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<span class="kw">let </span><font color="Maroon" title="c1">k</font>, <font color="Maroon" title="c2">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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">  for <font color="Olive" title="b1">f</font> being   <a href="valued_0.html#V6" title="VALUED_0:attr.6">natural-valued</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 holds <br/> <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Olive" title="b1">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">k</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Olive" title="b1">f</font>,<font color="Maroon" title="c1">k</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be   <a href="valued_0.html#V6" title="VALUED_0:attr.6">natural-valued</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</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="c2">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 implies  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">k</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">k</font>) )</span><br/>





<span class="kw">assume </span><a NAME="E1:43"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
<font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 ; <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">  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">k</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">k</font>)</span><br/>

<span class="kw">thus </span><a NAME="E2:43"/>
 <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">k</font></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">k</font>)
  <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="xboole_0.html#D10" onmouseover="rs('xboole_0/D10')" onmouseout="rh()">XBOOLE_0:def 10</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">  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">k</font></span>)</span>)</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="43_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</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"> (  not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">k</font></span>)</span>) or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">k</font>) )</span><br/>

<span class="kw">assume </span><a NAME="E1:43_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">k</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"> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">k</font>)</span><br/>

<a NAME="E2:43_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">k</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D17" onmouseover="rs('relat_1/D17')" onmouseout="rh()">RELAT_1:def 17</a></span>;<br/>
<a NAME="E3:43_1"/><span class="kw">then </span>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">k</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D7" onmouseover="rs('funct_1/D7')" onmouseout="rh()">FUNCT_1:def 7</a></span>;<br/>
<a NAME="E4:43_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A2</font></span>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c3">f</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">k</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a>, <a class="ref" href="flexary1.html#D4" target="_self" onmouseover="rs('flexary1/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> = 
<font color="Maroon" title="c2">n</font> <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="flexary1.html#D4" target="_self" onmouseover="rs('flexary1/D4')" onmouseout="rh()">Def4</a></span>
<br/>.= 
<font color="Maroon" title="c2">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font></span>)</span>

;<br/>
<a NAME="E6:43_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:43_1"><span class="lab"><font color="Green" title="E31">A2</font></span></a>, <a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="pepin.html#T30" onmouseover="rs('pepin/T30')" onmouseout="rh()">PEPIN:30</a></span>;<br/>
<a NAME="E7:43_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">k</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<a NAME="E8:43_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">f</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">k</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:43_1"><span class="lab"><font color="Green" title="E31">A2</font></span></a>, <a class="ref" href="funct_1.html#D7" onmouseover="rs('funct_1/D7')" onmouseout="rh()">FUNCT_1:def 7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:43_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">k</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D17" onmouseover="rs('relat_1/D17')" onmouseout="rh()">RELAT_1:def 17</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>

<span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</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"> (  not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">k</font>) or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">k</font></span>)</span>) )</span><br/>

<span class="kw">assume </span><a NAME="E3:43"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">k</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="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">k</font></span>)</span>)</span><br/>

<a NAME="E4:43"/><span class="kw">then </span>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">f</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">k</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D17" onmouseover="rs('relat_1/D17')" onmouseout="rh()">RELAT_1:def 17</a></span>;<br/>
<a NAME="E5:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A3</font></span>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c3">f</font> &amp; <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">k</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D7" onmouseover="rs('funct_1/D7')" onmouseout="rh()">FUNCT_1:def 7</a></span>;<br/>
<a NAME="E6:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A4</font></span>: 
( <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">k</font> &amp; <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a>, <a class="ref" href="flexary1.html#D4" target="_self" onmouseover="rs('flexary1/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> = 
<font color="Maroon" title="c2">n</font> <a href="power.html#K2" title="POWER:func.2">to_power</a> <font color="Maroon" title="c1">k</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="flexary1.html#D4" target="_self" onmouseover="rs('flexary1/D4')" onmouseout="rh()">Def4</a>, <a class="txt" href="#E5:43"><span class="lab"><font color="Green" title="E31">A3</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c2">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">k</font>

;<br/>
<a NAME="E8:43"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">k</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<a NAME="E9:43"/><span class="kw">then </span>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">k</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D7" onmouseover="rs('funct_1/D7')" onmouseout="rh()">FUNCT_1:def 7</a>, <a class="txt" href="#E6:43"><span class="lab"><font color="Green" title="E32">A4</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:43"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K10" title="RELAT_1:func.10">Coim</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="flexary1.html#K4" title="FLEXARY1:func.4">|^</a> <font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">k</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D17" onmouseover="rs('relat_1/D17')" onmouseout="rh()">RELAT_1:def 17</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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