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<b>consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="osalg_1.html#M1" target="_self">Element</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E2:92_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="osalg_1.html#R2" target="_self">&lt;=</a>  <a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="osalg_1.html#E1:92"><i><font color="Green">E50</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="osalg_1.html#K3" target="_self">LBound</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>
<a NAME="E3:92_1_1"/>
 <a href="osalg_1.html#K3" target="_self">LBound</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="osalg_1.html#R3" target="_self">has_least_args_for</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="osalg_1.html#E2:92_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="osalg_1.html#D15" target="_self">Def15</a></i>;<br/>
<a NAME="E4:92_1_1"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="osalg_1.html#R1" target="_self">~=</a>  <a href="osalg_1.html#K3" target="_self">LBound</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="osalg_1.html#R2" target="_self">&lt;=</a>  <a href="msualg_1.html#K1">the_arity_of</a> <span class="p1">(<span class="default"><a href="osalg_1.html#K3" target="_self">LBound</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="osalg_1.html#NM2">OperSymbol</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>4</sub></font> <a href="osalg_1.html#R1" target="_self">~=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="osalg_1.html#R2" target="_self">&lt;=</a>  <a href="msualg_1.html#K1">the_arity_of</a> <font color="Olive">b<sub>1</sub></font> holds <br/> <a href="msualg_1.html#K1">the_arity_of</a> <span class="p1">(<span class="default"><a href="osalg_1.html#K3" target="_self">LBound</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="osalg_1.html#R2" target="_self">&lt;=</a>  <a href="msualg_1.html#K1">the_arity_of</a> <font color="Olive">b<sub>1</sub></font> ) )
 
<b>by </b><i><a class="ref" href="osalg_1.html#D10" target="_self">Def10</a></i>;<br/>
<a NAME="E5:92_1_1"/><b>then </b><i><font color="Green">E52</font></i>: 
 <a href="osalg_1.html#K10" target="_self">Name</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="osalg_1.html#K10" target="_self">Name</a> <span class="p1">(<span class="default"><a href="osalg_1.html#K3" target="_self">LBound</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="osalg_1.html#T31" target="_self">Th31</a></i>;<br/>
<a NAME="E6:92_1_1"/><b>then </b><i><font color="Green">E53</font></i>: 
 <a href="osalg_1.html#K10" target="_self">Name</a> <span class="p1">(<span class="default"><a href="osalg_1.html#K3" target="_self">LBound</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="osalg_1.html#T33" target="_self">Th33</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> =  <a href="osalg_1.html#K3" target="_self">LBound</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> as    <a href="osalg_1.html#M1" target="_self">Element</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="osalg_1.html#T33" target="_self">Th33</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>6</sub></font>
;<br/>

<b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="osalg_1.html#M1" target="_self">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>

<b>assume </b><a NAME="E8:92_1_1"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="osalg_1.html#R2" target="_self">&lt;=</a>  <a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E9:92_1_1"/>
 <a href="osalg_1.html#K10" target="_self">Name</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="osalg_1.html#T33" target="_self">Th33</a></i>;<br/>
<a NAME="E10:92_1_1"/><b>then </b><i><font color="Green">E55</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="osalg_1.html#R1" target="_self">~=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="osalg_1.html#E5:92_1_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="osalg_1.html#E6:92_1_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="osalg_1.html#T31" target="_self">Th31</a></i>;<br/>
<a NAME="E11:92_1_1"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="osalg_1.html#E2:92_1_1"><i><font color="Green">E51</font></i></a>, <a class="txt" href="osalg_1.html#E8:92_1_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="osalg_1.html#D7" target="_self">Def7</a></i>;<br/>
<b>hence </b><a NAME="E12:92_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="osalg_1.html#K3" target="_self">LBound</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="osalg_1.html#E2:92_1_1"><i><font color="Green">E51</font></i></a>, <a class="txt" href="osalg_1.html#E8:92_1_1"><i><font color="Green">E54</font></i></a>, <a class="txt" href="osalg_1.html#E10:92_1_1"><i><font color="Green">E55</font></i></a>, <a class="ref" href="osalg_1.html#T34" target="_self">Th34</a></i>;<br/>


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