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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<a NAME="E1:55"/>
( (  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">n</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">m</font> implies  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">n</font> <a href="ordinal1.html#R1">c=</a>  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">m</font> ) &amp; (  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">n</font> <a href="ordinal1.html#R1">c=</a>  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">m</font> implies  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">n</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">m</font> ) &amp;  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> &amp; ( <font color="Maroon">n</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">m</font> implies <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font> ) &amp; ( <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font> implies <font color="Maroon">n</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">m</font> ) )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E2:55"/>
(  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">n</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">m</font> iff <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font> )
 ;<br/>


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