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<b>let </b><font color="Maroon" title="c1">X1</font>, <font color="Maroon" title="c2">Y1</font>, <font color="Maroon" title="c3">X2</font>, <font color="Maroon" title="c4">Y2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c2">Y1</font> &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c4">Y2</font> implies  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">X2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c2">Y1</font>,<font color="Maroon" title="c4">Y2</font></span>)</span> )</span><br/>







<b>assume </b><a NAME="E1:59"/>
(  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c2">Y1</font> &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c4">Y2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">X2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c2">Y1</font>,<font color="Maroon" title="c4">Y2</font></span>)</span></span><br/>

<a NAME="E2:59"/><b>then </b>
( <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">Y1</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  &amp; <font color="Maroon" title="c3">X2</font>,<font color="Maroon" title="c4">Y2</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  )
 
<b>by </b><i><a class="ref" href="card_1.html#T21" title="CARD_1:th.21">CARD_1:21</a></i>;<br/>
<b>hence </b><a NAME="E3:59"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">X2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c2">Y1</font>,<font color="Maroon" title="c4">Y2</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_5.html#T67" target="_self" title="FUNCT_5:th.67">Th67</a></i>; <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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