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<span class="kw">reconsider </span><font color="Maroon" title="c2">N</font> = <font color="Maroon" title="c1">F</font> as    <a href="supinf_2.html#M1" title="SUPINF_2:mode.1">Num</a> of  <a href="supinf_2.html#K17" title="SUPINF_2:func.17">rng</a> <font color="Maroon" title="c1">F</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="supinf_2.html#D10" target="_self" title="SUPINF_2:def.10">Def16</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c3">S1</font>, <font color="Maroon" title="c4">S2</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<a href="numbers.html#K7" title="NUMBERS:func.7">ExtREAL</a>; <a class="txt" 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="supinf_2.html#M1" title="SUPINF_2:mode.1">Num</a> of  <a href="supinf_2.html#K17" title="SUPINF_2:func.17">rng</a> <font color="Maroon" title="c1">F</font>  st <font color="Olive" title="b1">N</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c1">F</font> holds <br/><font color="Maroon" title="c3">S1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="supinf_2.html#K15" title="SUPINF_2:func.15">Ser</a> (<span class="p1">(<span class="default"><a href="supinf_2.html#K17" title="SUPINF_2:func.17">rng</a> <font color="Maroon" title="c1">F</font></span>)</span>,<font color="Olive" title="b1">N</font>) ) &amp; (  for <font color="Olive" title="b1">N</font> being    <a href="supinf_2.html#M1" title="SUPINF_2:mode.1">Num</a> of  <a href="supinf_2.html#K17" title="SUPINF_2:func.17">rng</a> <font color="Maroon" title="c1">F</font>  st <font color="Olive" title="b1">N</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c1">F</font> holds <br/><font color="Maroon" title="c4">S2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="supinf_2.html#K15" title="SUPINF_2:func.15">Ser</a> (<span class="p1">(<span class="default"><a href="supinf_2.html#K17" title="SUPINF_2:func.17">rng</a> <font color="Maroon" title="c1">F</font></span>)</span>,<font color="Olive" title="b1">N</font>) ) implies <font color="Maroon" title="c3">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">S2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:57_1_2"/><span class="lab"><font color="Green" title="E33">A1</font></span>: 
 for <font color="Olive" title="b1">N</font> being    <a href="supinf_2.html#M1" title="SUPINF_2:mode.1">Num</a> of  <a href="supinf_2.html#K17" title="SUPINF_2:func.17">rng</a> <font color="Maroon" title="c1">F</font>  st <font color="Olive" title="b1">N</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c1">F</font> holds <br/><font color="Maroon" title="c3">S1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="supinf_2.html#K15" title="SUPINF_2:func.15">Ser</a> (<span class="p1">(<span class="default"><a href="supinf_2.html#K17" title="SUPINF_2:func.17">rng</a> <font color="Maroon" title="c1">F</font></span>)</span>,<font color="Olive" title="b1">N</font>)
 <span class="kw">and </span><br/><a NAME="E3:57_1_2"/><span class="lab"><font color="Green" title="E34">A2</font></span>: 
 for <font color="Olive" title="b1">N</font> being    <a href="supinf_2.html#M1" title="SUPINF_2:mode.1">Num</a> of  <a href="supinf_2.html#K17" title="SUPINF_2:func.17">rng</a> <font color="Maroon" title="c1">F</font>  st <font color="Olive" title="b1">N</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c1">F</font> holds <br/><font color="Maroon" title="c4">S2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="supinf_2.html#K15" title="SUPINF_2:func.15">Ser</a> (<span class="p1">(<span class="default"><a href="supinf_2.html#K17" title="SUPINF_2:func.17">rng</a> <font color="Maroon" title="c1">F</font></span>)</span>,<font color="Olive" title="b1">N</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">S2</font></span><br/>

<span class="kw">thus </span><font color="Maroon" title="c3">S1</font> = 
 <a href="supinf_2.html#K15" title="SUPINF_2:func.15">Ser</a> (<span class="p1">(<span class="default"><a href="supinf_2.html#K17" title="SUPINF_2:func.17">rng</a> <font color="Maroon" title="c1">F</font></span>)</span>,<font color="Maroon" title="c2">N</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57_1_2"><span class="lab"><font color="Green" title="E33">A1</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c4">S2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:57_1_2"><span class="lab"><font color="Green" title="E34">A2</font></span></a></span>
; <a class="txt" 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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