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<div class="add">

<b>let </b><font color="Maroon">D1</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">D2</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/>



<b>thus </b><a NAME="E1:5"/>
 <a href="card_3.html#K4">product</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">D1</font>,<font color="Maroon">D2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">d1</font>,<font color="Olive">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> where <font color="Olive">d1</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D1</font>, <font color="Olive">d2</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D2</font> : verum </span>}</span> 
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:5_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">D1</font>,<font color="Maroon">D2</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 ;<br/>

<a NAME="E2:5_1"/><b>then </b>
 ex <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D1</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D2</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font></span><a href="finseq_1.html#K10">*&gt;</a></span> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:5_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">d1</font>,<font color="Olive">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> where <font color="Olive">d1</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D1</font>, <font color="Olive">d2</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D2</font> : verum </span>}</span> 
 ;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:5"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">d1</font>,<font color="Olive">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> where <font color="Olive">d1</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D1</font>, <font color="Olive">d2</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D2</font> : verum </span>}</span> 
 ;<br/>

<a NAME="E3:5"/><b>then </b>
 ex <font color="Olive">d1</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D1</font> ex <font color="Olive">d2</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D2</font> st <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">d1</font>,<font color="Olive">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 
;<br/>
<b>hence </b><a NAME="E4:5"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">D1</font>,<font color="Maroon">D2</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i/>;<br/>


</div>
