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<span class="kw">let </span><font color="Maroon" title="c4">op1</font>, <font color="Maroon" title="c5">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:()"><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="c4">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="c5">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="c4">op1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">op2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:92_1_2"/><span class="lab"><font color="Green" title="E51">A6</font></span>: 
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="c4">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>
 <span class="kw">and </span><br/><a NAME="E2:92_1_2"/><span class="lab"><font color="Green" title="E52">A7</font></span>: 
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">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">op1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">op2</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c6">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="E4:92_1_2"/><span class="lab"><font color="Green" title="E53">A8</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="c6">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/>
<a NAME="E5:92_1_2"/>
<font color="Maroon" title="c4">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="c6">op</font>,<font color="Maroon" title="c3">w</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:92_1_2"><span class="lab"><font color="Green" title="E53">A8</font></span></a>, <a class="txt" href="#E1:92_1_2"><span class="lab"><font color="Green" title="E51">A6</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:92_1_2"/>
<font color="Maroon" title="c4">op1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">op2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:92_1_2"><span class="lab"><font color="Green" title="E53">A8</font></span></a>, <a class="txt" href="#E2:92_1_2"><span class="lab"><font color="Green" title="E52">A7</font></span></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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