color="Olive" title="b1">CSeq</font> being   <a href="prob_1.html#NM4" title="PROB_1:NM.4">SetSequence</a> of <font color="Maroon" title="c2">Sigma</font> st <br/> for <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds <br/> ( <font color="Maroon" title="c4">BSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b2">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">CSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b2">n</font> &amp; <font color="Maroon" title="c3">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">CSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) )</span><br/>







<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> ,   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ] <span class="kw">means </span> for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b2">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $1 &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $2 holds <br/>( <font color="Olive" title="b2">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Sigma</font> &amp; <font color="Maroon" title="c4">BSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">y</font> &amp; <font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  );<br/>
<span class="kw">assume </span><a NAME="E1:41"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
 for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds  <font color="Maroon" title="c4">BSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b1">n</font> is    <a href="prob_4.html#M1" title="PROB_4:mode.1">thin</a> of <font color="Maroon" title="c3">P</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">  ex <font color="Olive" title="b1">CSeq</font> being   <a href="prob_1.html#NM4" title="PROB_1:NM.4">SetSequence</a> of <font color="Maroon" title="c2">Sigma</font> st <br/> for <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds <br/> ( <font color="Maroon" title="c4">BSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b2">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">CSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b2">n</font> &amp; <font color="Maroon" title="c3">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">CSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )</span><br/>

<a NAME="E2:41"/><span class="lab"><font color="Green" title="E33">A2</font></span>: 
 for <font color="Olive" title="b1">t</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   ex <font color="Olive" title="b2">A</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">Sigma</font> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">t</font>,<font color="Olive" title="b2">A</font>]
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="41_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">t</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</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">  ex <font color="Olive" title="b1">A</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">Sigma</font> st <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">t</font>,<font color="Olive" title="b1">A</font>]</span><br/>

<a NAME="E1:41_1"/>
<font color="Maroon" title="c4">BSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Maroon" title="c5">t</font> is    <a href="prob_4.html#M1" title="PROB_4:mode.1">thin</a> of <font color="Maroon" title="c3">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E32">A1</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">A</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <span class="kw"> such that </span><br/><a NAME="E3:41_1"/><span class="lab"><font color="Green" title="E34">A3</font></span>: 
<font color="Maroon" title="c6">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Sigma</font>
 <span class="kw">and </span><br/><a NAME="E4:41_1"/><span class="lab"><font color="Green" title="E35">A4</font></span>: 
( <font color="Maroon" title="c4">BSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Maroon" title="c5">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">A</font> &amp; <font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="prob_4.html#D4" target="_self" onmouseover="rs('prob_4/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">A</font> = <font color="Maroon" title="c6">A</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">Sigma</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:41_1"><span class="lab"><font color="Green" title="E34">A3</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c7">A</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">S<sub>1</sub></font>[<font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c7">A</font>]</span><br/>

<span class="kw">thus </span><a NAME="E6:41_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c7">A</font>]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:41_1"><span class="lab"><font color="Green" title="E35">A4</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/>


</div><span class="kw">end;</span></div>
<a NAME="E3:41"/>
 ex <font color="Olive" title="b1">G</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <font color="Maroon" title="c2">Sigma</font> st <br/> for <font color="Olive" title="b2">t</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b2">t</font>,<font color="Olive" title="b1">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">t</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="funct_2.html#S3" onmouseover="rs('funct_2/S3')" onmouseout="rh()">FUNCT_2:sch 3</a>(<a class="txt" href="#E2:41"><span class="lab"><font color="Green" title="E33">A2</font></span></a>);<br/></span>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">G</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <font color="Maroon" title="c2">Sigma</font><span class="kw"> such that </span><br/><a NAME="E5:41"/><span class="lab"><font color="Green" title="E34">A5</font></span>: 
 for <font color="Olive" title="b1">t</font>, <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b3">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">t</font> &amp; <font color="Olive" title="b3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">t</font> holds <br/>( <font color="Olive" title="b3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Sigma</font> &amp; <font color="Maroon" title="c4">BSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b2">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">y</font> &amp; <font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">CSeq</font> = <font color="Maroon" title="c5">G</font> as   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">Omega</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T7" onmouseover="rs('funct_2/T7')" onmouseout="rh()">FUNCT_2:7</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">CSeq</font> = <font color="Maroon" title="c6">CSeq</font> as   <a href="prob_1.html#NM4" title="PROB_1:NM.4">SetSequence</a> of <font color="Maroon" title="c2">Sigma</font> ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c7">CSeq</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">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds <br/> ( <font color="Maroon" title="c4">BSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">CSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b1">n</font> &amp; <font color="Maroon" title="c3">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">CSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E8:41"/>
 for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds <br/> ( <font color="Maroon" title="c4">BSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">CSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b1">n</font> &amp; <font color="Maroon" title="c3">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">CSeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:41"><span class="lab"><font color="Green" title="E34">A5</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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