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<b>consider </b><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><b> such that </b><br/><a NAME="E2:92_1_2"/><i><font color="Green" title="E51">A7</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="#E1:92"><i><font color="Green" title="E50">A1</font></i></a></i>;<br/>
<b>let </b><font color="Maroon" title="c5">op1</font>, <font color="Maroon" title="c6">op2</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:()"><i><font color="Red">::  thesis: </font></i></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="c5">op1</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> ) &amp; ( 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">op2</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> ) implies <font color="Maroon" title="c5">op1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">op2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E3:92_1_2"/><i><font color="Green" title="E52">A8</font></i>: 
for <font color="Olive" title="b1">op3</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">op3</font> holds <br/><font color="Maroon" title="c5">op1</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">op3</font>,<font color="Maroon" title="c3">w</font>
 <b>and </b><br/><a NAME="E4:92_1_2"/><i><font color="Green" title="E53">A9</font></i>: 
for <font color="Olive" title="b1">op3</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">op3</font> holds <br/><font color="Maroon" title="c6">op2</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">op3</font>,<font color="Maroon" title="c3">w</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">op1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">op2</font></span><br/>

<a NAME="E5:92_1_2"/>
( <font color="Maroon" title="c5">op1</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="c4">op</font>,<font color="Maroon" title="c3">w</font> &amp; <font color="Maroon" title="c6">op2</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="c4">op</font>,<font color="Maroon" title="c3">w</font> )
 
<b>by </b><i><a class="txt" href="#E2:92_1_2"><i><font color="Green" title="E51">A7</font></i></a>, <a class="txt" href="#E3:92_1_2"><i><font color="Green" title="E52">A8</font></i></a>, <a class="txt" href="#E4:92_1_2"><i><font color="Green" title="E53">A9</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:92_1_2"/>
<font color="Maroon" title="c5">op1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">op2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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