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<span class="kw">consider </span><font color="Maroon" title="c4">op</font> being    <a href="osalg_1.html#M1" title="OSALG_1:mode.1">Element</a> of <font color="Maroon" title="c2">on</font><span class="kw"> such that </span><br/><a NAME="E2:92_1_1"/><span class="lab"><font color="Green" title="E51">A2</font></span>: 
<font color="Maroon" title="c3">w</font> <a href="osalg_1.html#R2" title="OSALG_1:pred.2">&lt;=</a>  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c4">op</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:92"><span class="lab"><font color="Green" title="E50">A1</font></span></a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">Lo</font> =  <a href="osalg_1.html#K3" title="OSALG_1:func.3">LBound</a> <font color="Maroon" title="c4">op</font>,<font color="Maroon" title="c3">w</font>;<br/>
<a NAME="E3:92_1_1"/>
 <a href="osalg_1.html#K3" title="OSALG_1:func.3">LBound</a> <font color="Maroon" title="c4">op</font>,<font color="Maroon" title="c3">w</font> <a href="osalg_1.html#R3" title="OSALG_1:pred.3">has_least_args_for</a> <font color="Maroon" title="c4">op</font>,<font color="Maroon" title="c3">w</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:92_1_1"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="ref" href="osalg_1.html#D15" target="_self" title="OSALG_1:def.15">Def15</a></span>;<br/>
<a NAME="E4:92_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">op</font> <a href="osalg_1.html#R1" title="OSALG_1:pred.1">~=</a>  <a href="osalg_1.html#K3" title="OSALG_1:func.3">LBound</a> <font color="Maroon" title="c4">op</font>,<font color="Maroon" title="c3">w</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_1.html#D10" target="_self" title="OSALG_1:def.10">Def10</a></span>;<br/>
<a NAME="E5:92_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A3</font></span>: 
 <a href="osalg_1.html#K9" title="OSALG_1:func.9">Name</a> <font color="Maroon" title="c4">op</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_1.html#K9" title="OSALG_1:func.9">Name</a> <span class="p1">(<span class="default"><a href="osalg_1.html#K3" title="OSALG_1:func.3">LBound</a> <font color="Maroon" title="c4">op</font>,<font color="Maroon" title="c3">w</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_1.html#T31" target="_self" title="OSALG_1:th.31">Th31</a></span>;<br/>
<a NAME="E6:92_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A4</font></span>: 
 <a href="osalg_1.html#K9" title="OSALG_1:func.9">Name</a> <span class="p1">(<span class="default"><a href="osalg_1.html#K3" title="OSALG_1:func.3">LBound</a> <font color="Maroon" title="c4">op</font>,<font color="Maroon" title="c3">w</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">on</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_1.html#T33" target="_self" title="OSALG_1:th.33">Th33</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">Lo</font> =  <a href="osalg_1.html#K3" title="OSALG_1:func.3">LBound</a> <font color="Maroon" title="c4">op</font>,<font color="Maroon" title="c3">w</font> as    <a href="osalg_1.html#M1" title="OSALG_1:mode.1">Element</a> of <font color="Maroon" title="c2">on</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_1.html#T33" target="_self" title="OSALG_1:th.33">Th33</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c6">Lo</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">op</font> being   <a href="osalg_1.html#M1" title="OSALG_1:mode.1">Element</a> of <font color="Maroon" title="c2">on</font>  st <font color="Maroon" title="c3">w</font> <a href="osalg_1.html#R2" title="OSALG_1:pred.2">&lt;=</a>  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Olive" title="b1">op</font> holds <br/><font color="Maroon" title="c6">Lo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_1.html#K3" title="OSALG_1:func.3">LBound</a> <font color="Olive" title="b1">op</font>,<font color="Maroon" title="c3">w</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c7">op1</font> be    <a href="osalg_1.html#M1" title="OSALG_1:mode.1">Element</a> of <font color="Maroon" title="c2">on</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">w</font> <a href="osalg_1.html#R2" title="OSALG_1:pred.2">&lt;=</a>  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c7">op1</font> implies <font color="Maroon" title="c6">Lo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_1.html#K3" title="OSALG_1:func.3">LBound</a> <font color="Maroon" title="c7">op1</font>,<font color="Maroon" title="c3">w</font> )</span><br/>

<span class="kw">assume </span><a NAME="E8:92_1_1"/><span class="lab"><font color="Green" title="E54">A5</font></span>: 
<font color="Maroon" title="c3">w</font> <a href="osalg_1.html#R2" title="OSALG_1:pred.2">&lt;=</a>  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c7">op1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">Lo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_1.html#K3" title="OSALG_1:func.3">LBound</a> <font color="Maroon" title="c7">op1</font>,<font color="Maroon" title="c3">w</font></span><br/>

<a NAME="E9:92_1_1"/>
 <a href="osalg_1.html#K9" title="OSALG_1:func.9">Name</a> <font color="Maroon" title="c7">op1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">on</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_1.html#T33" target="_self" title="OSALG_1:th.33">Th33</a></span>;<br/>
<a NAME="E10:92_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">op1</font> <a href="osalg_1.html#R1" title="OSALG_1:pred.1">~=</a> <font color="Maroon" title="c4">op</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:92_1_1"><span class="lab"><font color="Green" title="E52">A3</font></span></a>, <a class="txt" href="#E6:92_1_1"><span class="lab"><font color="Green" title="E53">A4</font></span></a>, <a class="ref" href="osalg_1.html#T31" target="_self" title="OSALG_1:th.31">Th31</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:92_1_1"/>
<font color="Maroon" title="c6">Lo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_1.html#K3" title="OSALG_1:func.3">LBound</a> <font color="Maroon" title="c7">op1</font>,<font color="Maroon" title="c3">w</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:92_1_1"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E8:92_1_1"><span class="lab"><font color="Green" title="E54">A5</font></span></a>, <a class="ref" href="osalg_1.html#T34" target="_self" title="OSALG_1:th.34">Th34</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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