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<b>let </b><font color="Maroon" title="c1">SM</font> be  <a href="osalg_1.html#V8" title="OSALG_1:attr.8">monotone</a> <a href="osalg_1.html#NM3" title="OSALG_1:NM.3">OrderSortedSign</a>;<br/>

<b>assume </b><a NAME="E1:42"/><i><font color="Green" title="E26">A1</font></i>: 
<font color="Maroon" title="c1">SM</font> is <a href="osalg_1.html#V6" title="OSALG_1:attr.6">op-discrete</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">om</font> be   <a href="osalg_1.html#NM2" title="OSALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">SM</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="osalg_1.html#D14" target="_self" title="OSALG_1:def.14">OSALG_1:def 14</a><br/>

<b>thus </b><a NAME="E2:42"/>
<font color="Maroon" title="c2">om</font> is <a href="osalg_1.html#V7" title="OSALG_1:attr.7">monotone</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="osalg_1.html#D13" target="_self" title="OSALG_1:def.13">OSALG_1:def 13</a><br/>

<b>let </b><font color="Maroon" title="c3">wm1</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">SM</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ;<br/>

<b>assume </b><a NAME="E3:42"/><i><font color="Green" title="E27">A2</font></i>: 
<font color="Maroon" title="c3">wm1</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="c2">om</font>
 ;<br/>

<a NAME="E4:42"/>
<font color="Maroon" title="c2">om</font> <a href="osalg_1.html#R3" title="OSALG_1:pred.3">has_least_args_for</a> <font color="Maroon" title="c2">om</font>,<font color="Maroon" title="c3">wm1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:42_1"/>
( <font color="Maroon" title="c2">om</font> <a href="osalg_1.html#R1" title="OSALG_1:pred.1">~=</a> <font color="Maroon" title="c2">om</font> &amp; <font color="Maroon" title="c3">wm1</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="c2">om</font> )
 <b>by </b><i><a class="txt" href="osalg_1.html#E3:42"><i><font color="Green" title="E27">A2</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="osalg_1.html#D10" target="_self" title="OSALG_1:def.10">OSALG_1:def 10</a><br/>

<b>let </b><font color="Maroon" title="c4">om2</font> be   <a href="osalg_1.html#NM2" title="OSALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">SM</font>;<br/>

<b>assume </b><a NAME="E2:42_1"/>
( <font color="Maroon" title="c2">om</font> <a href="osalg_1.html#R1" title="OSALG_1:pred.1">~=</a> <font color="Maroon" title="c4">om2</font> &amp; <font color="Maroon" title="c3">wm1</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">om2</font> )
 ;<br/>

<b>hence </b><a NAME="E3:42_1"/>
 <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c2">om</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">om2</font>
 <b>by </b><i><a class="txt" href="osalg_1.html#E1:42"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="osalg_1.html#T3" target="_self" title="OSALG_1:th.3">Th3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:42"/>
 ex <font color="Olive" title="b1">o1</font> being  <a href="osalg_1.html#NM2" title="OSALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">SM</font> st <font color="Olive" title="b1">o1</font> <a href="osalg_1.html#R3" title="OSALG_1:pred.3">has_least_args_for</a> <font color="Maroon" title="c2">om</font>,<font color="Maroon" title="c3">wm1</font>
 ;<br/>


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