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<span class="kw">consider </span><font color="Maroon" title="c2">g</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font><span class="kw"> such that </span><br/><a NAME="E2:20_2_1"/><span class="lab"><font color="Green" title="E12">A12</font></span>: 
 for <font color="Olive" title="b1">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> holds <br/> ( <font color="Maroon" title="c2">g</font> <a href="nat_1.html#K9" title="NAT_1:func.9">.</a> (<font color="Olive" title="b1">a</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> &amp; (  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="Maroon" title="c2">g</font> <a href="nat_1.html#K9" title="NAT_1:func.9">.</a> (<font color="Olive" title="b1">a</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">R</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="nat_1.html#K9" title="NAT_1:func.9">.</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">n</font>)</span>)</span>,<font color="Olive" title="b1">a</font>) ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="binom.html#E4"><span class="lab"><font color="Green" title="E4">Lm2</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c2">g</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">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> holds <br/> ( <font color="Maroon" title="c2">g</font> <a href="nat_1.html#K9" title="NAT_1:func.9">.</a> (<font color="Olive" title="b1">a</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> &amp; (  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="Maroon" title="c2">g</font> <a href="nat_1.html#K9" title="NAT_1:func.9">.</a> (<font color="Olive" title="b1">a</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="nat_1.html#K9" title="NAT_1:func.9">.</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">n</font>)</span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b1">a</font> ) )</span><br/>

<span class="kw">thus </span><a NAME="E3:20_2_1"/>
 for <font color="Olive" title="b1">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> holds <br/> ( <font color="Maroon" title="c2">g</font> <a href="nat_1.html#K9" title="NAT_1:func.9">.</a> (<font color="Olive" title="b1">a</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> &amp; (  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="Maroon" title="c2">g</font> <a href="nat_1.html#K9" title="NAT_1:func.9">.</a> (<font color="Olive" title="b1">a</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="nat_1.html#K9" title="NAT_1:func.9">.</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">n</font>)</span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b1">a</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:20_2_1"><span class="lab"><font color="Green" title="E12">A12</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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