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<div class="add">

<b>set </b><font color="Maroon" title="c3">X</font> = <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ;<br/>
<b>consider </b><font color="Maroon" title="c4">ff</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E2:37_1_1"/><i><font color="Green" title="E30">A1</font></i>: 
( <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">ff</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">ff</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">ff</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  )
 <b>by </b><i><a class="ref" href="funct_2.html#D2" title="FUNCT_2:def.2">FUNCT_2:def 2</a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b>for <font color="Olive" title="b1">h</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>   st $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h</font> holds <br/>$2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><a href="graphsp.html#K8" title="GRAPHSP:func.8">LifeSpan</a> <font color="Maroon" title="c1">f</font>,<font color="Olive" title="b1">h</font>,<font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Olive" title="b1">h</font>;<br/>
<div><i><font color="Green" title="E31">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">xx</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">xx</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font> implies  ex <font color="Olive" title="b1">y1</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">xx</font>,<font color="Olive" title="b1">y1</font>] )</span><br/><b>assume </b><a NAME="E1:37_1_1_1"/>
<font color="Maroon" title="c5">xx</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">y1</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">xx</font>,<font color="Olive" title="b1">y1</font>]</span><br/><b>then reconsider </b><font color="Maroon" title="c6">h'</font> = <font color="Maroon" title="c5">xx</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <b>by </b><i><a class="txt" href="#E2:37_1_1"><i><font color="Green" title="E30">A1</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_1_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon" title="c7">yy</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><a href="graphsp.html#K8" title="GRAPHSP:func.8">LifeSpan</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c6">h'</font>,<font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c6">h'</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">h</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>   st <font color="Maroon" title="c5">xx</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h</font> holds <br/><font color="Maroon" title="c7">yy</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><a href="graphsp.html#K8" title="GRAPHSP:func.8">LifeSpan</a> <font color="Maroon" title="c1">f</font>,<font color="Olive" title="b1">h</font>,<font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Olive" title="b1">h</font></span><br/><b>let </b><font color="Maroon" title="c8">h</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">xx</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">h</font> implies <font color="Maroon" title="c7">yy</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><a href="graphsp.html#K8" title="GRAPHSP:func.8">LifeSpan</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c8">h</font>,<font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c8">h</font> )</span><br/><b>assume </b><a NAME="E1:37_1_1_1_1"/>
<font color="Maroon" title="c5">xx</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">h</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">yy</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><a href="graphsp.html#K8" title="GRAPHSP:func.8">LifeSpan</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c8">h</font>,<font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c8">h</font></span><br/><b>hence </b><a NAME="E2:37_1_1_1_1"/>
<font color="Maroon" title="c7">yy</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><a href="graphsp.html#K8" title="GRAPHSP:func.8">LifeSpan</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c8">h</font>,<font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c8">h</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E4:37_1_1_1"/>
 ex <font color="Olive" title="b1">y1</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">xx</font>,<font color="Olive" title="b1">y1</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c5">f'</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E5:37_1_1"/><i><font color="Green" title="E32">A5</font></i>: 
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font> &amp; ( for <font color="Olive" title="b1">xx</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">xx</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">xx</font>,<font color="Maroon" title="c5">f'</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">xx</font>] ) )
 <b>from </b><i><a class="ref" href="classes1.html#S1" title="CLASSES1:sch.1">CLASSES1:sch 1</a>(<a class="txt" href="#E3:37_1_1"><i><font color="Green" title="E31">A4</font></i></a>);<br/></i>
<a NAME="E6:37_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">f'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">f'</font> or <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  )</span><br/>

<b>assume </b><a NAME="E1:37_1_1_2"/>
<font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">f'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </span><br/>

<b>then consider </b><font color="Maroon" title="c7">xx</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:37_1_1_2"/><i><font color="Green" title="E33">A6</font></i>: 
( <font color="Maroon" title="c7">xx</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">f'</font> &amp; <font color="Maroon" title="c6">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f'</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">xx</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">h'</font> = <font color="Maroon" title="c7">xx</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <b>by </b><i><a class="txt" href="#E2:37_1_1"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="#E5:37_1_1"><i><font color="Green" title="E32">A5</font></i></a>, <a class="txt" href="#E3:37_1_1_2"><i><font color="Green" title="E33">A6</font></i></a></i>;<br/>
<a NAME="E5:37_1_1_2"/>
<font color="Maroon" title="c6">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><a href="graphsp.html#K8" title="GRAPHSP:func.8">LifeSpan</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c8">h'</font>,<font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c8">h'</font>
 
<b>by </b><i><a class="txt" href="#E5:37_1_1"><i><font color="Green" title="E32">A5</font></i></a>, <a class="txt" href="#E3:37_1_1_2"><i><font color="Green" title="E33">A6</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:37_1_1_2"/>
<font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c6">f'</font> = <font color="Maroon" title="c5">f'</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span>,<span class="p1">(<span class="default"><a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span> <b>by </b><i><a class="txt" href="#E2:37_1_1"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="#E5:37_1_1"><i><font color="Green" title="E32">A5</font></i></a>, <a class="ref" href="funct_2.html#D2" title="FUNCT_2:def.2">FUNCT_2:def 2</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">f'</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  &amp; ( for <font color="Olive" title="b1">h</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  holds  <font color="Maroon" title="c6">f'</font> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><a href="graphsp.html#K8" title="GRAPHSP:func.8">LifeSpan</a> <font color="Maroon" title="c1">f</font>,<font color="Olive" title="b1">h</font>,<font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Olive" title="b1">h</font> ) )</span><br/>

<b>thus </b><a NAME="E8:37_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 <b>by </b><i><a class="txt" href="#E2:37_1_1"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="#E5:37_1_1"><i><font color="Green" title="E32">A5</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">h</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  holds  <font color="Maroon" title="c6">f'</font> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><a href="graphsp.html#K8" title="GRAPHSP:func.8">LifeSpan</a> <font color="Maroon" title="c1">f</font>,<font color="Olive" title="b1">h</font>,<font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Olive" title="b1">h</font></span><br/>

<b>let </b><font color="Maroon" title="c7">h</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">f'</font> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c7">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><a href="graphsp.html#K8" title="GRAPHSP:func.8">LifeSpan</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c7">h</font>,<font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c7">h</font></span><br/>

<b>thus </b><a NAME="E9:37_1_1"/>
<font color="Maroon" title="c6">f'</font> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c7">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><a href="graphsp.html#K8" title="GRAPHSP:func.8">LifeSpan</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c7">h</font>,<font color="Maroon" title="c2">n</font></span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c7">h</font>
 <b>by </b><i><a class="txt" href="#E2:37_1_1"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="#E5:37_1_1"><i><font color="Green" title="E32">A5</font></i></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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