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<b>let </b><font color="Maroon" title="c4">n</font>, <font color="Maroon" title="c5">m</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <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">j</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">J</font> holds  <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">O</font> <a href="pralg_1.html#K14" title="PRALG_1:func.14">.</a> <font color="Olive" title="b1">j</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">j</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">J</font> holds  <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">O</font> <a href="pralg_1.html#K14" title="PRALG_1:func.14">.</a> <font color="Olive" title="b1">j</font></span>)</span> ) implies <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> )</span><br/>

<b>assume </b><a NAME="E1:45_1_2"/><i><font color="Green" title="E24">A1</font></i>: 
( ( for <font color="Olive" title="b1">j</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">J</font> holds  <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">O</font> <a href="pralg_1.html#K14" title="PRALG_1:func.14">.</a> <font color="Olive" title="b1">j</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">j</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">J</font> holds  <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">O</font> <a href="pralg_1.html#K14" title="PRALG_1:func.14">.</a> <font color="Olive" title="b1">j</font></span>)</span> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font></span><br/>

<b>consider </b><font color="Maroon" title="c6">j</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">J</font>;<br/>
<a NAME="E3:45_1_2"/>
( <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">O</font> <a href="pralg_1.html#K14" title="PRALG_1:func.14">.</a> <font color="Maroon" title="c6">j</font></span>)</span> &amp; <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">O</font> <a href="pralg_1.html#K14" title="PRALG_1:func.14">.</a> <font color="Maroon" title="c6">j</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="#E1:45_1_2"><i><font color="Green" title="E24">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:45_1_2"/>
<font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</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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