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<b>let </b><font color="Maroon" title="c1">F</font>, <font color="Maroon" title="c2">G</font> be    <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>; <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">f</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> <br/> for <font color="Olive" title="b2">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b2">i</font></span>)</span> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <font color="Olive" title="b1">f</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">f</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"> for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span></span><br/>





<b>set </b><font color="Maroon" title="c5">Fi</font> = <span class="p1">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">i</font>;<br/>
<b>set </b><font color="Maroon" title="c6">ff</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <font color="Maroon" title="c3">f</font>;<br/>
<b>set </b><font color="Maroon" title="c7">FFi</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">i</font></span>)</span>;<br/>
<a NAME="E1:33"/><i><font color="Green" title="E29">A1</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <font color="Maroon" title="c2">G</font></span>)</span> <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="graphsp.html#E29"><i><font color="Green" title="E27">Lm5</font></i></a></i>;<br/>
<a NAME="E2:33"/><i><font color="Green" title="E30">A2</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span> <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="graphsp.html#E29"><i><font color="Green" title="E27">Lm5</font></i></a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <font color="Maroon" title="c3">f</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <font color="Maroon" title="c3">f</font>
<b>by </b><i><a class="ref" href="graphsp.html#D2" target="_self" title="GRAPHSP:def.2">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <font color="Maroon" title="c3">f</font></span>)</span>
<b>by </b><i><a class="txt" href="#E2:33"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="funct_1.html#T22" title="FUNCT_1:th.22">FUNCT_1:22</a></i>
<br/>.= 
<font color="Maroon" title="c1">F</font> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="graphsp.html#K4" title="GRAPHSP:func.4">.</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:33"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="funct_1.html#T22" title="FUNCT_1:th.22">FUNCT_1:22</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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